{"id":34803,"date":"2022-04-01T16:21:30","date_gmt":"2022-04-01T10:51:30","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=34803"},"modified":"2022-04-07T11:37:29","modified_gmt":"2022-04-07T06:07:29","slug":"big-ideas-math-algebra-1-answers-chapter-2","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-2\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities"},"content":{"rendered":"<p>Clearing the math queries of algebra 1 concepts can be tricky for educators but we have shared an excellent guide for resolving all student&#8217;s issues while learning the concepts. The perfect study resource for students is <strong>Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities<\/strong> where it will help all of them score great marks in the exams. Using the best guide of Big ideas Math Book Answer Key Ch 2 Solving linear Functions, students can easily improve their math skills and problem-solving skills. Go through the below sections and find the BIM math book and observe Algebra 1 Ch 2\u00a0 Solving Linear Inequalities thoroughly for good results in exams.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities<\/h2>\n<p>Guys who want to score the highest marks in the examinations should refer to this <strong>Topic-wise BIM Math Book Algebra 1 Ch 2 Answers<\/strong> from the below links<strong>.<\/strong> In Big Ideas Math Book Algebra 1 Solution Key Chapter 2 Solving Linear Inequalities, students can practice various questions covered in Exercises, Chapter tests, performance tasks, vocabulary, practice tests, cumulative assessments, and others.<\/p>\n<p>Take a look at the comprehensive collection of Chapter 2 questions included in the Big Ideas Math Algebra 1 Solutions and become a master in maths. Also, you all can identify your weak areas by practicing the <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\">Big Ideas Math Answers Algebra 1<\/a> Ch 2<\/strong>. Download the common core curriculum standards provided Topic-wise BIM Algebra 1 Textbook Solutions Pdf through the below links and learn efficiently.<\/p>\n<ul>\n<li><a href=\"#Solving_Linear_Inequalities_Maintaining_Mathematical_Proficiency\">Solving Linear Inequalities Maintaining Mathematical Proficiency &#8211; Page 51<\/a><\/li>\n<li><a href=\"#Solving_Linear_Inequalities_Mathematical_Practices\">Solving Linear Inequalities Mathematical Practices &#8211; Page 52<\/a><\/li>\n<li><a href=\"#Lesson_2.1_Writing_and_Graphing_Inequalities\">Lesson 2.1 Writing and Graphing Inequalities &#8211; Page(53-60)<\/a><\/li>\n<li><a href=\"#Writing_and_Graphing_Inequalities_2.1_Exercises\">Writing and Graphing Inequalities 2.1 Exercises &#8211; Page(58-60)<\/a><\/li>\n<li><a href=\"#Lesson_2.2_Solving_Inequalities_Using_Addition_or_Subtraction\">Lesson 2.2 Solving Inequalities Using Addition or Subtraction &#8211; Page(61-66)<\/a><\/li>\n<li><a href=\"#Solving_Inequalities_Using_Addition_or_Subtraction_2.2_Exercises\">Solving Inequalities Using Addition or Subtraction 2.2 Exercises &#8211; Page(65-66)<\/a><\/li>\n<li><a href=\"#Lesson_2.3_Solving_Inequalities_Using_Multiplication_or_Division\">Lesson 2.3 Solving Inequalities Using Multiplication or Division &#8211; Page(67-72)<\/a><\/li>\n<li><a href=\"#Solving_Inequalities_Using_Multiplication_or_Division_2.3_Exercises\">Solving Inequalities Using Multiplication or Division 2.3 Exercises &#8211; Page(71-72)<\/a><\/li>\n<li><a href=\"#Lesson_2.4_Solving_Multi-step_Inequalities\">Lesson 2.4 Solving Multi-step Inequalities &#8211; Page(73-78)<\/a><\/li>\n<li><a href=\"#Solving_Multi-step_Inequalities_2.4_Exercises\">Solving Multi-step Inequalities 2.4 Exercises &#8211; Page(77-78)<\/a><\/li>\n<li><a href=\"_Analyzing_Your_Errors\">Solving Linear Inequalities Study Skills: Analyzing Your Errors &#8211; Page 79<\/a><\/li>\n<li><a href=\"#Solving_Linear_Inequalities_Maintaining_2.1_\u2013_2.4_Quiz\">Solving Linear Inequalities Maintaining 2.1 \u2013 2.4 Quiz &#8211; Page 80<\/a><\/li>\n<li><a href=\"#Lesson_2.5_Solving_Compound_Inequalities\">Lesson 2.5 Solving Compound Inequalities &#8211; Page(81-86)<\/a><\/li>\n<li><a href=\"#Solving_Compound_Inequalities_2.5_Exercises\">Solving Compound Inequalities 2.5 Exercises &#8211; Page(85-86)<\/a><\/li>\n<li><a href=\"#Lesson_2.6_Solving_Absolute_Value_Inequalities\">Lesson 2.6 Solving Absolute Value Inequalities &#8211; Page(87-92)<\/a><\/li>\n<li><a href=\"#Solving_Absolute_Value_Inequalities_2.6_Exercises\">Solving Absolute Value Inequalities 2.6 Exercises &#8211; Page(91-92)<\/a><\/li>\n<li><a href=\"_Grading_Calculations\">Solving Linear Inequalities Performance Task: Grading Calculations &#8211; Page 93<\/a><\/li>\n<li><a href=\"#Solving_Linear_Inequalities_Chapter_Review\">Solving Linear Inequalities Chapter Review &#8211; Page(94-96)<\/a><\/li>\n<li><a href=\"#Solving_Linear_Inequalities_Chapter_Test\">Solving Linear Inequalities Chapter Test &#8211; Page 97<\/a><\/li>\n<li><a href=\"#Solving_Linear_Inequalities_Maintaining_Cumulative_Assessment\">Solving Linear Inequalities Maintaining Cumulative Assessment &#8211; Page(98-99)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Solving_Linear_Inequalities_Maintaining_Mathematical_Proficiency\"><\/a>Solving Linear Inequalities Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Graph the number.<\/strong><\/p>\n<p><span style=\"font-size: 16px;\">Question 1.<br \/>\n<\/span>6<br \/>\n<span style=\"font-size: 16px;\">Answer:<br \/>\nThe number line representing 6 is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-1.jpg\" alt=\"\" width=\"686\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-1.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-1-300x61.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/> <\/span><\/p>\n<p>Question 2.<br \/>\n| 2 |<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nThe number line representing | 2 | is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-2.jpg\" alt=\"\" width=\"686\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-2.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-2-300x62.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 3.<br \/>\n| -1 |<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| -x | = x for x &gt; 0<br \/>\n| -x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nThe number line representing | -1 | is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-3.jpg\" alt=\"\" width=\"686\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-3.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-3-300x62.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 4.<br \/>\n2 + | -2 |<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n2 + | -2 |<br \/>\nWe know that,<br \/>\n| -x | =x for x &gt; 0<br \/>\n| -x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n2 + | -2 | = 2 + 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02 + | &#8211; 2 | = 2 &#8211; 2<br \/>\n= 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 0<br \/>\nHence,<br \/>\nThe number line representing the values of 2 + | &#8211; 2 | is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-5.jpg\" alt=\"\" width=\"686\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-5.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-5-300x62.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 5.<br \/>\n1 &#8211; | -4 |<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n1 &#8211; | &#8211; 4 |<br \/>\nWe know that,<br \/>\n| -x | = x for x &gt; 0<br \/>\n| &#8211; x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n1 &#8211; | &#8211; 4 | = 1 &#8211; 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1 &#8211; | &#8211; 4 | = 1 &#8211; ( -4 )<br \/>\n= -3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 5<br \/>\nHence,<br \/>\nThe number line representing the values of 1 &#8211; | &#8211; 4 | is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-6.jpg\" alt=\"\" width=\"686\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-6.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-6-300x61.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 6.<br \/>\n-5 + | 3 |<br \/>\nAnswer:<br \/>\nThe given absolute value expression is:<br \/>\n-5 + | 3 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n-5 + | 3 | = -5 + 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0-5 + | 3 | = -5 -3<br \/>\n= -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = -8<br \/>\nHence,<br \/>\nThe number line representing the values of -5 + | 3 | is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-7.jpg\" alt=\"\" width=\"686\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-7.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-7-300x59.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p><strong>Complete the statement with &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 1\" width=\"64\" height=\"32\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe order of the numbers in the ascending order is:<br \/>\n-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n2 &lt; 9<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 2\" width=\"74\" height=\"32\" \/><br \/>\nAnswer:<br \/>\nThe order of the numbers in the ascending order is:<br \/>\n-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-6 &lt; 5<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 3\" width=\"94\" height=\"35\" \/><br \/>\nAnswer:<br \/>\nThe order of the numbers in the ascending order is:<br \/>\n-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<br \/>\nWe know that,<br \/>\nThe greater number in the positive integers is the lesser number in the negative integers<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-12 &lt; -4<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 4\" width=\"90\" height=\"35\" \/><br \/>\nAnswer:<br \/>\nThe order of the numbers in the ascending order is:<br \/>\n-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<br \/>\nWe know that,<br \/>\nThe greater number in the positive integers is the lesser number in the negative integers<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-7 &gt; -13<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 5\" width=\"96\" height=\"32\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| -x | = x for x &gt; 0<br \/>\n| -x | = -x for x &lt; 0<br \/>\nThe order of the numbers in the ascending order is:<br \/>\n-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<br \/>\nWe know that,<br \/>\nThe greater number in the positive integers is the lesser number in the negative integers<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n8 = 8 ( or ) -8 = -8<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 6\" width=\"115\" height=\"38\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| -x | = x for x &gt; 0<br \/>\n| -x | = -x for x &lt; 0<br \/>\nThe order of the numbers in the ascending order is:<br \/>\n-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<br \/>\nWe know that,<br \/>\nThe greater number in the positive integers is the lesser number in the negative integers<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-10 &lt; 18\u00a0 \u00a0 ( or ) -10 &gt; -18<\/p>\n<p>Question 13.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nA number a is to the left of a number b on the number line. How do the numbers -a and -b compare?<br \/>\nAnswer:<br \/>\nIt is given that a number a is to the left of a number b on the number line.<br \/>\nSo,<br \/>\nThe representation of a and b on the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-10.jpg\" alt=\"\" width=\"686\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-10.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-10-300x39.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><br \/>\nHence, from the above number line<br \/>\nWe can conclude that<br \/>\n-a &gt; -b<\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Mathematical_Practices\"><\/a>Solving Linear Inequalities Mathematical Practices<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Use a graphing calculator to solve the inequality.<\/strong><\/p>\n<p>Question 1.<br \/>\n2x + 3 &lt; x &#8211; 1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2x + 3 &lt; x &#8211; 1<br \/>\nWe know that,<br \/>\nWhen we convert the mathematical symbols from LHS to RHS, the sign of that mathematical symbol change. i.e.,<br \/>\n+ will be converted into &#8211; and vice &#8211; versa<br \/>\n\u00d7 will be converted into \u00f7 and vice-versa<br \/>\nSo,<br \/>\n2x &#8211; x &lt; -1 &#8211; 3<br \/>\nx &lt; &#8211; 4<br \/>\nHence,<br \/>\nThe representation of the solved inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-12.jpg\" alt=\"\" width=\"682\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-12.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-12-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 2.<br \/>\n-x &#8211; 1 &gt; -2x + 2<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-x &#8211; 1 &gt; -2x + 2<br \/>\nWe know that,<br \/>\nWhen we convert the mathematical symbols from LHS to RHS, the sign of that mathematical symbol change. i.e.,<br \/>\n+ will be converted into &#8211; and vice &#8211; versa<br \/>\n\u00d7 will be converted into \u00f7 and vice-versa<br \/>\nSo,<br \/>\n-x + 2x &gt; 2 + 1<br \/>\nx &gt; 3<br \/>\nHence,<br \/>\nThe representation of the solved inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-13.jpg\" alt=\"\" width=\"682\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-13.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-13-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{2}\\)x + 1 &gt; \\(\\frac{3}{2}\\)x + 3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{1}{2}\\)x + 1 &gt; \\(\\frac{3}{2}\\)x + 3<br \/>\nWe know that,<br \/>\nWhen we convert the mathematical symbols from LHS to RHS, the sign of that mathematical symbol change. i.e.,<br \/>\n+ will be converted into &#8211; and vice &#8211; versa<br \/>\n\u00d7 will be converted into \u00f7 and vice-versa<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\)x &#8211; \\(\\frac{3}{2}\\)x &gt; 3 &#8211; 1<br \/>\n\\(\\frac{1 &#8211; 3}{2}\\)x &gt; 2<br \/>\n\\(\\frac{-2}{2}\\)x &gt; 2<br \/>\n\\(\\frac{-1}{1}\\)x &gt; 2<br \/>\n-x &gt; 2<br \/>\nMultiply with &#8211;\u00a0 both sides<br \/>\nSo,<br \/>\nx &gt; -2<br \/>\nHence,<br \/>\nThe representation of the solved inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-14.jpg\" alt=\"\" width=\"682\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-14.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-14-300x46.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<h3><a id=\"Lesson_2.1_Writing_and_Graphing_Inequalities\"><\/a>Lesson 2.1 Writing and Graphing Inequalities<\/h3>\n<p><strong>Essential Question<\/strong><\/p>\n<p>How can you use an inequality to describe a real-life statement?<br \/>\nAnswer:<br \/>\nInequality is just a relationship between two amounts, in which the amounts are not the same.<br \/>\nExample:<br \/>\nShe completed her work before anyone else. i.e., her finish time was less than everyone else<\/p>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Writing and Graphing Inequalities<\/strong><\/p>\n<p>Work with a partner. Write an inequality for each statement. Then sketch the graph of the numbers that make each inequality true.<br \/>\na. <strong>Statement<\/strong> The temperature t in Sweden is at least -10\u00b0C.<br \/>\n<strong>Inequality<\/strong> <img loading=\"lazy\" class=\"alignnone size-full wp-image-35032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 7\" width=\"126\" height=\"34\" \/><br \/>\n<strong>Graph<\/strong> <img loading=\"lazy\" class=\"alignnone size-full wp-image-35033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 8\" width=\"354\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-8.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-8-300x44.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 8\" width=\"354\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-8.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-8-300x44.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><br \/>\nIt s given that the temperature t in Sweden is at least -10\u00b0C<br \/>\nThe meaning of the above statement is that the temperature of Sweden is -10\u00b0C or greater than -10\u00b0C<br \/>\nHence,<br \/>\nThe representation of the temperature of Sweden in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-15.jpg\" alt=\"\" width=\"348\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-15.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-15-300x78.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>b. <strong>Statement<\/strong> The elevation e of Alabama is at most 2407 feet.<br \/>\n<strong>Inequality<\/strong> <img loading=\"lazy\" class=\"alignnone size-full wp-image-35034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 9\" width=\"127\" height=\"36\" \/><br \/>\n<strong>Graph<\/strong> <img loading=\"lazy\" class=\"alignnone size-full wp-image-35035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 10\" width=\"350\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-10.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-10-300x53.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 10\" width=\"350\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-10.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-10-300x53.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\nIt is given that the elevation &#8216; e &#8216; of Alabama is at most 2,407 feet<br \/>\nFrom the given graph,<br \/>\nWe can say that the gap between each elevation is 1,000 feet<br \/>\nSo,<br \/>\nThe elevation of Alabama will come between 2000 and 3000 in the number line<br \/>\nHence,<br \/>\nThe representation of the elevation of Alabama in the given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-16.jpg\" alt=\"\" width=\"345\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-16.jpg 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-16-300x86.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 11\" width=\"231\" height=\"182\" \/><br \/>\nAnswer:<br \/>\n<strong>EXPLORATION 2<\/strong><br \/>\n<strong>Writing Inequalities<\/strong><br \/>\n<strong>Work with a partner.<\/strong> Write an inequality for each graph. Then, in other words, describe all the values of x that make each inequality true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 12\" width=\"468\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-12.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-12-300x140.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\nAnswer:<br \/>\nThe given number lines are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 12\" width=\"468\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-12.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-12-300x140.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\na)<br \/>\nFrom the given number line,<br \/>\nThe value of x marked from 1 to 4<br \/>\nHence,<br \/>\nThe inequality representing the given number line is:<br \/>\nx \u2265 1<br \/>\nb)<br \/>\nFrom the given number line,<br \/>\nThe value of x marked after 1 till the end of the number line<br \/>\nHence,<br \/>\nThe inequality representing the given number line is:<br \/>\nx &gt; 1<br \/>\nc)<br \/>\nFrom the given number line,<br \/>\nThe value of x marked from 1 till the end of the left side of the number line.<br \/>\nHence,<br \/>\nThe inequality representing the given number line is:<br \/>\nx \u2264 1<br \/>\nd)<br \/>\nFrom the given number line,<br \/>\nThe value of x marked before 1 till the end of the left side of the number line<br \/>\nHence,<br \/>\nThe inequality representing the given number lie is:<br \/>\nx &lt; 1<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use an inequality to describe a real-life statement?<br \/>\nAnswer:<br \/>\nInequality is just a relationship between two amounts, in which the amounts are not the same.<br \/>\nExample:<br \/>\nA ball in the net is worth two in the bush. i.e., the value of a single ball in the net is greater than the value of a single ball in the bush.<\/p>\n<p>Question 4.<br \/>\nWrite a real-life statement that involves each inequality.<br \/>\na. x &lt; 3.5<br \/>\nb. x \u2264 6<br \/>\nc. x &gt; -2<br \/>\nd. x \u2265 10<br \/>\nAnswer:<br \/>\na)<br \/>\nThe given inequality is:<br \/>\nx &lt; 3.5<br \/>\nThe real-life situation that involves the given inequality is:<br \/>\nThe number of birds that are less than the height of 3.5 inches<br \/>\nb)<br \/>\nThe given inequality is:<br \/>\nx \u2264 6<br \/>\nThe real- life situation that involves the given inequality is:<br \/>\nThe number of people that are buying the mobiles from a mobile store<br \/>\nc)<br \/>\nThe given inequality is:<br \/>\nx &gt; -2<br \/>\nThe real-life situation that involves the given inequality is:<br \/>\nThe number of integers that are greater than -2<br \/>\nd)<br \/>\nThe given inequality is:<br \/>\nx \u2265 10<br \/>\nThe real-life situation that involves the given inequality is:<br \/>\nThe number of chocolates that are distributed greater than or equal to 10 children<\/p>\n<p><strong>2.1 Lesson<\/strong><\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Write the sentence as an inequality.<\/strong><\/p>\n<p>Question 1.<br \/>\nA number b is fewer than 30.4.<br \/>\nAnswer:<br \/>\nThe given sentence is:<br \/>\nA number b is fewer than 30.4<br \/>\nHence,<br \/>\nThe representation of the given sentence in the form of inequality is:<br \/>\nb &lt; 30.4<\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\frac{7}{10}\\) is at least twice a number k minus 4.<br \/>\nAnswer:<br \/>\nThe given sentence is:<br \/>\n&#8211;\\(\\frac{7}{10}\\) is at least twice a number k minus 4.<br \/>\nHence,<br \/>\nThe representation of the given sentence in the form of inequality is:<br \/>\n&#8211;\\(\\frac{7}{10}\\) = 2k &#8211; 4<\/p>\n<p><strong>Tell whether \u22126 is a solution to the inequality.<\/strong><\/p>\n<p>Question 3.<br \/>\nc + 4 &lt; -1<br \/>\nAnswer:<br \/>\n-6 is not a solution to the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nc + 4 = -1<br \/>\nSo,<br \/>\nc = -4 &#8211; 1<br \/>\nc = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that -6 is not a solution to the given inequality<\/p>\n<p>Question 4.<br \/>\n10 \u2264 3 &#8211; m<br \/>\nAnswer:<br \/>\n-6 is not a solution to the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n10 \u2264 3 &#8211; m<br \/>\nSo,<br \/>\n-m \u2264 10 &#8211; 3<br \/>\n-m \u2264 7<br \/>\nMultiply by &#8211; on both sides<br \/>\nm \u2264 -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that -6 is not a solution to the given inequality<\/p>\n<p>Question 5.<br \/>\n21 \u00f7 x \u2265 -3.5<br \/>\nAnswer:<br \/>\n-6 is a solution to the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n21 \u00f7 x \u2265 -3.5<br \/>\nSo,<br \/>\n-21 \u00f7 3.5 \u2265 x<br \/>\n-210 \u00f7 35 \u2265 x<br \/>\n-6 \u2265 x<br \/>\nx \u2264 -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that -6 is a solution to the given inequality<\/p>\n<p>Question 6.<br \/>\n4x &#8211; 25 &gt; -2<br \/>\nAnswer:<br \/>\n-6 is not a solution to the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n4x &#8211; 25 &gt; -2<br \/>\nSo,<br \/>\n4x &gt; -2 + 25<br \/>\n4x &gt; 23<br \/>\nx &gt; 23 \u00f7 4<br \/>\nx &gt; 5.75<br \/>\nHence, from the above,<br \/>\nWe can conclude that -6 is not a solution to the given inequality<\/p>\n<p><strong>Graph the inequality.<\/strong><\/p>\n<p>Question 7.<br \/>\nb &gt; -8<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nb &gt; -8<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-20.jpg\" alt=\"\" width=\"682\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-20.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-20-300x50.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 8.<br \/>\n1.4 \u2265 g<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n1.4 \u2265 g<br \/>\nSo,<br \/>\ng \u2264 1.4<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-21.jpg\" alt=\"\" width=\"348\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-21.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-21-300x48.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 9.<br \/>\nr &lt; \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nr &lt; \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nr &lt; 0.5<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-22.jpg\" alt=\"\" width=\"348\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-22.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-22-300x48.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 10.<br \/>\nv \u2265 \\(\\sqrt{36}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nv &gt; \\(\\sqrt{36}\\)<br \/>\nSo,<br \/>\nv &gt; 6<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-23.jpg\" alt=\"\" width=\"682\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-23.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-23-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 11.<br \/>\nWrite an inequality that represents the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 13\" width=\"386\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-13.png 386w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-13-300x38.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 13\" width=\"386\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-13.png 386w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-13-300x38.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><br \/>\nFrom the given graph,<br \/>\nWe can say that the marked line is from -6 and continued after -6 till the last number on the right side of the number line.<br \/>\nHence,<br \/>\nThe representation of the given number line in the form of inequality is:<br \/>\nx \u2265 -6<\/p>\n<h3><a id=\"Writing_and_Graphing_Inequalities_2.1_Exercises\"><\/a>Writing and Graphing Inequalities 2.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nA mathematical sentence using the symbols &lt;, &gt;, \u2264, or \u2265 is called a(n)_______.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 1\" width=\"570\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-1.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-1-300x33.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIs 5 in the solution set of x + 3 &gt; 8? Explain.<br \/>\nAnswer:<br \/>\n5 is not in the solution of the given inequality<br \/>\nx + 3 &gt; 8<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\nx + 3 &gt; 8<br \/>\nSo,<br \/>\nx &gt; 8 &#8211; 3<br \/>\nx &gt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that 5 is not in the solution of the given inequality<\/p>\n<p>Question 3.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nDescribe how to graph an inequality.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 3\" width=\"572\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-3.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-3-300x59.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Write \u201cboth\u201d inequalities.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 14\" width=\"441\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-14.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-14-300x63.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><br \/>\nAnswer:<br \/>\nThe given inequalities in the worded form are:<br \/>\na) w is greater than or equal to -7<br \/>\nb) w is not less than -7<br \/>\nc) w is no more than -7<br \/>\nd) w is at least -7<br \/>\nNow,<br \/>\na)<br \/>\nThe given worded form in the form of inequality is:<br \/>\nw \u2265 -7<br \/>\nb)<br \/>\nThe given worded form in the form of inequality is:<br \/>\nw &gt; -7<br \/>\nc)<br \/>\nThe given worded form in the form of inequality is:<br \/>\nw \u2265\u00a0-7<br \/>\nd)<br \/>\nThe given worded form in the form of inequality is:<br \/>\nw \u2265 -7<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201312, write the sentence as an inequality.<\/strong><\/p>\n<p>Question 5.<br \/>\nA number x is greater than 3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 5\" width=\"287\" height=\"120\" \/><\/p>\n<p>Question 6.<br \/>\nA number n plus 7 is less than or equal to 9.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number n plus 7 is less than or equal to 9<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nn + 7 \u2264 9<\/p>\n<p>Question 7.<br \/>\nFifteen is no more than a number t divided by 5.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 7\" width=\"458\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-7.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-7-300x108.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>Question 8.<br \/>\nThree times a number w is less than 18.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nThree times a number w is less than 18<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\n3w &lt; 18<\/p>\n<p>Question 9.<br \/>\nOne-half of a number y is more than 22.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 9\" width=\"383\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-9.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-9-300x104.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Question 10.<br \/>\nThree is less than the sum of a number s and 4.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nThree is less than the sum of a number s and 4<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\n3 &lt; s + 4<\/p>\n<p>Question 11.<br \/>\nThirteen is at least the difference between a number v and 1.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 11\" width=\"505\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-11.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-11-300x72.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 12.<br \/>\nFour is no less than the quotient of a number x and 2.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nFour is no less than the quotient of a number x and 2<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\n4 &gt; x \u00f7 2<\/p>\n<p>Question 13.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nOn a fishing trip, you catch two fish. The weight of the first fish is shown. The second fish weighs at least 0.5 pound more than the first fish. Write an inequality that represents the possible weights of the second fish.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 15\" width=\"109\" height=\"236\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 13\" width=\"571\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-13.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-13-300x78.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThere are 430 people in a wave pool. Write an inequality that represents how many more people can enter the pool.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-16.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 16\" width=\"236\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the number of more people that can enter the pool is:<br \/>\n430 + x = 600<br \/>\nWhere,<br \/>\nx is the number of more people that can enter the pool<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 430 people in a wave pool<br \/>\nIt is also given that the maximum capacity in a pool is: 600<br \/>\nLet,<br \/>\nx be the number of more people that can enter the pool<br \/>\nHence,<br \/>\nThe inequality that represents the number of more people that can enter the pool is:<br \/>\n430 + x = 600<\/p>\n<p><strong>In Exercises 15\u201324, tell whether the value is a solution to the inequality.<\/strong><\/p>\n<p>Question 15.<br \/>\nr + 4 &gt; 8; r = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 15\" width=\"406\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-15.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-15-300x109.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 16.<br \/>\n5 &#8211; x &lt; 8; x = -3<br \/>\nAnswer:<br \/>\n-3 is not a solution of the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n5 &#8211; x &lt; 8<br \/>\nIt is given that x = -3<br \/>\nSo,<br \/>\n5 &#8211; ( -3 ) &lt; 8<br \/>\n5 + 3 &lt; 8<br \/>\n8 &lt; 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that x = -3 is not a solution to the given inequality<\/p>\n<p>Question 17.<br \/>\n3s \u2264 19; s = -6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 17\" width=\"392\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-17.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-17-300x112.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 18.<br \/>\n17 \u2265 2y ; y = 7<br \/>\nAnswer:<br \/>\ny = 7 is a solution of the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n17 \u2265 2y<br \/>\nIt is given that y = 7<br \/>\nSo,<br \/>\n17 \u2265 2 ( 7 )<br \/>\n17 \u2265 14<br \/>\nHence, from the above,<br \/>\nWe can conclude that y = 7 is a solution of the given inequality<\/p>\n<p>Question 19.<br \/>\n-1 &gt; &#8211;\\(\\frac{x}{2}\\); x = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 19\" width=\"373\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-19.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-19-300x160.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 20.<br \/>\n&#8211;\\(\\frac{4}{z}\\) \u2265 3; z = 2<br \/>\nAnswer:<br \/>\nz = 2 is not a solution of the given inequality<\/p>\n<p>Explanation;<br \/>\nThe given inequality is:<br \/>\n&#8211;\\(\\frac{4}{z}\\) \u2265 3<br \/>\nIt is given that z = 2<br \/>\nSo,<br \/>\n&#8211;\\(\\frac{4}{2}\\) \u2265 3<br \/>\n-2 \u2265 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that z = 2 is not a solution of the given inequality<\/p>\n<p>Question 21.<br \/>\n14 \u2265 -2n + 4; n = -5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 21\" width=\"391\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-21.png 391w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-21-300x147.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/p>\n<p>Question 22.<br \/>\n-5 \u00f7 (2s) &lt; -1; s = 10<br \/>\nAnswer:<br \/>\ns = 10 is a solution of the given inequality<\/p>\n<p>Explaantion:<br \/>\nThe given inequality is:<br \/>\n-5 \u00f7 ( 2s ) &lt; -1<br \/>\nIt is given that s = 10<br \/>\nSo,<br \/>\n-5 \u00f7 2 ( 10 ) &lt; -1<br \/>\n-5 \u00f7 20 &lt; -1<br \/>\n&#8211;\\(\\frac{1}{4}\\) &lt; -1<br \/>\n\\(\\frac{1}{4}\\) &lt; 1<br \/>\n1 &lt; 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that s = 10 is a solution of the given inequality<\/p>\n<p>Question 23.<br \/>\n20 \u2264 \\(\\frac{10}{2z}\\) + 20; z = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 23\" width=\"376\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-23.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-23-300x225.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{3m}{6}\\) &#8211; 2 &gt; 3; m = 8<br \/>\nAnswer:<br \/>\nm = 8 is not a solution of the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{3m}{6}\\) &#8211; 2 &gt; 3<br \/>\nIt is given that m = 8<br \/>\nSo,<br \/>\n\\(\\frac{3 \u00d7 8}{6}\\) &gt; 3 + 2<br \/>\n4\u00a0 3 + 2<br \/>\n4 &gt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that m = 8 is not a solution of the given inequality<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe tallest person who ever lived was approximately 8 feet 11 inches tall.<br \/>\na. Write an inequality that represents the heights of every other person who has ever lived.<br \/>\nb. Is 9 feet a solution of the inequality? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 25\" width=\"579\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-25.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-25-300x154.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nThe winner of a weight-lifting competition bench-pressed 400 pounds. The other competitors all bench-pressed at least 23 pounds less.<br \/>\na. Write an inequality that represents the weights that the other competitors bench-pressed.<br \/>\nAnswer:<br \/>\nIt is given that the winner of a weight-lifting competition bench pressed 400 pounds whereas the other competitors all bench-pressed at least 23 pounds less.<br \/>\nLet,<br \/>\nx be the number of pounds that all the other competitors&#8217; bench-pressed<br \/>\nSo,<br \/>\nThe inequality that represents the weights that the other competitors bench-pressed is:<br \/>\nx\u00a0 + 23 \u2264 400<\/p>\n<p>b. Was one of the other competitors able to bench-press 379 pounds? Explain.<br \/>\nAnswer:<br \/>\nNo, one of the other competitors won&#8217;t be able to bench-press 379 pounds<\/p>\n<p>Explanation:<br \/>\nFrom part (a),<br \/>\nThe inequality that represents the weights that the other competitors bench-pressed is:<br \/>\nx + 23 \u2264 400<br \/>\nx \u2264 400 &#8211; 23<br \/>\nx \u2264 377 pounds<br \/>\nHence, from the above,<br \/>\nWe can conclude that one of the other competitors won&#8217;t be able to bench-press 379 pounds<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\n<strong>In Exercises 27 and 28, describe and correct the error in determining whether 8 is in the solution set of the inequality.<\/strong><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 17\" width=\"253\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 27\" width=\"564\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-27.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-27-300x123.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-18.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 18\" width=\"254\" height=\"149\" \/><br \/>\nAnswer:<br \/>\n8 is a solution set of the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{1}{2}\\)x + 2 \u2264 6<br \/>\nIt is given that x = 8<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 8 \u2264 6 &#8211; 2<br \/>\n\\(\\frac{8}{2}\\) \u2264 4<br \/>\n4 \u2264 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that 8 is a solution set of the given inequality<\/p>\n<p><strong>In Exercises 29\u201336, graph the inequality.<\/strong><\/p>\n<p>Question 29.<br \/>\nx \u2265 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 29\" width=\"211\" height=\"54\" \/><\/p>\n<p>Question 30.<br \/>\nz \u2264 5<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nz \u2264 5<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-24.jpg\" alt=\"\" width=\"682\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-24.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-24-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 31.<br \/>\n-1 &gt; t<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 31\" width=\"214\" height=\"106\" \/><\/p>\n<p>Question 32.<br \/>\n-2 &lt; w<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-2 &lt; w<br \/>\nSo,<br \/>\nw &gt; -2<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-25.jpg\" alt=\"\" width=\"682\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-25.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-25-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 33.<br \/>\nv \u2264 -4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 33\" width=\"207\" height=\"81\" \/><\/p>\n<p>Question 34.<br \/>\ns &lt; 1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\ns &lt; 1<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-26.jpg\" alt=\"\" width=\"682\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-26.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-26-300x50.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 35.<br \/>\n\\(\\frac{1}{4}\\) &lt; p<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 35\" width=\"238\" height=\"121\" \/><\/p>\n<p>Question 36.<br \/>\nr \u2265 -| 5 |<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nr \u2265 &#8211; | 5 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nr \u2265 -5\u00a0 \u00a0( or ) r \u2265 5<br \/>\nHence,<br \/>\nThe representation of the given inequalities in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-27.jpg\" alt=\"\" width=\"682\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-27.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-27-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>In Exercises 37\u201340, write and graph an inequality for the given solution set.<\/strong><\/p>\n<p>Question 37.<br \/>\n{x | x &lt; 7}<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 37\" width=\"268\" height=\"98\" \/><\/p>\n<p>Question 38.<br \/>\n{n | n \u2265 -2}<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n{n | n \u2265 -2}<br \/>\nThe given inequality can be rewritten as:<br \/>\nn \u2265 -2<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-28.jpg\" alt=\"\" width=\"682\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-28.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-28-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 39.<br \/>\n{z | 1.3 \u2264 z}<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 39\" width=\"210\" height=\"101\" \/><\/p>\n<p>Question 40.<br \/>\n{w | 5.2 &gt; w}<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n{w | 5.2 &gt; w}<br \/>\nThe given inequality can be rewritten as:<br \/>\n5.2 &gt; w<br \/>\nSo,<br \/>\nw &lt; 5.2<br \/>\nFrom the above value,<br \/>\nWe can say that 5.2 lies between 5 and 6<br \/>\nHence,<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-29.jpg\" alt=\"\" width=\"682\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-29.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-29-300x49.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>In Exercises 41\u201344, write an inequality that represents the graph.<\/strong><\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 19\" width=\"330\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-19.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-19-300x45.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 41\" width=\"212\" height=\"32\" \/><\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 21\" width=\"329\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-21.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-21-300x57.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 21\" width=\"329\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-21.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-21-300x57.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can say that the marked line started from -2 and ended at the last value on the right side of the number line.<br \/>\nHence,<br \/>\nThe representation of the inequality for the given number line is:<br \/>\nx \u2265 -2<\/p>\n<p>Question 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-22.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 22\" width=\"326\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-22.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-22-300x44.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 43\" width=\"213\" height=\"35\" \/><\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 23\" width=\"330\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-23.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-23-300x43.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 23\" width=\"330\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-23.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-23-300x43.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can say that the marked line started from -1 excluding &#8211; and continued till the end of the number line in the left side of the number line<br \/>\nHence,<br \/>\nThe representation of the inequality for the given number line is:<br \/>\nx &lt; -1<\/p>\n<p>Question 45.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThe water temperature of a swimming pool must be no less than 76\u00b0F. The temperature is currently 74\u00b0F. Which graph correctly shows how much the temperature needs to increase? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-24.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 24\" width=\"327\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-24.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-24-300x191.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 45\" width=\"560\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-45.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-45-300x62.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAccording to state law for vehicles traveling on state roads, the maximum total weight of a vehicle and its contents depends on the number of axles on the vehicle. For each type of vehicle, write and graph an inequality that represents the possible total weights w (in pounds) of the vehicle and its contents.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 25\" width=\"348\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-25.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-25-300x113.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\nAnswer:<br \/>\nIt is given that the maximum total weight of a vehicle and its contents depends on the number of axles on the vehicle.<br \/>\nNow,<br \/>\nLet,<br \/>\nw be the total weight of the vehicle and its contents<br \/>\nFor the 2 axles vehicle, if the maximum weight is 40,000 lb and w is the possible total weight of the vehicle and its contents, then<br \/>\nw &lt; 40,000<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-30.jpg\" alt=\"\" width=\"345\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-30.jpg 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-30-300x89.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nFor the 3 axles vehicle, if the maximum weight is 60,000 lb and w is the possible total weight of the vehicle and its contents, then<br \/>\nw &lt; 60,000<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-31.jpg\" alt=\"\" width=\"345\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-31.jpg 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-31-300x89.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nFor the 4 axles vehicle, if the maximum weight is 80,000 lb and w is the possible total weight of the vehicle and its contents, then<br \/>\nw &lt; 80,000<br \/>\nThe representation of the given inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-32.jpg\" alt=\"\" width=\"345\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-32.jpg 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-32-300x89.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe Xianren Bridge is located in Guangxi Province, China. This arch is the world\u2019s longest natural arch, with a length of 400 feet. Write and graph an inequality that represents the lengths \u2113 (in inches) of all other natural arches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-26.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 26\" width=\"295\" height=\"207\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 47\" width=\"576\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-47.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-47-300x70.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nA student works no more than 25 hours each week at a part-time job. Write an inequality that represents how many hours the student can work each day.<br \/>\nAnswer:<br \/>\nIt is given that a student works no more than 25 hours each week at a part-time job<br \/>\nLet the number of days that students work each week be x<br \/>\nSo,<br \/>\nThe inequality that represents the number of hours the students work each week is:<br \/>\nx &lt; 25<br \/>\nWe know that,<br \/>\n1 week = 7 days<br \/>\nSo,<br \/>\n7x &lt; 25<br \/>\nHence,<br \/>\nThe inequality that represents the number of hours the students work each day is:<br \/>\nx &lt; \\(\\frac{25}{7}\\)<br \/>\nx &lt; 3.5<br \/>\nHence,<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-33.jpg\" alt=\"\" width=\"345\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-33.jpg 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-33-300x53.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<p>Question 49.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe a real-life situation modeled by the inequality 23 + x \u2264 31.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 49\" width=\"572\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-49.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-49-300x45.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph represents the known melting points of all metallic elements (in degrees Celsius). <img loading=\"lazy\" class=\"alignnone size-full wp-image-35052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 27\" width=\"281\" height=\"41\" \/><br \/>\na. Write an inequality represented by the graph.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 27\" width=\"281\" height=\"41\" \/><br \/>\nFrom the above graph,<br \/>\nWe can say that the marked line started from -38.87 and continued till the end of the right line of the number line<br \/>\nHence,<br \/>\nThe inequality that represents the given number line is:<br \/>\nx \u2265 -38.87<\/p>\n<p>b. Is it possible for a metallic element to have a melting point of -38.87\u00b0C? Explain.<br \/>\nAnswer:<br \/>\nYes, it is possible for a metallic element to have a melting point of -38.87\u00b0C.<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 27\" width=\"281\" height=\"41\" \/><br \/>\nFrom the above graph,<br \/>\nThe starting point is -38.87<br \/>\nHence, from the above,<br \/>\nWe can conclude that it is possible for a metallic element to have a melting point of -38.87\u00b0C<\/p>\n<p>Question 51.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nA one-way ride on a subway costs $0.90. A monthly pass costs $24. Write an inequality that represents how many one-way rides you can buy before it is cheaper to buy the monthly pass. Is it cheaper to pay the one-way fare for 25 rides? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 27.1\" width=\"240\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 51\" width=\"588\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-51.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-51-300x197.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nThe inequality x \u2264 1324 represents the weights (in pounds) of all mako sharks ever caught using a rod and reel. Your friend says this means no one using a rod and reel has ever caught a mako shark that weighs 1324 pounds. Your cousin says this means someone using a rod and reel has caught a mako shark that weighs 1324 pounds. Who is correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYour cousin is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that the inequality x \u2264 1324 represents the weights (in pounds) of all mako sharks ever caught using a rod and reel. Your friend says this means no one using a rod and reel has ever caught a mako shark that weighs 1324 pounds. Your cousin says this means someone using a rod and reel has caught a mako shark that weighs 1324 pounds.<br \/>\nNow,<br \/>\nThe given inequality is:<br \/>\nx \u2264 1324<br \/>\nThe meaning of inequality is the value of x is less than or equal to 1324 pounds<br \/>\nNow,<br \/>\nYour friend says this means no one using a rod and reel has ever caught a mako shark that weighs 1324 pounds<br \/>\nBut, from the given inequality,<br \/>\nThe statement of your friend is wrong<br \/>\nYour cousin says this means someone using a rod and reel has caught a mako shark that weighs 1324 pounds<br \/>\nBut from the given inequality,<br \/>\nThe statement of your cousin is correct.<br \/>\nHence, from the above,<br \/>\nWe can conclude that your cousin is correct<\/p>\n<p>Question 53.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDescribe a real-life situation that can be modeled by more than one inequality.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 53\" width=\"577\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-53.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-53-300x73.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn 1997, Superman\u2019s cape from the 1978 movie Superman was sold at an auction. The winning bid was $17,000. Write and graph an inequality that represents the amounts all the losing bids.<br \/>\nAnswer:<br \/>\nIt is given that in 1997, Superman\u2019s cape from the 1978 movie Superman was sold at an auction. The winning bid was $17,000.<br \/>\nSo,<br \/>\nThe bid must not be less than $17,000, otherwise, the bid will lose<br \/>\nHence,<br \/>\nThe inequality that represents the amounts of all losing bids is:<br \/>\nx &lt; 17,000<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-34.jpg\" alt=\"\" width=\"345\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-34.jpg 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-34-300x42.jpg 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\n<strong>In Exercises 55\u201358, write an inequality that represents the missing dimension x.<\/strong><\/p>\n<p>Question 55.<br \/>\nThe area is less than 42 square meters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-28.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 28\" width=\"148\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 55\" width=\"563\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-55.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-55-300x47.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 56.<br \/>\nThe area is greater than or equal to 8 square feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 29\" width=\"117\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the value of x is:<br \/>\nx \u2265 \\(\\frac{8}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 29\" width=\"117\" height=\"127\" \/><br \/>\nFrom the above figure,<br \/>\nWe can say that the given figure is a Right-angled triangle<br \/>\nWe know that,<br \/>\nThe area of the triangle = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 x \u00d7 10<br \/>\n= 5x<br \/>\nIt is given that the area of the triangle is greater than or equal to 8 square feet<br \/>\nSo,<br \/>\n5x \u2265 8 square feet<br \/>\nx \u2265 \\(\\frac{8}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents x is:<br \/>\nx \u2265 \\(\\frac{8}{5}\\)<\/p>\n<p>Question 57.<br \/>\nThe area is less than 18 square centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-30.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 30\" width=\"178\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 57\" width=\"557\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-57.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-57-300x53.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 58.<br \/>\nThe area is greater than 12 square inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 31\" width=\"68\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the value of x is:<br \/>\nx &gt; 6<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 31\" width=\"68\" height=\"133\" \/><br \/>\nFrom the above figure,<br \/>\nWe can say that the given figure is the rectangle.<br \/>\nWe know that,<br \/>\nThe area of the rectangle = Length \u00d7 Width<br \/>\n= 2 \u00d7 x<br \/>\nIt is given that the area of the rectangle is greater than 12 square inches<br \/>\nSo,<br \/>\n2x &gt; 12<br \/>\nx &gt; 12 \/ 2<br \/>\nx &gt; 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents the value of x is:<br \/>\nx &gt; 6<\/p>\n<p>Question 59.<br \/>\n<strong>WRITING<\/strong><br \/>\nA runner finishes a 200-meter dash in 35 seconds. Let r represent any speed (in meters per second) faster than the runner\u2019s speed.<br \/>\na. Write an inequality that represents r. Then graph the inequality.<br \/>\nb. Every point on the graph represents a speed faster than the runner\u2019s speed. Do you think every point could represent the speed of a runner? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 59\" width=\"581\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-59.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-59-300x138.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong>(Section 1.1)<\/p>\n<p>Question 60.<br \/>\nx + 2 = 3<br \/>\nAnswer:<br \/>\nThe value of x is: 1<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx + 2 = 3<br \/>\nSo,<br \/>\nx = 3 &#8211; 2<br \/>\nx = 1<br \/>\nHence, from the above<br \/>\nWe can conclude that the value of x is: 1<\/p>\n<p>Question 61.<br \/>\ny &#8211; 9 = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 61\" width=\"400\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-61.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-61-300x104.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 62.<br \/>\n6 = 4 + y<br \/>\nAnswer:<br \/>\nThe value of y is: 2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n6 = 4 + y<br \/>\nSo,<br \/>\n6 &#8211; 4 = y<br \/>\n2 = y<br \/>\ny = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 2<\/p>\n<p>Question 63.<br \/>\n-12 = y &#8211; 11<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 63\" width=\"418\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-63.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-63-300x99.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p><strong>Solve the literal equation for x.<\/strong>(Section 1.5)<\/p>\n<p>Question 64.<br \/>\nv = x \u2022 y \u2022 z<br \/>\nAnswer:<br \/>\nThe value of x is: \\(\\frac{v}{yz}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nv = x \u22c5 y \u22c5 z<br \/>\nx = \\(\\frac{v}{yz}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{v}{yz}\\)<\/p>\n<p>Question 65.<br \/>\ns = 2r + 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-65.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 65\" width=\"417\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-65.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-65-300x189.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\n<p>Question 66.<br \/>\nw = 5 + 3(x &#8211; 1)<br \/>\nAnswer:<br \/>\nThe value of x is: \\(\\frac{w &#8211; 2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nw = 5 + 3 ( x &#8211; 1 )<br \/>\nSo,<br \/>\nw = 5 + 3 ( x ) &#8211; 3 ( 1 )<br \/>\nw = 5 + 3x &#8211; 3<br \/>\nw = 3x + 2<br \/>\n3x = w &#8211; 2<br \/>\nx = \\(\\frac{w &#8211; 2}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{w &#8211; 2}{3}\\)<\/p>\n<p>Question 67.<br \/>\nn = \\(\\frac{2x + 1}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.1 Question 67\" width=\"399\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-67.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.1-Question-67-300x289.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<h3><a id=\"Lesson_2.2_Solving_Inequalities_Using_Addition_or_Subtraction\"><\/a>Lesson 2.2 Solving Inequalities Using Addition or Subtraction<\/h3>\n<p><strong>Essential Question<\/strong><br \/>\nHow can you use addition or subtraction to solve an inequality?<br \/>\n<strong>EXPLORATION 1<\/strong><br \/>\n<strong>Quarterback Passing Efficiency<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\nThe National Collegiate Athletic Association (NCAA) uses the following formula to rank the passing efficiencies P of quarterbacks.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-32.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 32\" width=\"754\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-32.png 754w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-32-300x135.png 300w\" sizes=\"(max-width: 754px) 100vw, 754px\" \/><br \/>\nAnswer:<br \/>\nThe formula used to rank the passing efficiencies P of the quarterbacks is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-35.jpg\" alt=\"\" width=\"545\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-35.jpg 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-35-300x73.jpg 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><br \/>\nBy comparing the coefficients, we get<br \/>\nY = 8.4<br \/>\nC = 100<br \/>\nT = 330<br \/>\nN = 200<br \/>\nA = 1<br \/>\nNow,<br \/>\na) T &lt; C<br \/>\n= 330 &lt; 100<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given inequality is not true<br \/>\nb) C + N \u2264 A<br \/>\n= ( 100 + 200 ) \u2264 1<br \/>\n= 300 \u2264 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given inequality is not true<br \/>\nc) N &lt; A<br \/>\n= 200 &lt; 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given inequality is not true<br \/>\nd) A &#8211; C \u2265 M<br \/>\nWe know that,<br \/>\nM = C &#8211; N<br \/>\nSo,<br \/>\nA-C \u2265 C &#8211; N<br \/>\n( 1 &#8211; 100 ) \u2265 ( 100 &#8211; 200 )<br \/>\n= -99 \u2265 -100<br \/>\n= 99 \u2265 100<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given inequality is not true<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Finding Solutions of Inequalities<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\nUse the passing efficiency formula to create a passing record that makes each inequality true. Record your results in the table. Then describe the values of P that make each inequality true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 33\" width=\"488\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-33.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-33-300x40.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\na. P &lt; 0<br \/>\nb. P + 100 \u2265 250<br \/>\nc. P &#8211; 250 &gt; -80<br \/>\nAnswer:<br \/>\nUsing the data from Exploration 1,<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-36.jpg\" alt=\"\" width=\"514\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-36.jpg 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-36-300x38.jpg 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><br \/>\nNow,<br \/>\nThe formula for passing efficiency is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-37.jpg\" alt=\"\" width=\"290\" height=\"47\" \/><br \/>\na) P &lt; 0<br \/>\nTo make P &lt; 0,<br \/>\nThe value of A or any of the values of the numerator must be less than 0<br \/>\nb) P + 100 \u2265 250<br \/>\nP \u2265 250 &#8211; 100<br \/>\nP \u2265 150<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of P must be greater than or equal to 150<br \/>\nc ) P &#8211; 250 &gt; -80<br \/>\nP &gt; -80 + 250<br \/>\nP &gt; 170<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of P must be greater than 170<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use addition or subtraction to solve an inequality?<br \/>\nAnswer:<br \/>\nIf you want to add or subtract from one side of the equation, you must perform the same operation to the other side of the equation. When solving inequalities by adding or subtracting, our goal is to have the variable on its own<\/p>\n<p>Question 4.<br \/>\nSolve each inequality.<br \/>\na. x + 3 &lt; 4 b. x &#8211; 3 \u2265 5 c. 4 &gt; x &#8211; 2<br \/>\nd. -2 \u2264 x + 1<br \/>\nAnswer:<br \/>\nThe given inequalities are:<br \/>\na) x + 3 &lt; 4<br \/>\nb) x &#8211; 3 \u2265 5<br \/>\nc) 4 &gt; x &#8211; 2<br \/>\nd) -2 \u2264 x + 1<br \/>\nNow,<br \/>\na)<br \/>\nThe given inequality is:<br \/>\nx + 3 &lt; 4<br \/>\nSo,<br \/>\nx &lt; 4 &#8211; 3<br \/>\nx &lt; 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that x &lt; 1<br \/>\nb)<br \/>\nThe given inequality is:<br \/>\nx &#8211; 3 \u2265 5<br \/>\nx \u2265 5 + 3<br \/>\nx \u2265 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that x \u2265 8<br \/>\nc)<br \/>\nThe given inequality is:<br \/>\n4 &gt; x &#8211; 2<br \/>\nSo,<br \/>\n4 + 2 &gt; x<br \/>\n6 &gt; x<br \/>\nx &lt; 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that x &lt; 6<br \/>\nd)<br \/>\nThe given inequality is:<br \/>\n-2 \u2264 x + 1<br \/>\nSo,<br \/>\n-2 &#8211; 1 \u2264 x<br \/>\n-3 \u2264 x<br \/>\nx \u2265 -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that x \u2265 -3<\/p>\n<p><strong>2.2 Lesson<\/strong><\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 1.<br \/>\nb &#8211; 2 &gt; -9<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nb &#8211; 2 &gt; -9<br \/>\nSo,<br \/>\nb &gt; -9 + 2<br \/>\nb &gt; -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of b is greater than -7<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-38.jpg\" alt=\"\" width=\"682\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-38.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-38-300x46.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 2.<br \/>\nm &#8211; 3 \u2264 5<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nm &#8211; 3 \u2264 5<br \/>\nSo,<br \/>\nm \u2264 5 + 3<br \/>\nm \u2264 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is less than or equal to 8<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-39.jpg\" alt=\"\" width=\"682\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-39.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-39-300x50.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{4}\\) &gt; y &#8211; \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{1}{4}\\) &gt; y &#8211; \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) &gt; y<br \/>\n\\(\\frac{1 + 1}{4}\\) &gt; y<br \/>\n\\(\\frac{2}{4}\\) &gt; y<br \/>\n\\(\\frac{1}{2}\\) &gt; y<br \/>\ny &lt; \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is less than \\(\\frac{1}{2}\\)<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-40.jpg\" alt=\"\" width=\"682\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-40.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-40-300x53.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 4.<br \/>\nk + 5 \u2264 -3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nk + 5 \u2264 -3<br \/>\nSo,<br \/>\nk \u2264 -3 &#8211; 5<br \/>\nk \u2264 -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of k is less than or equal to -8<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-41.jpg\" alt=\"\" width=\"348\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-41.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-41-300x44.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{5}{6}\\) \u2264 z + \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{5}{6}\\) \u2264 z + \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) &#8211; \\(\\frac{1}{6}\\) \u2264 z<br \/>\n\\(\\frac{5 &#8211; 1}{6}\\) \u2264 z<br \/>\n\\(\\frac{4}{6}\\) \u2264 z<br \/>\n\\(\\frac{2}{3}\\) \u2264 z<br \/>\nz \u2265 \\(\\frac{2}{3}\\)<br \/>\nz \u2265 0.6<br \/>\nz \u2265 1 ( Approx. )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of z is approximately greater than or equal to 1<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-42.jpg\" alt=\"\" width=\"682\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-42.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-42-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 6.<br \/>\np + 0.7 &gt; -2.3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\np + 0.7 &gt; -2.3<br \/>\nSo,<br \/>\np &gt; -2.3 &#8211; 0.7<br \/>\np &gt; -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of p is greater than -3<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-43.jpg\" alt=\"\" width=\"682\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-43.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-43-300x49.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 7.<br \/>\nThe microwave oven uses only 1000 watts of electricity. Does this allow you to have both the microwave oven and the toaster plugged into the circuit at the same time? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, this allows you to have both the microwave oven and the toaster plugged into the circuit at the same time<\/p>\n<p>Explanation:<br \/>\nIt is given that the microwave oven uses only 1000 watts of electricity.<br \/>\nWe know that,<br \/>\nThe toaster consumes less electricity than the microwave oven<br \/>\nHence, from the above,<br \/>\nWe can conclude that 1000 watts of electricity allow you to have both the microwave oven and the toaster plugged into the circuit at the same time<\/p>\n<h3><a id=\"Solving_Inequalities_Using_Addition_or_Subtraction_2.2_Exercises\"><\/a>Solving Inequalities Using Addition or Subtraction 2.2 Exercises<\/h3>\n<p><strong>In Exercises 3\u22126, tell which number you would add to or subtract from each side of the inequality to solve it.<\/strong><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b><br \/>\nwhy is the inequality x \u2264 6 equivalent to the inequality x &#8211; 5 \u2264 6 &#8211; 5 ?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 1\" width=\"567\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-1.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-1-300x47.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<br \/>\n<\/b>Compare solving equations using addition with solving inequalities using addition.<br \/>\nAnswer:<br \/>\nSolving equations and inequalities using addition is very similar. You have to add the same quantity on every side and the sign between the two sides does not change.<br \/>\nIt remains the equal sign\u00a0 &#8220;=&#8221;\u00a0 in the case of equations and the inequality sign in the case of inequalities<\/p>\n<p>Question 3.<br \/>\nk + 11 &lt; -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 3\" width=\"356\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-3.png 356w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-3-300x52.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p>Question 4.<br \/>\nv &#8211; 2 &gt; 14<br \/>\nAnswer:<br \/>\nThe value of v is: 16<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nv &#8211; 2 &gt; 14<br \/>\nSo,<br \/>\nv\u00a0 &#8211; 2 + 2 &gt; 14 + 2<br \/>\nv &gt; 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that we have to add 2 on both sides<\/p>\n<p>Question 5.<br \/>\n-1 \u2265 b &#8211; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 5\" width=\"285\" height=\"62\" \/><\/p>\n<p>Question 6.<br \/>\n-6 \u2264 17 + p<br \/>\nAnswer:<br \/>\nThe value of p is: p \u2265 -23<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n-6 \u2264 17 + p<br \/>\nSo,<br \/>\n-6 + 6 \u2264 17 + 6 + p<br \/>\n0 \u2264 23 + p<br \/>\n-23 \u2264 p<br \/>\np \u2265 -23<br \/>\nHence, from the above,<br \/>\nWe can conclude that we have to add 6 on both sides<\/p>\n<p><strong>In Exercises 7\u221220, solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 7.<br \/>\nx &#8211; 4 &lt; -5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 7\" width=\"278\" height=\"207\" \/><\/p>\n<p>Question 8.<br \/>\n1 \u2264 s &#8211; 8<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n1 \u2264 s &#8211; 8<br \/>\n1 + 8 \u2264 s &#8211; 8 + 8<br \/>\n9 \u2264 s<br \/>\ns \u2265 9<br \/>\nHence,<br \/>\nThe solution to the given inequality is:<br \/>\ns \u2265 9<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-44.jpg\" alt=\"\" width=\"682\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-44.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-44-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 9.<br \/>\n6 \u2265 m &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 9\" width=\"268\" height=\"205\" \/><\/p>\n<p>Question 10.<br \/>\nc &#8211; 12 &gt; -4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nc &#8211; 12 &gt; -4<br \/>\nSo,<br \/>\nc &#8211; 12 + 4 &gt; -4 + 4<br \/>\nc &#8211; 8 &gt; 0<br \/>\nc &gt; 0 + 8<br \/>\nc &gt; 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\nc &gt; 8<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-45.jpg\" alt=\"\" width=\"682\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-45.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-45-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 11.<br \/>\nr + 4 &lt; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 11\" width=\"276\" height=\"205\" \/><\/p>\n<p>Question 12.<br \/>\n-8 \u2264 8 + y<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-8 \u2264 8 + y<br \/>\nSo,<br \/>\n-8 + 8 \u2264 8 + 8 + y<br \/>\n0 \u2264 16 + y<br \/>\n-16 \u2264 y<br \/>\ny \u2265 -16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\ny \u2265 -16<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-46.jpg\" alt=\"\" width=\"348\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-46.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-46-300x50.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 13.<br \/>\n9 + w &gt; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 13\" width=\"274\" height=\"184\" \/><\/p>\n<p>Question 14.<br \/>\n15 \u2265 q + 3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n15 \u2265 q + 3<br \/>\nSo,<br \/>\n15 &#8211; 15 \u2265 q + 3 &#8211; 15<br \/>\n0 \u2265 q &#8211; 12<br \/>\n12 \u2265 q<br \/>\nq \u2264\u00a012<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\nq \u2264 12<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-47.jpg\" alt=\"\" width=\"682\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-47.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-47-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 15.<br \/>\nh &#8211; (-2) \u2265 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 15\" width=\"275\" height=\"243\" \/><\/p>\n<p>Question 16.<br \/>\n-6 &gt; t &#8211; (-13)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-6 &gt; t &#8211; ( -13 )<br \/>\nSo,<br \/>\n-6 + 6 &gt; t + 13 + 6<br \/>\n0 &gt; t + 19<br \/>\n-19 &gt; t<br \/>\nt &lt; -19<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\nt &lt; -19<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-48.jpg\" alt=\"\" width=\"348\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-48.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-48-300x50.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 17.<br \/>\nj + 9 &#8211; 3 &lt; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 17\" width=\"272\" height=\"220\" \/><\/p>\n<p>Question 18.<br \/>\n1 &#8211; 12 + y \u2265 -5<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n1 &#8211; 12 + y \u2265 -5<br \/>\nSo,<br \/>\n-11 + y \u2265 -5<br \/>\n-11 + 5 + y \u2265 -5 + 5<br \/>\n6 + y \u2265 0<br \/>\ny \u2265 -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\ny \u2265 -6<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-49.jpg\" alt=\"\" width=\"682\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-49.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-49-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 19.<br \/>\n10 \u2265 3p &#8211; 2p &#8211; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 19\" width=\"270\" height=\"217\" \/><\/p>\n<p>Question 20.<br \/>\n18 &#8211; 5z + 6z &gt; 3 + 6<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n18 &#8211; 5z + 6z &gt; 3 + 6<br \/>\nSo,<br \/>\n18 + z &gt; 9<br \/>\n18 &#8211; 9 + z &gt; 9 &#8211; 9<br \/>\nz + 9 &gt; 0<br \/>\nz &gt; -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\nz &gt; -9<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-50.jpg\" alt=\"\" width=\"682\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-50.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-50-300x46.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>In Exercises 21\u221224, write the sentence as an inequality. Then solve the inequality.<\/strong><\/p>\n<p>Question 21.<br \/>\nA number plus 8 is greater than 11.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 21\" width=\"495\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-21.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-21-300x137.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 22.<br \/>\nA number minus 3 is at least -5.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number minus 3 is at least -5<br \/>\nLet the number be x<br \/>\nSo,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nx &#8211; 3 \u2265 -5<br \/>\nSo,<br \/>\nx &#8211; 3 + 5 \u2265 -5 + 5<br \/>\nx + 2 \u2265 0<br \/>\nx \u2265 -2<br \/>\nHence, the solution to the given worded form inequality is:<br \/>\nx \u2265 -2<\/p>\n<p>Question 23.<br \/>\nThe difference of a number and 9 is fewer than 4.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 23\" width=\"492\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-23.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-23-300x139.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 24.<br \/>\nSix is less than or equal to the sum of a number and 15.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nSix is less than or equal to the sum of a number and 15<br \/>\nLet the number be x<br \/>\nSo,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\n6 \u2264\u00a0x + 15<br \/>\n6 &#8211; 6 \u2264 x + 15 &#8211; 6<br \/>\n0 \u2264 x + 9<br \/>\n-9 \u2264 x<br \/>\nx \u2265 -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given worded form of the inequality is:<br \/>\nx \u2265 -9<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are riding a train. Your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds.<br \/>\na. Write and solve an inequality that represents how much weight you can add to your bag.<br \/>\nb. Can you add both a 9-pound laptop and a 5-pound pair of boots to your bag without going over the weight limit? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 25\" width=\"585\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-25.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-25-300x285.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou order the hardcover book shown from a website that offers free shipping on orders of $25 or more. Write and solve an inequality that represents how much more you must spend to get free shipping.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-34.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 34\" width=\"224\" height=\"145\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the more money you must spend to get free shipping is:<\/p>\n<p>Explanation:<br \/>\nIt is given that you order the hardcover book shown from a website that offers free shipping on orders of $25 or more.<br \/>\nFrom the figure,<br \/>\nThe cost of a hardcover book is: $19.76<br \/>\nLet<br \/>\nThe amount more money you must spend to get free shipping to be x<br \/>\nSo,<br \/>\nx + 19.76 \u2265 25<br \/>\nx + 19.76 &#8211; 25 \u2265 25 &#8211; 25<br \/>\nx &#8211; 5.24 \u2265 0<br \/>\nx \u2265 $5.24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount more money you must spend to get free shipping is: $5.24<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\n<strong>In Exercises 27 and 28, describe and correct the error in solving the inequality or graphing the solution.<\/strong><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 35\" width=\"259\" height=\"131\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 27\" width=\"510\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-27.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-27-300x161.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-36.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 36\" width=\"258\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-10 + x \u2265 -9<br \/>\n-10 + 9 + x \u2265 -9 + 9<br \/>\n-1 + x \u2265 0<br \/>\nx \u2265 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\nx \u2265 1<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-51.jpg\" alt=\"\" width=\"682\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-51.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-51-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nAn NHL hockey player has 59 goals so far in a season. What are the possible numbers of additional goals the player can score to match or break the NHL record of 92 goals in a season?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 29\" width=\"558\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-29.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-29-300x205.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nIn an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 37\" width=\"270\" height=\"99\" \/><\/p>\n<p>a. Describe the score that you must earn on your second jump to beat your competitor.<br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 37\" width=\"270\" height=\"99\" \/><br \/>\nLet the score of your second acrobatic ski jump be x<br \/>\nNow,<br \/>\nFrom the above table,<br \/>\nWe can say that your score must be greater than your competitor&#8217;s score to beat your competitor<br \/>\nHence,<br \/>\nThe inequality that represents the score you must earn on your second jump to beat your competitor is:<br \/>\nx &gt; 119.8<\/p>\n<p>b. Your coach says that you will beat your competitor if you score 118.4 points. A teammate says that you only need 117.5 points. Who is correct? Explain.<br \/>\nAnswer:<br \/>\nYour coach and your teammate both are correct<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 37\" width=\"270\" height=\"99\" \/><br \/>\nFrom the above table,<br \/>\nIn the 1st acrobatic ski jump,<br \/>\nYour competitor&#8217;s score is: 117.1<br \/>\nYour score is: 119.5<br \/>\nIf you want to beat your competitor, then you have to score more than 117.1<br \/>\nSo,<br \/>\nx &gt; 117.1<br \/>\nIt is given that your coach says that you will beat your competitor if you score 118.4 points. A teammate says that you only need 117.5 points<br \/>\nSo,<br \/>\nAccording to your coach,<br \/>\nYou have to score 118.4 points to beat your competitor<br \/>\nSo,<br \/>\n118.4 &gt; 117.1<br \/>\nAccording to a teammate,<br \/>\nYou have to score 117.5 points to beat your competitor<br \/>\nSo,<br \/>\n117.5 &gt; 117.1<br \/>\nHence, from the above,<br \/>\nWe can conclude that your coach and your teammate both are correct<\/p>\n<p>Question 31.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich of the following inequalities are equivalent to the inequality x &#8211; b &lt; 3, where b is a constant? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-38.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 38\" width=\"318\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-38.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-38-300x61.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 31\" width=\"570\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-31.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-31-300x94.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\n<strong>In Exercises 32 and 33, write and solve an inequality to find the possible values of x.<\/strong><\/p>\n<p>Question 32.<br \/>\nPerimeter &lt; 51.3 inches<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 39\" width=\"169\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nThe value of x is greater than 21.6 inches<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 39\" width=\"169\" height=\"116\" \/><br \/>\nFrom the above figure,<br \/>\nWe can say that the figure is the triangle<br \/>\nWe know that,<br \/>\nThe perimeter is the sum of all of the sides<br \/>\nSo,<br \/>\nThe perimeter of the triangle = 15.5 + 14.2 + x<br \/>\nIt is given that<br \/>\nPerimeter &lt; 51.3 inches<br \/>\nSo,<br \/>\n51.3 &lt; 29.7 + x<br \/>\n51.3 &#8211; 29.7 &lt; x<br \/>\n21.6 &lt; x<br \/>\nx &gt; 21.6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is greater than 21.6 inches<\/p>\n<p>Question 33.<br \/>\nPerimeter \u2264 18.7 feet<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-39.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 39.1\" width=\"197\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 33\" width=\"418\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-33.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-33-300x151.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nWrite an inequality that has the solution shown in the graph. Describe a real-life situation that can be modeled by inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-40.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 40\" width=\"308\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-40.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-40-300x43.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-40.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 40\" width=\"308\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-40.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-40-300x43.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that the marked line is starting from 16 and continued till the left end of the number line<br \/>\nSo,<br \/>\nThe inequality that represents the given number line is:<br \/>\nx \u2264 16<br \/>\nThe real-life situation that can be modeled by inequality is:<br \/>\nA lift carrying no more than 16 people<\/p>\n<p>Question 35.<br \/>\n<strong>WRITING<\/strong><br \/>\nIs it possible to check all the numbers in the solution set of an inequality? When you solve the inequality x &#8211; 11 \u2265 -3, which numbers can you check to verify your solution? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 35\" width=\"588\" height=\"331\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-35.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-35-300x169.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe diagram represents the numbers of students in a school with brown eyes, brown hair, or both.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 41\" width=\"240\" height=\"151\" \/><br \/>\nDetermine whether each inequality must be true. Explain your reasoning.<br \/>\na. H \u2265 E<br \/>\nb. H + 10 \u2265 E<br \/>\nc. H \u2265 X<br \/>\nd. H + 10 \u2265 X<br \/>\ne. H &gt; X<br \/>\nf. H + 10 &gt; X<br \/>\nAnswer:<br \/>\nThe given diagram is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 41\" width=\"240\" height=\"151\" \/><br \/>\nFrom the above diagram,<br \/>\nWe can observe that,<br \/>\nThe spaces occupied by H and E are equal<br \/>\nThe spaces occupied by H and E are greater than X<br \/>\nSo,<br \/>\nWe can say that<br \/>\nH = E; H &gt; X; E &gt; X<br \/>\nNow,<br \/>\na. H \u2265 E<br \/>\nFrom the above diagram,<br \/>\nThe given inequality is not true<br \/>\nb. H + 10 \u2265 E<br \/>\nFrom the above diagram,<br \/>\nThe given inequality is not true<br \/>\nc. H \u2265 X<br \/>\nFrom the above diagram,<br \/>\nThe given inequality is not true<br \/>\nd. H + 10 \u2265 X<br \/>\nFrom the above diagram,<br \/>\nThe given inequality is not true<br \/>\ne. H &gt; X<br \/>\nFrom the above diagram,<br \/>\nThe given inequality is true<br \/>\nf. H + 10 &gt; X<br \/>\nFrom the above diagram,<br \/>\nThe given inequality is true<\/p>\n<p>Question 37.<br \/>\n<strong>REASONING<\/strong><br \/>\nWrite and graph an inequality that represents the numbers that are not solutions to each inequality.<br \/>\na. x + 8 &lt; 14<br \/>\nb. x &#8211; 12 \u2265 5.7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 37\" width=\"557\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-37.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-37-300x226.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nUse the inequalities c &#8211; 3 \u2265 d, b + 4 &lt; a + 1, and a &#8211; 2 \u2264 d &#8211; 7 to order a, b, c, and d from least to greatest.<br \/>\nAnswer:<br \/>\nThe order of a, b, c, and d from least to greatest is:<br \/>\nb, a, c, and d<\/p>\n<p>Explanation:<br \/>\nThe given inequalities are:<br \/>\nA) c &#8211; 3 \u2265 d<br \/>\nB) b + 4 &lt; a + 1<br \/>\nC) a &#8211; 2 \u2264 d &#8211; 7<br \/>\nNow,<br \/>\nA)<br \/>\nThe given inequality is:<br \/>\nc &#8211; 3 \u2265 d<br \/>\nc \u2265 d + 3<br \/>\nB)<br \/>\nThe given inequality is:<br \/>\nb + 4 &lt; a + 1<br \/>\nb &lt; a + 1 &#8211; 4<br \/>\nb &lt; a &#8211; 3<br \/>\nb + 3 &lt; a<br \/>\na &gt; b + 3<br \/>\nC)<br \/>\nThe given inequality is:<br \/>\na &#8211; 2 \u2264 d &#8211; 7<br \/>\na \u2264 d &#8211; 7 + 2<br \/>\na \u2264 d &#8211; 5<br \/>\na + 5 \u2264 d<br \/>\nd \u2265 a + 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the order of a, b, c, d from least to greatest is:<br \/>\nb, a, c, and d<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Find the product or quotient.<\/strong><\/p>\n<p>Question 39.<br \/>\n7 \u2022 (-9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 39\" width=\"160\" height=\"33\" \/><\/p>\n<p>Question 40.<br \/>\n-11 \u2022 (-12)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n-11 \u22c5 ( -12 )<br \/>\n= 11 \u22c5 12 [ Since we know that &#8211; \u00d7 &#8211; = + ]<br \/>\n= 132<br \/>\nHence, from the above,<br \/>\nWe can conclude that the product of the given expression is: 132<\/p>\n<p>Question 41.<br \/>\n-27 \u00f7 (-3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 41\" width=\"168\" height=\"32\" \/><\/p>\n<p>Question 42.<br \/>\n20 \u00f7 (-5)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n20 \u00f7 ( -5 )<br \/>\n= -20 \u00f7 5 [ Since we know that + \u00f7 &#8211; = &#8211; ]<br \/>\n= -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the product of the given expression is: -4<\/p>\n<p><strong>Solve the equation. Check your solution<\/strong>.(Section 1.1)<\/p>\n<p>Question 43.<br \/>\n6x = 24<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 43\" width=\"346\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-43.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-43-300x127.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Question 44.<br \/>\n-3y = -18<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-3y = -18<br \/>\ny = -18 \u00f7 ( -3 )<br \/>\ny = 6 [ Sice we know that &#8211; \u00f7 &#8211; = + ]<br \/>\nHence, fro the above,<br \/>\nWe can conclude that the value of y in the given equation is: 6<\/p>\n<p>Question 45.<br \/>\n\\(\\frac{s}{-8}\\) = 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.2 Question 45\" width=\"420\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-45.png 420w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.2-Question-45-300x124.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\n<p>Question 46.<br \/>\n\\(\\frac{n}{4}\\) = -7.3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{n}{4}\\) = -7.3<br \/>\nn = -7.3 \u00d7 4<br \/>\nn = -29.2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n in the given equation is: -29.2<\/p>\n<h3><a id=\"Lesson_2.3_Solving_Inequalities_Using_Multiplication_or_Division\"><\/a>Lesson 2.3 Solving Inequalities Using Multiplication or Division<\/h3>\n<p><strong>Essential Question<\/strong><\/p>\n<p><strong>How can you use division to solve inequality?<\/strong><\/p>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Writing a Rule<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Copy and complete the table. Decide which graph represents the solution of the inequality 6 &lt; 3x. Write the solution to the inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-42.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 42\" width=\"722\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-42.png 722w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-42-300x88.png 300w\" sizes=\"(max-width: 722px) 100vw, 722px\" \/><br \/>\nAnswer:<br \/>\na)<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-52.jpg\" alt=\"\" width=\"494\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-52.jpg 494w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-52-300x70.jpg 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><br \/>\nThe given number lines are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-53.jpg\" alt=\"\" width=\"468\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-53.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-53-300x24.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\nFrom the above two number lines,<br \/>\nWe can say that the expression 6 &lt; 3x will be true if the value of x is greater than 2<br \/>\nFrom the 2nd number line,<br \/>\nWe can observe that the value of x is greater than 2<br \/>\nb)<br \/>\nRule:<br \/>\nDivision Property of Inequality:<br \/>\nIf you divide\u00a0one side of an\u00a0inequality\u00a0by a number, you can\u00a0divide\u00a0the other side of the\u00a0inequality\u00a0by the same number.The given inequality is:<br \/>\n6 &lt; 3x<br \/>\n3x &gt; 6<br \/>\nx &gt; 6 \u00f7 3<br \/>\nx &gt; 2<br \/>\nSo,<br \/>\nFrom the table,<br \/>\nx &gt; 2 means x = 3, 4, 5<br \/>\nSo,<br \/>\nThe value of x is: 3, 4, 5<br \/>\nNow,<br \/>\ni. 2x &lt; 4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2x &lt; 4<br \/>\nx &lt; 4 \/ 2<br \/>\nx &lt; 2<br \/>\nNow,<br \/>\nFrom the above table,<br \/>\nWe can observe that x &lt; 2 will be held true if the value of x is -1, 0, 1<\/p>\n<p>ii. 3 \u2265 3x<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3 \u2265 3x<br \/>\n1 \u2265 x<br \/>\nx \u2264 1<br \/>\nNow,<br \/>\nFrom the above table,<br \/>\nWe can observe that x \u2264 1 will be held true if the value of the x is -1, 0, 1<\/p>\n<p>iii. 2x &lt; 8<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2x &lt; 8<br \/>\nx &lt; 8 \/ 2<br \/>\nx &lt; 4<br \/>\nNow,<br \/>\nFrom the above table,<br \/>\nWe can observe that x &lt; 4 will be held true if the value of x is -1, 0, 1, 2, 3<\/p>\n<p>iv. 6 \u2265 3x<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n6 \u2265 3x<br \/>\nSo,<br \/>\n6 \/ 3 \u2265 x<br \/>\n2 \u2265 x<br \/>\nx \u2264 2<br \/>\nNow,<br \/>\nfrom the above table,<br \/>\nWe can observe that x \u2264 2 will be held true if the value of x is -1, 0, 1, 2<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Writing a Rule<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Copy and complete the table. Decide which graph represents the solution of the inequality 6 &lt; -3x. Write the solution of the inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 43\" width=\"491\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-43.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-43-300x101.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nAnswer:<br \/>\nThe complete table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-54.jpg\" alt=\"\" width=\"519\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-54.jpg 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-54-300x90.jpg 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><br \/>\nFrom the given number lines,<br \/>\nThe first graph indicates the inequality<br \/>\nx &lt; -2<br \/>\nThe second graph indicates the inequality<br \/>\nx &gt; -2<br \/>\nHence, from the table and the number line,<br \/>\nThe inequality that represents the table is:<br \/>\nx &lt; -2<\/p>\n<p>b. Use a table to solve each inequality. Then write a rule that describes how to use division to solve the inequalities.<br \/>\nRule:<br \/>\nDivision Property of Inequality:<br \/>\nIf you divide\u00a0one side of an\u00a0inequality\u00a0by a number, you can\u00a0divide\u00a0the other side of the\u00a0inequality\u00a0by the same number.<br \/>\ni. -2x &lt; 4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-2x &lt; 4<br \/>\n-x &lt; 4 \/ 2<br \/>\n-x &lt; 2<br \/>\nx &lt; -2<br \/>\nHence,<br \/>\nFrom the above table,<br \/>\nWe can observe that the values of x for the inequality x &lt; -2 is -5, -4, -3<\/p>\n<p>ii. 3 \u2265 -3x<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3 \u2265 -3x<br \/>\n1 \u2265 -x<br \/>\n-1 \u2265 x<br \/>\nx \u2264 -1<br \/>\nHence,<br \/>\nFrom the above table,<br \/>\nWe can observe that the values of x for the inequality x \u2264 -1 is -5, -4, -3, -2, -1<\/p>\n<p>iii. -2x &lt; 8<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-2x &lt; 8<br \/>\nx &lt; -8 \/2<br \/>\nx &lt; -4<br \/>\nHence,<br \/>\nFrom the above table,<br \/>\nWe can observe that the values of x for the inequality x &lt; -4 is\u00a0 -5<\/p>\n<p>iv.6 \u2265 -3x<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n6 \u2265 -3x<br \/>\n6 \/ ( -3 ) \u2265 x<br \/>\n-2 \u2265 x<br \/>\nx \u2264 -2<br \/>\nHence,<br \/>\nFrom the above table,<br \/>\nWe can observe that the values of x for the inequality x \u2264 -2 is -5, -4, -3, -2<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use division to solve inequality?<br \/>\nAnswer:<br \/>\nYou can use division to solve the inequality by using the Division Property of Inequality<br \/>\nDivision Property of Inequality:<br \/>\nIf you divide\u00a0one side of an\u00a0inequality\u00a0by a number, you can\u00a0divide\u00a0the other side of the\u00a0inequality\u00a0by the same number.<\/p>\n<p>Question 4.<br \/>\nUse the rules you wrote in Explorations 1(b) and 2(b) to solve each inequality.<br \/>\na. 7x &lt; -21<br \/>\nb. 12 \u2264 4x<br \/>\nc. 10 &lt; -5x d. -3x \u2264 0<br \/>\nAnswer:<br \/>\nRule:<br \/>\nDivision Property of Inequality:<br \/>\nIf you divide\u00a0one side of an\u00a0inequality\u00a0by a number, you can\u00a0divide\u00a0the other side of the\u00a0inequality\u00a0by the same number.<br \/>\nBy using the above rule, solve the given inequalities<br \/>\nNow,<br \/>\na. 7x &lt; -21<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n7x &lt; -21<br \/>\nx &lt; -21 \/<br \/>\nx &lt; -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &lt; -3<\/p>\n<p>b. 12 \u2264 4x<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n12 \u2264 4x<br \/>\n12 \/ 4 \u2264 x<br \/>\n3 \u2264 x<br \/>\nx \u2265 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2265 3<\/p>\n<p>c. 10 &lt; -5x<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n10 &lt; -5x<br \/>\n10 \/ -5 &lt; x<br \/>\n2 &lt; x<br \/>\nx &gt; 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &gt; 2<\/p>\n<p>d. -3x \u2264 0<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-3x \u2264 0<br \/>\nx \u2264 0 \/ -3<br \/>\nx \u2264 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2264 0<\/p>\n<p><b>2.3 <span style=\"font-size: 16px;\">Lesson\u00a0<\/span><\/b><\/p>\n<p><span style=\"font-size: 16px;\"><b>Monitoring Progress Solve the inequality. Graph the solution.\u00a0<\/b><\/span><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{n}{7}\\) \u2265 -1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{n}{7}\\) \u2265 -1<br \/>\nn \u2265 -1 ( 7 )<br \/>\nn \u2265 -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution o the inequality is n \u2265 -7<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-56.jpg\" alt=\"\" width=\"682\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-56.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-56-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 2.<br \/>\n-6.4 \u2265 \\(\\frac{1}{5}\\)w<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-6.4 \u2265 \\(\\frac{1}{5}\\)w<br \/>\n-6.4 ( 5 ) \u2265 w<br \/>\n-32 \u2265 w<br \/>\nw \u2264 -32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is w \u2264 -32<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-55.jpg\" alt=\"\" width=\"348\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-55.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-55-300x48.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 3.<br \/>\n4b \u2265 36<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4b \u2265 36<br \/>\nb \u2265 36 \/ 4<br \/>\nb \u2265 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is b \u2265 9<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-57.jpg\" alt=\"\" width=\"682\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-57.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-57-300x46.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 4.<br \/>\n-18 &gt; 1.5q<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-18 &gt; 1.5q<br \/>\n-18 \/ 1.5 &gt; q<br \/>\n-180 \/ 15 &gt; q<br \/>\n-12 &gt; q<br \/>\nq &lt; -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is q &lt; -12<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-58.jpg\" alt=\"\" width=\"348\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-58.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-58-300x44.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{p}{-4}\\) &lt; 7<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{p}{-4}\\) &lt; 7<br \/>\n&#8211;\\(\\frac{p}{4}\\) &lt; 7<br \/>\n-p &lt; 7 ( 4 )<br \/>\n-p &lt; 28<br \/>\np &lt; -28<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is p &lt; -28<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-59.jpg\" alt=\"\" width=\"348\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-59.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-59-300x42.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{x}{-5}\\) \u2264 -5<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{x}{-5}\\) \u2264 -5<br \/>\n&#8211;\\(\\frac{x}{5}\\) \u2264 -5<br \/>\n\\(\\frac{x}{5}\\) \u2264 5<br \/>\nx \u2264 5 ( 5 )<br \/>\nx \u2264 25<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2264 25<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-60.jpg\" alt=\"\" width=\"348\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-60.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-60-300x42.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 7.<br \/>\n-1 \u2265 &#8211;\\(\\frac{1}{10}\\)z<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-1 \u2265 &#8211;\\(\\frac{1}{10}\\)z<br \/>\n1 \u2265 \\(\\frac{1}{10}\\)z<br \/>\n1 ( 10 ) \u2265 z<br \/>\n10 \u2265 z<br \/>\nz \u2264 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is z \u2264 10<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-61.jpg\" alt=\"\" width=\"682\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-61.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-61-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 8.<br \/>\n-9m &gt; 63<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-9m &gt; 63<br \/>\nm &gt; -63 \/ 9<br \/>\nm &gt; -7<br \/>\nHence, from the above<br \/>\nWe can conclude that the solution to the given inequality is m &gt; -7<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-62.jpg\" alt=\"\" width=\"682\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-62.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-62-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 9.<br \/>\n-2r \u2265 -22<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-2r \u2265 -22<br \/>\n2r \u2265 22<br \/>\nr \u2265 22 \/ 2<br \/>\nr \u2265 11<br \/>\nHence, from the above<br \/>\nWe can conclude that the solution to the given inequality is r \u2265 11<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-63.jpg\" alt=\"\" width=\"682\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-63.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-63-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 10.<br \/>\n-0.4y \u2265 -12<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-0.4y \u2265 -12<br \/>\n0.4y \u2265 12<br \/>\ny \u2265 12 \/ 0.4<br \/>\ny \u2265 120 \/ 4<br \/>\ny \u2265 30<br \/>\nHence, from the above<br \/>\nWe can conclude that the solution to the given inequality is y \u2265 30<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-64.jpg\" alt=\"\" width=\"348\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-64.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-64-300x45.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 11.<br \/>\nYou have at most $3.65 to make copies. Each copy costs $0.25. Write and solve an inequality that represents the number of copies you can make.<br \/>\nAnswer:<br \/>\nThe inequality that represents the number of copies you can make is:<br \/>\nx + 0.25 \u2264 3.65<\/p>\n<p>Explanation:<br \/>\nIt is given that you have at most $3.65 i.e., you have a maximum of only $3.65 to make copies and it is also given that each copy costs $0.25.<br \/>\nLet,<br \/>\nThe additional cost to make the copies be $x<br \/>\nSo,<br \/>\nThe total cost = x + 0.25<br \/>\nBut,<br \/>\nThe total cost won&#8217;t be greater than 3.65<br \/>\nHence,<br \/>\nThe inequality that represents the number of copies you can make is:<br \/>\nx + 0.25 \u2264 3.65<\/p>\n<p>Question 12.<br \/>\nThe maximum speed limit for a school bus is 55 miles per hour. Write and solve an inequality that represents the number of hours it takes to travel 165 miles in a school bus.<br \/>\nAnswer:<br \/>\nThe inequality that represents the number of hours it takes to travel 165 miles in a school bus is:<br \/>\nx \u2265 3<\/p>\n<p>Explanation:<br \/>\nIt is given that the maximum speed limit for a school bus is 55 miles per hour.<br \/>\nLet,<br \/>\nx be the number of hours<br \/>\nSo,<br \/>\nThe inequality that represents the number of hours it takes to travel 165 miles in a school bus is:<br \/>\n55x \u2265 165<br \/>\nx \u2265 165 \/ 55<br \/>\nx \u2265 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents the number of hours it takes to travel 165 miles in a school bus is:<br \/>\nx \u2265 3<\/p>\n<h3><a id=\"Solving_Inequalities_Using_Multiplication_or_Division_2.3_Exercises\"><\/a>Solving Inequalities Using Multiplication or Division 2.3 Exercises<\/h3>\n<p><strong>In Exercises 3\u201310, solve the inequality. Graph the solution.<\/strong><\/p>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how solving 2x &lt; -8 is different from solving -2x &lt; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 1\" width=\"548\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-1-300x94.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an inequality that is solved using the Division property of Inequality where the inequality symbol needs to be reversed.<br \/>\nAnswer:<br \/>\nThe required inequality is:<br \/>\n-6 &lt; 3x<br \/>\nUsing the Division Property of Inequality,<br \/>\n-6 \/ 3 &lt; ( 3 \/ 3 )x<br \/>\n-2 &lt; x<br \/>\nx &gt; -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality is solved using the Division Property of Inequality wheer the inequality symbol needs to be reversed<\/p>\n<p>Question 3.<br \/>\n4x &lt; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 3\" width=\"236\" height=\"203\" \/><\/p>\n<p>Question 4.<br \/>\n3y \u2264 -95.<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3y \u2264 -95<br \/>\ny \u2264 -95 \/ 3<br \/>\ny \u2264 -31.6<br \/>\ny \u2264 -32 [ Approximate value ]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y \u2264 -32<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-65.jpg\" alt=\"\" width=\"348\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-65.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-65-300x46.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 5.<br \/>\n-20 \u2264 10n<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 5\" width=\"234\" height=\"201\" \/><\/p>\n<p>Question 6.<br \/>\n35 &lt; 7t<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n35 &lt; 7t<br \/>\n35 \/ 7 &lt; t<br \/>\n5 &lt; t<br \/>\nt &gt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is t &gt; 5<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-66.jpg\" alt=\"\" width=\"682\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-66.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-66-300x49.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 7.<br \/>\n\\(\\frac{x}{2}\\) &gt; -2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 7\" width=\"236\" height=\"213\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{a}{4}\\) &lt; 10.2<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{a}{4}\\) &lt; 10.2<br \/>\na &lt; 10.2 ( 4 )<br \/>\na &lt; 40.8<br \/>\na &lt; 40 [ Approximate value ]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is a &lt; 40<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-67.jpg\" alt=\"\" width=\"348\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-67.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-67-300x47.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 9.<br \/>\n20 \u2265 \\(\\frac{4}{5}\\)w<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 9\" width=\"250\" height=\"214\" \/><\/p>\n<p>Question 10.<br \/>\n-16 \u2264 \\(\\frac{8}{3}\\)t<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-16 \u2264 \\(\\frac{8}{3}\\)t<br \/>\n-16 ( 3) \u2264 8t<br \/>\n-48 \u2264 8t<br \/>\n-48 \/ 8 \u2264 t<br \/>\n-6 \u2264 t<br \/>\nt \u2265 -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is t \u2265 -6<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-68.jpg\" alt=\"\" width=\"682\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-68.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-68-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>In Exercises 11\u201318, solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 11.<br \/>\n-6t &lt; 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 11\" width=\"231\" height=\"201\" \/><\/p>\n<p>Question 12.<br \/>\n-9y &gt; 9<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-9y &gt; 9<br \/>\ny &gt; -9 \/ 9<br \/>\ny &gt; -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y &gt; -1<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-69.jpg\" alt=\"\" width=\"682\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-69.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-69-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 13.<br \/>\n-10 \u2265 -2z<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 13\" width=\"234\" height=\"223\" \/><\/p>\n<p>Question 14.<br \/>\n-15 \u2264 -3c<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-15 \u2264 -3c<br \/>\n15 \u2264 3c<br \/>\n15 \/ 3 \u2264 c<br \/>\n5 \u2264 c<br \/>\nc \u2265 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is c \u2265 5<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-70.jpg\" alt=\"\" width=\"682\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-70.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-70-300x51.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 15.<br \/>\n\\(\\frac{n}{-3}\\) \u2265 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 15\" width=\"229\" height=\"238\" \/><\/p>\n<p>Question 16.<br \/>\n\\(\\frac{w}{-5}\\) \u2264 16<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{w}{-5}\\) \u2264 16<br \/>\nw \u2264 -16 ( 5 )<br \/>\nw \u2264 -80<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is w \u2264 -80<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-71.jpg\" alt=\"\" width=\"348\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-71.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-71-300x49.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 17.<br \/>\n-8 &lt; &#8211;\\(\\frac{1}{4}\\)m<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 17\" width=\"247\" height=\"210\" \/><\/p>\n<p>Question 18.<br \/>\n-6y &gt; &#8211;\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-6 &gt; &#8211;\\(\\frac{2}{3}\\)y<br \/>\n6\u00a0 &gt; \\(\\frac{2}{3}\\)y<br \/>\n6 ( 3 ) &gt; 2y<br \/>\n18 &gt; 2y<br \/>\n18 \/ 2 &gt; y<br \/>\n9 &gt; y<br \/>\ny &lt; 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y &lt; 9<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-72.jpg\" alt=\"\" width=\"682\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-72.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-72-300x50.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 19.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou have $12 to buy five goldfish for your new fish tank. Write and solve an inequality that represents the prices you can pay per fish.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 19\" width=\"571\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-19.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-19-300x175.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA weather forecaster predicts that the temperature in Antarctica will decrease by 8\u00b0F each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36\u00b0F.<br \/>\nAnswer:<br \/>\nThe inequality to determine the number of hours it will take for the temperature to drop at least 36\u00b0 F is:<br \/>\nx \u2265 4.5<\/p>\n<p>Explanation:<br \/>\nIt is given that a weather forecaster predicts that the temperature in Antarctica will decrease by 8\u00b0F each hour for the next 6 hours.<br \/>\nNow,<br \/>\nLet the number of hours that will take to drop the temperature be x<br \/>\nSo,<br \/>\n8x \u2265 36<br \/>\nx \u2265 36 \/ 8<br \/>\nx \u2265 4.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality to determine the number of hours it will take for the temperature to drop at least 36\u00b0 F is:<br \/>\nx \u2265 4.5 hours<\/p>\n<p><strong>USING TOOLS<\/strong><br \/>\n<strong>In Exercises 21\u201326, solve the inequality. Use a graphing calculator to verify your answer.<\/strong><\/p>\n<p>Question 21.<br \/>\n36 &lt; 3y<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 21\" width=\"445\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-21.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-21-300x111.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p>Question 22.<br \/>\n17v \u2265 51<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n17v \u2265 51<br \/>\nv \u2265 51 \/ 17<br \/>\nv \u2265 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is v \u2265 3<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-73.jpg\" alt=\"\" width=\"682\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-73.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-73-300x49.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 23.<br \/>\n2 \u2264 &#8211;\\(\\frac{2}{9}\\)x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 23\" width=\"450\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-23.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-23-300x116.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Question 24.<br \/>\n4 &gt; \\(\\frac{n}{-4}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4 &gt; \\(\\frac{n}{-4}\\)<br \/>\n4 ( -4 ) &gt; n<br \/>\n-16 &gt; n<br \/>\nn &lt; -16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is n &lt; -16<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-74.jpg\" alt=\"\" width=\"348\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-74.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-74-300x47.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 25.<br \/>\n2x &gt; \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 25\" width=\"451\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-25.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-25-300x114.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p>Question 26.<br \/>\n1.1y &lt; 4.4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n1.1y &lt; 4.4<br \/>\n\\(\\frac{11}{10}\\)y &gt; \\(\\frac{44}{10}\\)<br \/>\ny &gt; \\(\\frac{10 \u00d7 44}{11 \u00d7 10}\\)<br \/>\ny &gt; 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y &gt; 4<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-75.jpg\" alt=\"\" width=\"682\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-75.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-75-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>ERROR ANALYSIS <\/strong><br \/>\n<strong>In Exercises 27 and 28, describe and correct the error in solving the inequality.<\/strong><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 45\" width=\"249\" height=\"194\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 27\" width=\"564\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-27.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-27-300x107.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-46.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 46\" width=\"257\" height=\"157\" \/><br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-4y \u2264 -32<br \/>\n4y \u2264 32<br \/>\ny \u2264 32 \/4<br \/>\ny \u2264 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\ny \u2264 8<\/p>\n<p>Question 29.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nYou have $700 to buy a new carpet for your bedroom. Write and solve an inequality that represents the costs per square foot that you can pay for the new carpet. Specify the units of measure in each step.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 47\" width=\"169\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 29\" width=\"581\" height=\"506\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-29.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-29-300x261.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nLet m &gt; 0. Match each inequality with its graph. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-48.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 48\" width=\"310\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-48.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-48-300x241.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nAnswer:<br \/>\nThe given inequalities are:<br \/>\na. \\(\\frac{x}{m}\\) &lt; -1<br \/>\nb. \\(\\frac{x}{m}\\) &gt; 1<br \/>\nc. \\(\\frac{x}{m}\\) &lt; 1<br \/>\nd. &#8211;\\(\\frac{x}{m}\\) &lt; 1<br \/>\nIt is given that m &gt; 0 i.e., m is a positive number<br \/>\nLet,<br \/>\nThe value of x is: 1<br \/>\nNow,<br \/>\na.<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{x}{m}\\) &lt; -1<br \/>\n\\(\\frac{1}{m}\\) &lt; -1<br \/>\n1 &lt; -m<br \/>\n-1 &lt; m<br \/>\nm &gt; -1<br \/>\nHence,,<br \/>\nFrom the number lines, D) represents the required number line\u00a0 for this inequality<br \/>\nb.<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{x}{m}\\) &gt; 1<br \/>\nx &gt; m<br \/>\n1 &gt; m<br \/>\nm &lt; 1<br \/>\nHence,<br \/>\nFrom the number lines, B) represents the required number line for this inequality<br \/>\nc.<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{x}{m}\\) &lt; 1<br \/>\nx &lt; m<br \/>\n1 &lt; m<br \/>\nm &gt; 1<br \/>\nHence,<br \/>\nFrom the number lines, A) represents the required number line for this inequality<br \/>\nd.<br \/>\nThe given inequality is:<br \/>\n&#8211;\\(\\frac{x}{m}\\) &lt; 1<br \/>\n-x &lt; -m<br \/>\nx &lt; m<br \/>\n1 &lt; m<br \/>\nm &gt; 1<br \/>\nHence,<br \/>\nFrom the number lines, A) represents the required number line for this inequality<\/p>\n<p>Question 31.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou run for 2 hours at a speed no faster than 6.3 miles per hour.<br \/>\na. Write and solve an inequality that represents the possible numbers of miles you run.<br \/>\nb. A marathon is approximately 26.2 miles. Your friend says that if you continue to run at this speed, you will not be able to complete a marathon in less than 4 hours. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 31\" width=\"630\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-31.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-31-300x224.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nThe inequality<br \/>\n\\(\\frac{x}{4}\\) \u2264 5 has a solution of x = p. Write a second inequality that also has a solution of x = p.<br \/>\nAnswer:<br \/>\nThe second inequality that also has a solution x = p is:<br \/>\nx \u2264 20<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{x}{4}\\) \u2264 5<br \/>\nIt is given that the given inequality has a solution of x = p<br \/>\nSo,<br \/>\nThe second inequality that also has a second solution of x = p is:<br \/>\n\\(\\frac{x}{4}\\) \u2264 5<br \/>\nx \u2264 5 ( 4 )<br \/>\nx \u2264 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the second inequality that also has a solution of x = p is:<br \/>\nx \u2264 20<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe U.S. Mint pays $0.02 to produce every penny. How many pennies are produced when the U.S. Mint pays more than $6 million in production costs?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 33\" width=\"575\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-33.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-33-300x203.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>REASONING<\/strong><br \/>\nAre x \u2264 \\(\\frac{2}{3}\\) and -3x \u2264 -2 equivalent? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes,<br \/>\nx \u2264 \\(\\frac{2}{3}\\) and -3x \u2264 -2 are equivalent<\/p>\n<p>Explanation:<br \/>\nThe given inequalities are -3x \u2264 -2 and x \u2264 \\(\\frac{2}{3}\\)<br \/>\nNow,<br \/>\nx \u2264 \\(\\frac{2}{3}\\)<br \/>\n3x \u2264 2<br \/>\nNow,<br \/>\n-3x \u2264 -2<br \/>\nMultiply with &#8216;-&#8216; on both sides<br \/>\nWe know that,<br \/>\n&#8211; \u00d7 &#8211; = +<br \/>\nSo,<br \/>\n3x \u2264 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given two inequalities are equivalent<\/p>\n<p>Question 35.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nConsider the number line shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 49\" width=\"274\" height=\"54\" \/><br \/>\na. Write an inequality relating A and B.<br \/>\nb. Write an inequality relating -A and -B.<br \/>\nc. Use the results from parts (a) and (b) to explain why the direction of the inequality symbol must be reversed when multiplying or dividing each side of an inequality by the same negative number.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 35\" width=\"572\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-35.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-35-300x83.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhy might solving the inequality \\(\\frac{4}{x}\\) \u2265 2 by multiplying each side by x lead to an error? (Hint: Consider x &gt; 0 and x &lt; 0.)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{4}{x}\\) \u2265 2<br \/>\n4 \u2265 2x<br \/>\n4 \/ 2 \u2265 x<br \/>\n2 \u2265 x<br \/>\nx \u2264 2<br \/>\nIt is given that to consider x &gt; 0 and x &lt; 0 i.e., x as a positive number and a negative number<br \/>\nNow,<br \/>\nMultiply the given inequality by x on both sides and consider x as positive<br \/>\n4x \u2265 2x\u00b2<br \/>\n4x \/ 2 \u2265 x\u00b2<br \/>\n2x \/ x \u2265 x<br \/>\n2 \u2265 x<br \/>\nx \u2264 2<br \/>\nNow,<br \/>\nMultiply the given inequality by x on both sides and consider x as negative<br \/>\n-4x \u2265 -2x\u00b2<br \/>\n4x \/ 2 \u2265 x\u00b2<br \/>\n2x \u2265 x\u00b2<br \/>\n2x \/ x \u2265 x<br \/>\n2 \u2265 x<br \/>\nx \u2264 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that there will be no error even when we multiply the given inequality with x on both sides<\/p>\n<p>Question 37.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe radius of a circle is represented by the formula r = \\(\\frac{C}{2\u03c0}\\). Write and solve an inequality that represents the possible circumferences C of the circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-50.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 50\" width=\"123\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 37\" width=\"563\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-37.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-37-300x124.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA water-skiing instructor recommends that a boat pulling a beginning skier has a speed less than 18 miles per hour. Write and solve an inequality that represents the possible distances d (in miles) that a beginner can travel in 45 minutes of practice time.<br \/>\nAnswer:<br \/>\nThe inequality that represents the possible distances that a beginner can travel in 45 minutes of practice time is:<br \/>\nd &lt; 13.5 miles<\/p>\n<p>Explanation:<br \/>\nIt is given that a water-skiing instructor recommends that a boat pulling a beginning skier has a speed less than 18 miles per hour<br \/>\nThe given speed is in terms of miles per hour<br \/>\nSo,<br \/>\nThe time should also be in hours<br \/>\nBut the given time is in minutes<br \/>\nSo,<br \/>\nWe know that,<br \/>\n60 minutes = 1 hour<br \/>\nSo,<br \/>\n45 minutes = \\(\\frac{45}{60}\\) hours<br \/>\n= \\(\\frac{3}{4}\\) hours<br \/>\nIt is also given that the distance is d<br \/>\nWe know that,<br \/>\nSpeed = \\(\\frac{Distance}{Time}\\)<br \/>\nSo,<br \/>\nDistance = Speed \u00d7 Time<br \/>\nHence,<br \/>\nThe inequality that represents the possible distances that a beginner can travel in 45 minutes of practice time is:<br \/>\nd &lt; 18 ( \\(\\frac{3}{4}\\) )<br \/>\nd &lt; \\(\\frac{18 \u00d7 3}{4}\\)<br \/>\nd &lt; \\(\\frac{54}{4}\\)<br \/>\nd &lt; \\(\\frac{27}{2}\\)<br \/>\nd &lt; 13.5 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents the possible distances that a beginner can travel in 45 minutes of practice time is:<br \/>\nd &lt; 13.5 miles<\/p>\n<p>Question 39.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA local zoo employs 36 people to take care of the animals each day. At most, 24 of the employees work full time. Write and solve an inequality that represents the fraction of employees who work part-time. Graph the solution. Maintaining Mathematical Proficiency Solve the equation. Check your solution. (Section 1.2 and Section 1.3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 39\" width=\"581\" height=\"525\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-39.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-39-300x271.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 40.<br \/>\n5x + 3 = 13<br \/>\nAnswer:<br \/>\nThe given equaltion is:<br \/>\n5x + 3 = 13<br \/>\n5x = 13 &#8211; 3<br \/>\n5x = 10<br \/>\nx = 10 \/ 2<br \/>\nx = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given equaltion is x = 5<\/p>\n<p>Question 41.<br \/>\n\\(\\frac{1}{2}\\)y &#8211; 8 = -10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 41\" width=\"494\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-41.png 494w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-41-300x145.png 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p>Question 42.<br \/>\n-3n + 2 = 2n &#8211; 3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-3n + 2 = 2n &#8211; 3<br \/>\n-3n &#8211; 2n = -3 &#8211; 2<br \/>\n-5n = -5<br \/>\n5n = 5<br \/>\nn = 5 \/ 5<br \/>\nn = 1<br \/>\nHence, from the above,<br \/>\nWe can conclud ethat the solution to the given equation is n = 1<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{1}{2}\\)z + 4 = \\(\\frac{5}{2}\\)z &#8211; 8 Tell which number is greater.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 43\" width=\"461\" height=\"561\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-43.png 461w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-43-247x300.png 247w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Question 44.<br \/>\n0.8, 85%<br \/>\nAnswer:<br \/>\nThe relation between the given numbers are:<br \/>\n0.8 &lt; 85%<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 0.8 and 85%<br \/>\nWe know that,<br \/>\nx% = \\(\\frac{x}{100}\\)<br \/>\nWe can rewrite 0.8 as 0.80 since both 0.8 and 0.80 are the same<br \/>\nSo,<br \/>\n85% = \\(\\frac{85}{100}\\)<br \/>\n0.8 = \\(\\frac{80}{100}\\)<br \/>\nBy comparison, we can get<br \/>\n0.8 is less than 85%<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n0.8 &lt; 85%<\/p>\n<p>Question 45.<br \/>\n\\(\\frac{16}{30}\\), 50%<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 45\" width=\"206\" height=\"86\" \/><\/p>\n<p>Question 46.<br \/>\n120%, 0.12<br \/>\nAnswer:<br \/>\nThe relation between the given numbers are:<br \/>\n120% &gt; 0.12<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 120% and 0.12<br \/>\nWe know that,<br \/>\nx% = \\(\\frac{x}{100}\\)<br \/>\nNow,<br \/>\n120% = \\(\\frac{120}{100}\\)<br \/>\n0.12 = \\(\\frac{12}{100}\\)<br \/>\nBy comparison, we can get<br \/>\n120% is greater than 0.12<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n120% &gt; 0.12<\/p>\n<p>Question 47.<br \/>\n60%, \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.3 Question 47\" width=\"302\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-47.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.3-Question-47-300x83.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<h3><a id=\"Lesson_2.4_Solving_Multi-step_Inequalities\"><\/a>Lesson 2.4 Solving Multi-step Inequalities<\/h3>\n<p><strong>Essential Question<\/strong><br \/>\nHow can you solve a multi-step inequality?<\/p>\n<p><strong>EXPLORATION 1 <\/strong><br \/>\n<strong>Solving a Multi-Step Inequality <\/strong><br \/>\n<strong>Work with a partner.<\/strong><\/p>\n<p>\u2022 Use what you already know about solving equations and inequalities to solve each multi-step inequality. Justify each step.<br \/>\n\u2022 Match each inequality with its graph. Use a graphing calculator to check your answer.<br \/>\na. 2x + 3 \u2264 x + 5<br \/>\nb. -2x + 3 &gt; x + 9<br \/>\nc. 27 \u2265 5x + 4x<br \/>\nd. -8x + 2x &#8211; 16 &lt; -5x + 7x<br \/>\ne. 3(x &#8211; 3) &#8211; 5x &gt; -3x &#8211; 6<br \/>\nf. -5x &#8211; 6x \u2264 8 &#8211; 8x &#8211; x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 51\" width=\"216\" height=\"180\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 51.1\" width=\"472\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.1.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.1-300x264.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><br \/>\nAnswer:<br \/>\nThe given inequalities are:<br \/>\na. 2x + 3 \u2264 x + 5<br \/>\nb. -2x + 3 &gt; x + 9<br \/>\nc. 27 \u2265 5x + 4x<br \/>\nd. -8x + 2x &#8211; 16 &lt; -5x + 7x<br \/>\ne. 3(x &#8211; 3) &#8211; 5x &gt; -3x &#8211; 6<br \/>\nf. -5x &#8211; 6x \u2264 8 &#8211; 8x &#8211; x<br \/>\nThe given graphing calculators are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 51.1\" width=\"472\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.1.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-51.1-300x264.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><br \/>\nNow,<br \/>\nFrom the graphing calculators, we can observe that the graph is divided into 4 parts.<br \/>\nThe first part indicates +x<br \/>\nThe second part indicates -x<br \/>\nNow,<br \/>\na.<br \/>\nThe given inequality is:<br \/>\n2x + 3 \u2264 x + 5<br \/>\nSo,<br \/>\n2x &#8211; x \u2264 5 &#8211; 3<br \/>\nx \u2264 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2264 2<br \/>\nThe graph B) matches the solution of the given inequality<\/p>\n<p>b.<br \/>\nThe given inequality is:<br \/>\n-2x + 3 &gt; x + 9<br \/>\nSo,<br \/>\n-2x &#8211; x &gt; 9\u00a0 -3<br \/>\n-3x &gt; 6<br \/>\nx &gt; -6 \/ 3<br \/>\nx &gt; -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &gt; -2<br \/>\nThe graph C) matches the solution of the given inequality<\/p>\n<p>c.<br \/>\nThe given inequality is:<br \/>\n27 \u2265 5x + 4x<br \/>\nSo,<br \/>\n27 \u2265 9x<br \/>\n27 \/ 9 \u2265 x<br \/>\n3 \u2265 x<br \/>\nx \u2264 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2264 3<br \/>\nThe graph E) matches the solution of the given inequality<\/p>\n<p>d.<br \/>\nThe given inequality is:<br \/>\n-8x + 2x &#8211; 16 &lt; -5x + 7x<br \/>\nSo,<br \/>\n-6x &#8211; 16 &lt; 2x<br \/>\n-6x &#8211; 2x &lt; 16<br \/>\n-8x &lt; 16<br \/>\nx &lt; -16 \/ 8<br \/>\nx &lt; -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &lt; -2<br \/>\nGraph A) matches the solution of the given inequality<\/p>\n<p>e.<br \/>\nThe given inequality is:<br \/>\n3(x &#8211; 3) &#8211; 5x &gt; -3x &#8211; 6<br \/>\nSo,<br \/>\n3 ( x ) &#8211; 3 ( 3 ) &#8211; 5x &gt; -3x &#8211; 6<br \/>\n3x &#8211; 9 &#8211; 5x &gt; -3x &#8211; 6<br \/>\n-2x &#8211; 9 &gt; -3x &#8211; 6<br \/>\n-2x + 3x &gt; -6 + 9<br \/>\nx &gt; 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &gt; 3<br \/>\nThe graph D) matches the solution of the given inequality<\/p>\n<p>f.<br \/>\nThe given inequality is:<br \/>\n-5x &#8211; 6x \u2265 8 &#8211; 8x &#8211; x<br \/>\nSo,<br \/>\n-11x \u2265\u00a08 &#8211; 9x<br \/>\n-11x + 9x \u2265\u00a08<br \/>\n-2x \u2265\u00a08<br \/>\nx \u2265\u00a0-8 \/ 2<br \/>\nx \u2265\u00a0-4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2265 -4<br \/>\nThe graph F) matches the solution of the given inequality<\/p>\n<p>Question 2.<br \/>\nHow can you solve a multi-step inequality?<br \/>\nAnswer:<br \/>\nThe general procedure for solving multi-step inequality is as follows:<br \/>\na) Clear parenthesis i.e., Brackets on both sides of the inequality and collect like terms<br \/>\nb) Addor subtract terms so the variable is on one side and the constant is on another side of the inequality sign<\/p>\n<p>Question 3.<br \/>\nWrite two different multi-step inequalities whose solutions are represented by the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-52.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 52\" width=\"410\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-52.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-52-300x40.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-52.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 52\" width=\"410\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-52.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-52-300x40.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that the marking started from -1 but by excluding -1 and continued till the left end of the graph<br \/>\nSo,<br \/>\nThe inequality represented by the graph is given as:<br \/>\nx &lt; -1<\/p>\n<p><strong>2.4 Lesson<\/strong><\/p>\n<p><strong>Monitoring Progress<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 1.<br \/>\n4b &#8211; 1 &lt; 7<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4b &#8211; 1 &lt; 7<br \/>\nSo,<br \/>\n4b &lt; 7 + 1<br \/>\n4b &lt; 8<br \/>\nb &lt; 8 \/ 4<br \/>\nb &lt; 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is b &lt; 2<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-76.jpg\" alt=\"\" width=\"682\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-76.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-76-300x48.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 2.<br \/>\n8 &#8211; 9c \u2265 -28<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n8 &#8211; 9c \u2265 -28<br \/>\n-9c \u2265 -28 &#8211; 8<br \/>\n-9c \u2265 -36<br \/>\n9c \u2265 36<br \/>\nc \u2265 36 \/ 9<br \/>\nc \u2265 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is c \u2265 4<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-77.jpg\" alt=\"\" width=\"682\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-77.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-77-300x46.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{n}{-2}\\) + 11 &gt; 12<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{n}{-2}\\) + 11 &gt; 12<br \/>\n\\(\\frac{n}{-2}\\) &gt; 12 &#8211; 11<br \/>\n\\(\\frac{n}{-2}\\) &gt; 1<br \/>\nn &gt; 1 (-2)<br \/>\nn &gt; -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is n &gt; -2<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-78.jpg\" alt=\"\" width=\"682\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-78.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-78-300x49.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 4.<br \/>\n6 \u2265 5 &#8211; \\(\\frac{v}{3}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n6 \u2265 5 &#8211; \\(\\frac{v}{3}\\)<br \/>\n6 &#8211; 5 \u2265 &#8211; \\(\\frac{v}{3}\\)<br \/>\n-1 \u2265 \\(\\frac{v}{3}\\)<br \/>\n-3 \u2265 v<br \/>\nv \u2264 -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is v \u2264 -3<br \/>\nThe representation of the inequality in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-79.jpg\" alt=\"\" width=\"682\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-79.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-79-300x46.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p><strong>Solve the inequality.<\/strong><\/p>\n<p>Question 5.<br \/>\n5x &#8211; 12 \u2264 3x &#8211; 4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n5x &#8211; 12 \u2264 3x &#8211; 4<br \/>\n5x &#8211; 3x \u2264 12 &#8211; 4<br \/>\n2x \u2264 8<br \/>\nx \u2264 8 \/ 2<br \/>\nx \u2264 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2264 4<\/p>\n<p>Question 6.<br \/>\n2(k &#8211; 5) &lt; 2k + 5<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2 ( k &#8211; 5 ) &lt; 2k + 5<br \/>\nSo,<br \/>\n2 ( k ) &#8211; 2 ( 5 ) &lt; 2k + 5<br \/>\n2k &#8211; 10 &lt; 2k + 5<br \/>\n2k &#8211; 2k &lt; 5 + 10<br \/>\n-10 &lt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 7.<br \/>\n-4(3n &#8211; 1) &gt; -12n + 5.2<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-4 ( 3n &#8211; 1 ) &gt; -12n + 5.2<br \/>\nSo,<br \/>\n-4 ( 3n ) &#8211; 4 ( -1 ) &gt; -12n + 5.2<br \/>\n-12n + 4 &gt; -12n + 5.2<br \/>\n-12n + 12n + 4 &gt; 5.2<br \/>\n4 &gt; 5.2<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 8.<br \/>\n3(2a &#8211; 1) \u2265 10a &#8211; 11<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3 ( 2a &#8211; 1 ) \u2265 10a &#8211; 11<br \/>\nSo,<br \/>\n3 ( 2a ) &#8211; 3 ( 1 ) \u2265 10a &#8211; 11<br \/>\n6a &#8211; 3 \u2265 10a &#8211; 11<br \/>\n6a &#8211; 10a \u2265 -11 + 3<br \/>\n-4a \u2265 -8<br \/>\n4a \u2265 8<br \/>\na \u2265 8 \/ 4<br \/>\na \u2265 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is a \u2265 2<\/p>\n<p>Question 9.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou need a mean score of at least 85 points to advance to the next round. What scores in the fifth game will allow you to advance?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Multi-step_Inequalities_2.4_Exercises\"><\/a>Solving Multi-step Inequalities 2.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare solving multi-step inequalities and solving multi-step equations.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 1\" width=\"579\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-1-300x104.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nWithout solving, how can you tell that the inequality 4x + 8 \u2264 4x &#8211; 3 has no solution?<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4x + 8\u00a0 \u2264 4x &#8211; 3<br \/>\nRearrange the variables ad constant terms<br \/>\nSo,<br \/>\n4x &#8211; 4x \u2264 -3 &#8211; 8<br \/>\n0 + 8 \u2264 -3<br \/>\n8 \u2264 -3<br \/>\nHence, from the above,<br \/>\nWe can observe that there is no variable x<br \/>\nHence,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p><strong>In Exercises 3\u20136, match the inequality with its graph.<\/strong><\/p>\n<p>Question 3.<br \/>\n7b &#8211; 4 \u2264 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 3\" width=\"505\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-3.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-3-300x133.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 4.<br \/>\n4p + 4 \u2265 12<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4p + 4 \u2265 12<br \/>\nSo,<br \/>\n4p\u00a0\u2265 12 &#8211; 4<br \/>\n4p \u2265 8<br \/>\np \u2265 8 \/ 4<br \/>\np \u2265 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is p \u2265 2<br \/>\nThe graph represented for the solution is A) [ Se the graphs from Exercise 6 ]<\/p>\n<p>Question 5.<br \/>\n-6g + 2 \u2265 20<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 5\" width=\"522\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-5.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-5-300x129.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 6.<br \/>\n3(2 &#8211; f) \u2264 15<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 53\" width=\"341\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-53.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-53-300x209.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3 (2 &#8211; f) \u2264\u00a0 15<br \/>\nSo,<br \/>\n3 (2) &#8211; 3 (f) \u2264\u00a0 15<br \/>\n6 &#8211; 3f \u2264\u00a0 15<br \/>\n-3f \u2264\u00a0 15 &#8211; 6<br \/>\n-3f \u2264\u00a0 9<br \/>\nf \u2264\u00a0 -9 \/ 3<br \/>\nf \u2264\u00a0 -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is f \u2264\u00a0 -3<br \/>\nThe graph C) represents the solution of the given inequality<\/p>\n<p><strong>In Exercises 7\u201316, solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 7.<br \/>\n2x &#8211; 3 &gt; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 7\" width=\"235\" height=\"290\" \/><\/p>\n<p>Question 8.<br \/>\n5y + 9 \u2264 4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n5y + 9 \u2264 4<br \/>\nSo,<br \/>\n5y \u2264\u00a0 4\u00a0 -9<br \/>\n5y \u2264\u00a0 -5<br \/>\ny \u2264\u00a0 -5 \/ 5<br \/>\ny \u2264\u00a0 -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y \u2264\u00a0 -1<br \/>\nThe representation of the solution in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-80.jpg\" alt=\"\" width=\"682\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-80.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-80-300x47.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p>Question 9.<br \/>\n-9 \u2264 7 &#8211; 8v<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 9\" width=\"235\" height=\"271\" \/><\/p>\n<p>Question 10.<br \/>\n2 &gt; -3t &#8211; 10<br \/>\n<span style=\"font-size: 16px;\">Answer:<br \/>\nThe given inequality is:<br \/>\n2 &gt; -3t &#8211; 10<br \/>\nSo,<br \/>\n2 + 10 &gt; -3t<br \/>\n12 &gt; -3t<br \/>\n-12 \/ 3 &gt; t<br \/>\n-4 &gt; t<br \/>\nt &lt; -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is t &lt; -4<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-81.jpg\" alt=\"\" width=\"682\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-81.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-81-300x49.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><br \/>\n<\/span><\/p>\n<p>Question 11.<br \/>\n\\(\\frac{w}{2}\\) + 4 &gt; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 11\" width=\"235\" height=\"301\" \/><\/p>\n<p>Question 12.<br \/>\n1 + \\(\\frac{m}{3}\\) \u2264 6<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n1 + \\(\\frac{m}{3}\\) \u2264 6<br \/>\nSo,<br \/>\n\\(\\frac{m}{3}\\) \u2264 6 &#8211; 1<br \/>\n\\(\\frac{m}{3}\\) \u2264 5<br \/>\nm \u2264 5 (3)<br \/>\nm \u2264 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is m \u2264 15<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-52997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-82.jpg\" alt=\"\" width=\"348\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-82.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-82-300x46.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 13.<br \/>\n\\(\\frac{p}{-8}\\) + 9 &gt; 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 13\" width=\"249\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-13.png 249w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-13-241x300.png 241w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><\/p>\n<p>Question 14.<br \/>\n3 + \\(\\frac{r}{-4}\\) \u2264 6<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3 + \\(\\frac{r}{-4}\\) \u2264 6<br \/>\n\\(\\frac{r}{-4}\\) \u2264 6 &#8211; 3<br \/>\n\\(\\frac{r}{-4}\\) \u2264 3<br \/>\nr \u2264 3 (-4)<br \/>\nr \u2264 -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is r \u2264 -12<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-83.jpg\" alt=\"\" width=\"348\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-83.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-83-300x44.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 15.<br \/>\n6 \u2265 -6(a + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 15\" width=\"238\" height=\"294\" \/><\/p>\n<p>Question 16.<br \/>\n18 \u2264 3(b &#8211; 4)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n18 \u2264 3 (b &#8211; 4)<br \/>\nSo,<br \/>\n18 \u2264 3 (b) &#8211; 3 (4)<br \/>\n18 \u2264 3b &#8211; 12<br \/>\n18 + 12 \u2264 3b<br \/>\n30 \u2264 3b<br \/>\n30 \/ 3 \u2264 b<br \/>\n10 \u2264 b<br \/>\nb \u2265 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is b \u2265 10<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-53167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-84.jpg\" alt=\"\" width=\"348\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-84.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-84-300x53.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p><strong>In Exercises 17\u201328, solve the inequality.<\/strong><\/p>\n<p>Question 17.<br \/>\n4 &#8211; 2m &gt; 7 &#8211; 3m<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 17\" width=\"217\" height=\"201\" \/><\/p>\n<p>Question 18.<br \/>\n8n+ 2 \u2264 8n &#8211; 9<br \/>\nAnswer:<br \/>\nThe given nequality is:<br \/>\n8n + 2 \u2264 8n &#8211; 9<br \/>\nSo,<br \/>\n8n &#8211; 8n + 2 \u2264 -9<br \/>\n2 \u2264 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 19.<br \/>\n-2d &#8211; 2 &lt; 3d + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 19\" width=\"233\" height=\"298\" \/><\/p>\n<p>Question 20.<br \/>\n8 + 10f &gt; 14 &#8211; 2f<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n8 + 10f &gt; 14 &#8211; 2f<br \/>\n10f + 2f &gt; 14 &#8211; 8<br \/>\n12f &gt; 6<br \/>\nf &gt; 6 \/ 12<br \/>\nf &gt; \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is f &gt; \\(\\frac{1}{2}\\)<\/p>\n<p>Question 21.<br \/>\n8g &#8211; 5g &#8211; 4 \u2264 -3 + 3g<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 21\" width=\"519\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-21.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-21-300x113.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 22.<br \/>\n3w &#8211; 5 &gt; 2w + w &#8211; 7<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3w &#8211; 5 &gt; 2w + w &#8211; 7<br \/>\nSo,<br \/>\n3w &#8211; 5 &gt; 3w &#8211; 7<br \/>\n3w &#8211; 5 &#8211; 3w &gt; -7<br \/>\n-5 &gt; -7<br \/>\n5 &gt; 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 23.<br \/>\n6(\u2113 + 3) &lt; 3(2\u2113 + 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 23\" width=\"505\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-23.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-23-300x127.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 24.<br \/>\n2(5c &#8211; 7) \u2265 10(c &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2 (5c &#8211; 7) \u2265 10 (c &#8211; 3)<br \/>\nSo,<br \/>\n2 (5c) &#8211; 2 (7) \u2265 10 (c) &#8211; 10 (3)<br \/>\n10c &#8211; 14 \u2265 10c &#8211; 30<br \/>\n10c &#8211; 10c &#8211; 14 \u2265 -30<br \/>\n-14 \u2265 -30<br \/>\n14 \u2265 30<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 25.<br \/>\n4 (\\(\\frac{1}{2}\\)t &#8211; 2 )&gt; 2(t &#8211; 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 25\" width=\"527\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-25.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-25-300x132.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Question 26.<br \/>\n15 (\\(\\frac{1}{3}\\)b + 3 ) \u2264 6(b + 9)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n15 ( (\\(\\frac{1}{3}\\)b + 3 ) ) \u2264 6 (b + 9)<br \/>\nSo,<br \/>\n15 ( (\\(\\frac{1}{3}\\)b ) ) + 15 (3) \u2264 6 (b) + 6 (9)<br \/>\n5b + 45 \u2264 6b + 54<br \/>\n5b &#8211; 6b \u2264 54 &#8211; 45<br \/>\n-b \u2264 9<br \/>\nb \u2264 -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is b \u2264 -9<\/p>\n<p>Question 27.<br \/>\n9j &#8211; 6 + 6j \u2265 3(5j &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 27\" width=\"516\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-27.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-27-300x134.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 28.<br \/>\n6h &#8211; 6 + 2h &lt; 2(4h &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n6h &#8211; 6 + 2h &lt; 2 (4h &#8211; 3)<br \/>\nSo,<br \/>\n8h &#8211; 6 &lt; 2 (4h) &#8211; 2 (3)<br \/>\n8h &#8211; 6 &lt; 8h &#8211; 6<br \/>\n8h &#8211; 8h &lt; -6 + 6<br \/>\n0 &lt; 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p><strong>ERROR ANALYSIS<\/strong><br \/>\n<strong>In Exercises 29 and 30, describe and correct the error in solving the inequality.<\/strong><\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-54.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 54\" width=\"209\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 29\" width=\"565\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-29.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-29-300x188.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 55\" width=\"281\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-2 (1 &#8211; x) \u2264 2x &#8211; 7<br \/>\n-2 (1) + 2 (x) \u2264 2x &#8211; 7<br \/>\n-2 + 2x \u2264 2x &#8211; 7<br \/>\n-2 + 2x &#8211; 2x \u2264 -7<br \/>\n-2 \u2264 -7<br \/>\n2 \u2264\u00a0 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given inequality has no solution<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nWrite and solve an inequality that represents how many $20 bills you can withdraw from the account without going below the minimum balance.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-56.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 56\" width=\"243\" height=\"175\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 31\" width=\"549\" height=\"372\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-31.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-31-300x203.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA woodworker wants to earn at least $25 an hour making and selling cabinets. He pays $125 for materials. Write and solve an inequality that represents how many hours the woodworker can spend building the cabinet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 57\" width=\"131\" height=\"242\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the number of hours the woodworker can spend build the cabinet is:<br \/>\nx \u2265 5<\/p>\n<p>Explanation:<br \/>\nIt is given that a woodworker wants to earn at least $25 an hour making and selling cabinets. He pays $125 for materials.<br \/>\nLet x be the number of hours taken by the woodworker to build the cabinet<br \/>\nSo,<br \/>\nThe inequality that represents the number of hours the woodworker can spend build the cabinet is:<br \/>\n25 (x) \u2265 125<br \/>\nx \u2265 125 \/ 25<br \/>\nx \u2265 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents the number of hours the woodworker can spnd build the cabinet is x \u2265 5<\/p>\n<p>Question 33.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe area of the rectangle is greater than 60 square feet. Write and solve an inequality to find the possible values of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-58.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 58\" width=\"263\" height=\"113\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 33\" width=\"381\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-33.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-33-300x286.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nForest Park Campgrounds charges a $100 membership fee plus $35 per night. Woodland Campgrounds charges a $20 membership fee plus $55 per night. Your friend says that if you plan to camp for four or more nights, then you should choose Woodland Campgrounds. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that the Forest Park Campgrounds charges a $100 membership fee plus $35 per night and the Woodland Campgrounds charges a $20 membership fee plus $55 per night.<br \/>\nIt is also given that your friend says that if you plan to camp for four or more nights, then you should choose Woodland Campgrounds.<br \/>\nSo,<br \/>\nLet x be the number of nights you spend<br \/>\nNow,<br \/>\nThe charge of the Forest Park Campgrounds for x nights = 100 + 35x<br \/>\nThe charge of the Woodland Campgrounds = 20 + 55x<br \/>\nNow,<br \/>\nIt is given that for four or more nights i.e., x \u2265 4, you will choose Woodland Campgrounds<br \/>\nSo,<br \/>\nWe have to verify the above statement<br \/>\nSo,<br \/>\n20 + 55x \u2265 100 + 35x<br \/>\n55x &#8211; 35x \u2265 100 &#8211; 20<br \/>\n20x \u2265 80<br \/>\nx \u2265 80 \/ 20<br \/>\nx \u2265 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct.<\/p>\n<p>Question 35.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe height of one story of a building is about 10 feet. The bottom of the ladder on the truck must be at least 24 feet away from the building. How many stories can the ladder reach? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 59\" width=\"237\" height=\"213\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 35.1\" width=\"581\" height=\"443\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-35.1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-35.1-300x229.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 35.2\" width=\"565\" height=\"392\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-35.2.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-35.2-300x208.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows your budget and the total cost of x gallons of gasoline and a car wash. You want to determine the possible amounts (in gallons) of gasoline you can buy within your budget.<br \/>\na. What is your budget?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-60.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 60\" width=\"246\" height=\"177\" \/><br \/>\nAnswer:<br \/>\nYour budget is: $40<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-60.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 60\" width=\"246\" height=\"177\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that x-axis represents the amount of gasoline ( gallons ) and the y-axis represents the budget<br \/>\nFrom the graph,<br \/>\nThe line is represented parallel to the x-axis i.e., Budget<br \/>\nSo,<br \/>\nFrom the graph,<br \/>\nThe given equation is:<br \/>\ny = 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that the budget is: $40<\/p>\n<p>b. How much does a gallon of gasoline cost? How much does a car wash cost?<br \/>\nAnswer:<br \/>\nThe cost of a gallon of gasoline is: $3.55<br \/>\nThe cost of a car wash is: $8<\/p>\n<p>Explanation:<br \/>\nIt is given that the graph shows your budget and the total cost of x gallons of gasoline and a car wash.<br \/>\nFrom the graph,<br \/>\nWe know that,<br \/>\nThe x-axis represents the amount of gasoline ( gallons )<br \/>\nSo,<br \/>\nThe equation represented by the x-axis is:<br \/>\ny = 3.55x + 8<br \/>\nSo,<br \/>\nFrom the equation,<br \/>\nWe know that,<br \/>\nThe coefficient of x represents the cost of x gallons of gasoline and the constant term represents the cost of a car wash<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe cost of a gallon of gasoline is: $3.55<br \/>\nThe cost of a car wash is: $8<\/p>\n<p>c. Write an inequality that represents the possible amounts of gasoline you can buy.<br \/>\nAnswer:<br \/>\nThe inequality that represents the possible amounts of gasoline you can buy is:<br \/>\nx \u2264 9 gallons<\/p>\n<p>Explanation:<br \/>\nFrom the graph,<br \/>\nWe know that,<br \/>\nThe x-axis represents the amounts of gasoline you can buy<br \/>\nWe know that,<br \/>\ny = 3.55x + 8<br \/>\nWe know that,<br \/>\nThe budget will be less than or equal to $40<br \/>\nSo,<br \/>\n3.55x + 8 \u2264 40<br \/>\n3.55x \u2264 40 &#8211; 8<br \/>\n3.55x \u2264 32<br \/>\nx \u2264 32 \/ 3.55<br \/>\nx \u2264 9 [ Approx. ]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents the possible amounts of gasoline you can buy is:<br \/>\nx \u2264 9<\/p>\n<p>d. Use the graph to estimate the solution of your inequality in part (c).<br \/>\nAnswer:<br \/>\nFrom part (c),<br \/>\nThe required inequality is:<br \/>\n3.55x + 8 \u2264 40<br \/>\nFrom the graph,<br \/>\nWe can observe the x-axis and y-axis intersected at one particular point.<br \/>\nThe particular point is the estimated solution of the inequality<br \/>\nSo,<br \/>\nThe particular point = (x , y ) = ( 9 , 40 )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the estimated solution of your inequality in part (c) is ( 9, 40 )<\/p>\n<p>Question 37.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nFor what r values of r will the area of the shaded region be greater than or equal to 9(\u03c0 &#8211; 2)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 37\" width=\"524\" height=\"372\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-37.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-37-300x213.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nA runner\u2019s times (in minutes) in the four races he has completed are 25.5, 24.3, 24.8, and 23.5. The runner plans to run at least one more race and wants to have an average time of less than 24 minutes. Write and solve an inequality to show how the runner can achieve his goal.<br \/>\nAnswer:<br \/>\nThe inequality that shows the runner can achieve his goal is:<br \/>\nx &lt; 21.9 minutes<\/p>\n<p>Explanation:<br \/>\nIt is given that a runner\u2019s times (in minutes) in the four races he has completed are 25.5, 24.3, 24.8, and 23.5.<br \/>\nIt is also given that the runner plans to run at least one more race and wants to have an average time of less than 24 minutes.<br \/>\nNow,<br \/>\nLet x be the time in the fifth race [ Since it is given that the runner plans to run at least one more race ]<br \/>\nWe know that,<br \/>\nAverage = \\(\\frac{The sum of all the items}{The number of items}\\)<br \/>\nNow,<br \/>\nAverage = \\(\\frac{25.5 + 24.3 + 24.8 + 23.5 + x}{5}\\)<br \/>\nAverage = \\(\\frac{98.1 + x}{5}\\)<br \/>\nIt is given that the average time will be less than 24 minutes<br \/>\nSo,<br \/>\n\\(\\frac{98.1 + x}{5}\\) &lt; 24<br \/>\n98.1 + x &lt; 24 (5)<br \/>\n98.1 + x &lt; 120<br \/>\nx &lt; 120 &#8211; 98.1<br \/>\nx &lt; 21.9 minutes<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that shows the runner can achieve his goal is x &lt; 21.9 minutes<\/p>\n<p><strong>REASONING<\/strong><br \/>\n<strong>In Exercises 39 and 40, find the value of a for which the solution of the inequality is all real numbers.<\/strong><\/p>\n<p>Question 39.<br \/>\na(x + 3) &lt; 5x + 15 &#8211; x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 39\" width=\"572\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-39.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-39-300x114.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 40.<br \/>\n3x + 8 + 2ax \u2265 3ax &#8211; 4a<br \/>\nAnswer:<br \/>\nThe value of a is: 3<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n3x + 8 + 2ax \u2265 3ax &#8211; 4a<br \/>\nSo,<br \/>\n3x + 2ax &#8211; 3ax \u2265 -4a &#8211; 8<br \/>\n3x &#8211; ax \u2265 -4a &#8211; 8<br \/>\nIt is given that the solution of the given inequality is all real numbers<br \/>\nSo,<br \/>\nx = 0<br \/>\nSo,<br \/>\nTo make x = 0,<br \/>\nWe can observe from the inequality that &#8216;a&#8217; must be equal to 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: 3<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><br \/>\n<strong>Write the sentence as an inequality.<\/strong> (Section 2.1)<\/p>\n<p>Question 41.<br \/>\nSix times a number y is less than or equal to 10.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 41\" width=\"453\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-41.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-41-300x81.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 42.<br \/>\nA number p plus 7 is greater than 24.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number p plus 7 is greater than 24<br \/>\nHence,<br \/>\nThe representation of the worded form in the form of inequality is:<br \/>\np + 7 &gt; 24<\/p>\n<p>Question 43.<br \/>\nThe quotient of a number r and 7 is no more than 18.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.4 Question 43\" width=\"500\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-43.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.4-Question-43-300x91.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Study_Skills:_Analyzing_Your_Errors\"><\/a>Solving Linear Inequalities Study Skills: Analyzing Your Errors<\/h3>\n<p><strong>2.1\u20132.4 What Did You Learn? <\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 61\" width=\"520\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-61.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-61-300x40.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<strong>Section 2.1<\/strong><br \/>\nRepresenting Linear Inequalities, p. 57<\/p>\n<p><strong>Section 2.2<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-62.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 62\" width=\"582\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-62.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-62-300x16.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p><strong>Section 2.3<\/strong><br \/>\nMultiplication and Division Properties of Inequality (c &gt; 0), p. 68<br \/>\nMultiplication and Division Properties of Inequality (c &lt; 0), p. 69<\/p>\n<p><strong>Section 2.4<\/strong><br \/>\nSolving Multi-Step Inequalities, p. 74<br \/>\nSpecial Solutions of Linear Inequalities, p. 75<\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nExplain the meaning of the inequality symbol in your answer to Exercise 47 on page 59. How did you know which symbol to use?<br \/>\nAnswer:<br \/>\nIn Exercise 47 on page 59,<br \/>\nThe inequality symbol we used is: \u2264<br \/>\nThe meaning of \u2264 is &#8221; Less than or equal to &#8221;<br \/>\nIn Exercise 47,<br \/>\nIt is given that the Xianren bridge arch is the longest natural arch with a length of 400 feet i.e., there is no arch longer than the Xianren bridge arch and the remaining natural arches are shorter than the Xianren arch<br \/>\nHence,<br \/>\nThe lengths of all the arches including the Xianren arch will be represented by the inequality symbol &#8220;\u2264&#8221;<\/p>\n<p>Question 2.<br \/>\nIn Exercise 30 on page 66, why is it important to check the reasonableness of your answer in part (a) before answering part (b)?<br \/>\nAnswer:<br \/>\nIn part (a), it is given that you have to beat your competitor with your score.<br \/>\nSo,<br \/>\nYour score must be greater than your competitor<br \/>\nThen only you can solve part (b).<\/p>\n<p>Question 3.<br \/>\nExplain how considering the units involved in Exercise 29 on page 71 helped you answer the question.<br \/>\nAnswer:<br \/>\nIn Exercise 29 on page 71,<br \/>\nThe mat that is given is in the form of the square since its length and width both are the same<br \/>\nSo,<br \/>\nWe know that,<br \/>\nArea of the square = Side\u00b2<br \/>\nLet the cost per square foot be x<br \/>\nSo,<br \/>\nThe inequality formed will be like:<br \/>\n( Area of the square ) \u22c5 x \u2264 $700<\/p>\n<p><strong>Study Skills<\/strong><\/p>\n<p><strong>Analyzing Your Errors<\/strong><\/p>\n<p><strong>Application Errors<\/strong><br \/>\n<strong>What Happens:<\/strong> You can do numerical problems, but you struggle with problems that have context.<br \/>\n<strong>How to Avoid This Error:<\/strong> Do not just mimic the steps of solving an application problem. Explain out loud what the question is asking and why you are doing each step. After solving the problem, ask yourself, \u201cDoes my solution make sense?\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 63\" width=\"375\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-63.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-63-300x226.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Maintaining_2.1_\u2013_2.4_Quiz\"><\/a>Solving Linear Inequalities Maintaining 2.1 &#8211; 2.4 Quiz<\/h3>\n<p><strong>Write the sentence as an inequality<\/strong>. (Section 2.1)<\/p>\n<p>Question 1.<br \/>\nA number z minus 6 is greater than or equal to 11.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number z minus 6 is greater than or equal to 11<br \/>\nHence,<br \/>\nThe representation of the worded form in the form of inequality is:<br \/>\nz &#8211; 6 \u2265 11<\/p>\n<p>Question 2.<br \/>\nTwelve is no more than the sum of -1.5 times a number w and 4.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nTwelve is no more than the sum of -1.5 times a number w and 4<br \/>\nHence,<br \/>\nThe representation of the worded form in the form of inequality is:<br \/>\n12 \u2264 -1.5w + 4<\/p>\n<p><strong>Write an inequality that represents the graph.<\/strong>(Section 2.1)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-64.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 64\" width=\"374\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-64.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-64-300x41.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the given graph is:<br \/>\nx &lt; 0<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-64.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 64\" width=\"374\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-64.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-64-300x41.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nFrom the above number line,<br \/>\nWe can observe that the marked line started from 0 that excludes 0 and continued till the left end of the number line<br \/>\nHence,<br \/>\nThe inequality that represents the given graph is:<br \/>\nx &lt; 0<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 65\" width=\"378\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-65.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-65-300x48.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nAnswer:<br \/>\nThe inequality that represents the given graph is:<br \/>\nx \u2265 8<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 65\" width=\"378\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-65.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-65-300x48.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nFrom the above graph,<br \/>\nThe marked line started from 8 that includes 8 and continued till the right end of the number line.<br \/>\nHence,<br \/>\nThe inequality that represents the given graph is:<br \/>\nx \u2265 8<\/p>\n<p><strong>Solve the inequality. Graph the solution. <\/strong>(Section 2.2 and Section 2.3)<\/p>\n<p>Question 5.<br \/>\n9 + q \u2264 15<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\nq \u2264 6<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n9 + q \u2264 15<br \/>\nSo,<br \/>\nq \u2264 15 &#8211; 9<br \/>\nq \u2264 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is q \u2264 6<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-85.jpg\" alt=\"\" width=\"680\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-85.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-85-300x44.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 6.<br \/>\nz &#8211; (-7) &lt; 5<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\nz &lt; -2<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\nz &#8211; (-7) &lt; 5<br \/>\nSo,<br \/>\nz + 7\u00a0 &lt; 5<br \/>\nz &lt; 5 &#8211; 7<br \/>\nz &lt; -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is z &lt; -2<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-86.jpg\" alt=\"\" width=\"680\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-86.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-86-300x41.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 7.<br \/>\n-3 &lt; y &#8211; 4<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\ny &gt; 1<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n-3 &lt; y &#8211; 4<br \/>\nSo,<br \/>\n-3 + 4 &lt; y<br \/>\n1 &lt; y<br \/>\ny &gt; 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y &gt; 1<br \/>\nThe representation of the solution of inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-87.jpg\" alt=\"\" width=\"680\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-87.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-87-300x44.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 8.<br \/>\n3p \u2265 18<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\np \u2265 6<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n3p \u2265 18<br \/>\np \u2265 18 \/ 3<br \/>\np \u2265 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is p \u2265 6<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-88.jpg\" alt=\"\" width=\"680\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-88.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-88-300x41.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 9.<br \/>\n6 &gt; \\(\\frac{w}{-2}\\)<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\nw &lt; -12<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n6 &gt; \\(\\frac{w}{-2}\\)<br \/>\nSo,<br \/>\n6 (-2) &gt; w<br \/>\n-12 &gt; w<br \/>\nw &lt; -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is w &lt; -12<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-89.jpg\" alt=\"\" width=\"348\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-89.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-89-300x47.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 10.<br \/>\n-20x &gt; 5<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\nx &gt; &#8211; \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nx &gt; -0.25<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n-20x &gt; 5<br \/>\nSo,<br \/>\nx &gt; -5 \/ 20<br \/>\nx &gt; &#8211; \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &gt; &#8211;\\(\\frac{1}{4}\\)<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-90.jpg\" alt=\"\" width=\"348\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-90.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-90-300x38.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p><strong>Solve the inequality. <\/strong>(Section 2.4)<\/p>\n<p>Question 11.<br \/>\n3y &#8211; 7 \u2265 17<br \/>\nAnswer:<br \/>\nThe solution to the given inequality is:<br \/>\ny \u2265 8<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n3y &#8211; 7 \u2265 17<br \/>\nSo,<br \/>\n3y \u2265 17 + 7<br \/>\n3y \u2265 24<br \/>\ny \u2265 24 \/ 3<br \/>\ny \u2265 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is y \u2265 8<\/p>\n<p>Question 12.<br \/>\n8(3g &#8211; 2) \u2264 12(2g + 1)<br \/>\nAnswer:<br \/>\nThere is no soution for the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n8 (3g &#8211; 2) \u2264 12 (2g + 1)<br \/>\nSo,<br \/>\n8 (3g) &#8211; 8 (2) \u2264 12 (2g) + 12 (1)<br \/>\n24g &#8211; 16 \u2264 24g + 12<br \/>\n24g &#8211; 24g &#8211; 16 \u2264 12<br \/>\n-16 \u2264 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 13.<br \/>\n6(2x &#8211; 1) \u2265 3(4x + 1)<br \/>\nAnswer:<br \/>\nThere is no solution for the given inequality<\/p>\n<p>Explanation:<br \/>\nThe given inequality is:<br \/>\n6 (2x &#8211; 1)\u2265 3 (4x + 1)<br \/>\nSo,<br \/>\n6 (2x) &#8211; 6 (1) \u2265 3 (4x) + 3 (1)<br \/>\n12x &#8211; 6 \u2264 12x + 3<br \/>\n12x &#8211; 6 &#8211; 12x \u2264 3<br \/>\n-6 \u2264 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 14.<br \/>\n<strong>Three requirements for a lifeguard training course are shown.<\/strong> (Section 2.1)<br \/>\na. Write and graph three inequalities that represent the requirements.<br \/>\nb. You can swim 250 feet, tread water for 6 minutes, and swim 35 feet underwater without taking a breath. Do you satisfy the requirements of the course? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-66.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 66\" width=\"221\" height=\"208\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\nThe given requirements are:<br \/>\n1. Swim at least 100 yards<br \/>\n2. Tread water for at least 5 minutes<br \/>\n3. Swim 10 yards or more underwater without taking a breath<br \/>\nNow,<br \/>\n1.<br \/>\nThe inequality that represents the first requirement is:<br \/>\nx \u2265 100 yards<br \/>\n2.<br \/>\nThe inequality that represents the second requirement is:<br \/>\nx \u2265 5 minutes<br \/>\n3.<br \/>\nThe inequality that represents the third requirement is:<br \/>\nx \u2265 10 yards<\/p>\n<p>b.<br \/>\nIt is given that you can swim 250 feet, tread water for 6 minutes, and swim 35 feet underwater without taking a breath.<br \/>\nFrom part (a),<br \/>\nThe inequalities for the three requirements are:<br \/>\nx \u2265 100 yards<br \/>\nx \u2265 5 minutes<br \/>\nx \u2265 10 yards<br \/>\nHence, from the above,<br \/>\nWe can conclude that you satisfied the requirements of the course<\/p>\n<p>Question 15.<br \/>\nThe maximum volume of an American white pelican\u2019s bill is about 700 cubic inches. A pelican scoops up 100 cubic inches of water. Write and solve an inequality that represents the additional volumes the pelican\u2019s bill can contain. (Section 2.2)<br \/>\nAnswer:<br \/>\nThe inequality that represents the additional volumes of the pelican&#8217;s bill can contain is:<br \/>\nx\u00a0 \u2264 600<\/p>\n<p>Explanation:<br \/>\nIt is given that the maximum volume of an American white pelican\u2019s bill is about700 cubic inches. A pelican scoops up 100 cubic inches of water.<br \/>\nLet x be the additional volumes the pelican&#8217;s bill can contain<br \/>\nIt is also given that the maximum volume is 700 cubic inches and a pelican&#8217;s bill scoops up 100 cubic inches of water<br \/>\nHence,<br \/>\nThe inequality that represents the additional volumes of the pelican&#8217;s bill can contain is:<br \/>\nx + 100 \u2264 700<br \/>\nx \u2264 700 &#8211; 100<br \/>\nx \u2264 600<\/p>\n<p>Question 16.<br \/>\nYou save $15 per week to purchase one of the bikes shown. (Section 2.3and Section 2.4)<br \/>\na. Write and solve an inequality to find the numbers of weeks you need to save to purchase a bike.<br \/>\nb. Your parents give you $65 to help you buy the new bike. How does this affect your answer in part (a)? Use an inequality to justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 67\" width=\"257\" height=\"234\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that you save $15 per week to purchase one of the bikes<br \/>\nFrom the fig,<br \/>\nIt is given that the starting price of the bike is $120<br \/>\nNow,<br \/>\nLet x be the number of weeks<br \/>\nHence,<br \/>\nThe inequality that representing the number of weeks you need to save to purchase a bike is:<br \/>\n15 \u22c5 x \u2265 120<br \/>\n15x \u2265 120<br \/>\nx \u2265 120 \/ 15<br \/>\nx \u2265 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of weeks you need to save to purchase a bike is 8 weeks<\/p>\n<p>b.<br \/>\nIt is given that your parents give you $65 to help you buy the new bike.<br \/>\nWe know that,<br \/>\nThe starting price of the bike is: $120<br \/>\nSo,<br \/>\nThe remaining amount that needs to purchase a bike = 120 &#8211; 65<br \/>\n= $55<\/p>\n<h3><a id=\"Lesson_2.5_Solving_Compound_Inequalities\"><\/a>Lesson 2.5 Solving Compound Inequalities<\/h3>\n<p><strong>Essential Question<\/strong><br \/>\nHow can you use inequalities to describe intervals on the real number line?<br \/>\n<strong>EXPLORATION 1<\/strong><br \/>\n<strong>Describing Intervals on the Real Number<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\nIn parts (a)\u2013(d), use two inequalities to describe the interval.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-68.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 68\" width=\"716\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-68.png 716w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-68-300x116.png 300w\" sizes=\"(max-width: 716px) 100vw, 716px\" \/><br \/>\ne. Do you use \u201cand\u201d or \u201cor\u201d to connect the two inequalities in parts (a)\u2013(d)? Explain.<br \/>\nAnswer:<br \/>\n(a) &#8211; (d):<br \/>\nThe given graphs are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-68.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 68\" width=\"716\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-68.png 716w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-68-300x116.png 300w\" sizes=\"(max-width: 716px) 100vw, 716px\" \/><br \/>\nFrom the given graphs,<br \/>\nWe can observe that the marked lines are from a certain number to a certain number<br \/>\nNow,<br \/>\na.<br \/>\nIn the given graph,<br \/>\nThe marked line starting from -3 excluding -3 and continued till -6 including -6<br \/>\nSo,<br \/>\nThe inequality that represents the given interval is:<br \/>\nx \u2265 -6 and x &lt; -3<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-6 \u2264 x &lt; -3<\/p>\n<p>b.<br \/>\nIn the given graph,<br \/>\nThe marked line starting from -5 excluding -5 and continued till 4 including 4<br \/>\nSo,<br \/>\nThe inequality that represents the given interval is:<br \/>\nx &gt; -5 and x &lt; 4<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-5 &lt; x &lt; 4<\/p>\n<p>c.<br \/>\nIn the given graph,<br \/>\nThe marked line starting from -4 including -4 and continued till 5 including 5<br \/>\nSo,<br \/>\nThe inequality that represents the given interval is:<br \/>\nx \u2265 -4 and x \u2264 5<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-4 \u2264 x \u2264 5<\/p>\n<p>d.<br \/>\nIn the given graph,<br \/>\nThe marked line starting from -3 excluding -3 and continued till 6 including 6<br \/>\nSo,<br \/>\nThe inequality that represents the given interval is:<br \/>\nx &gt; -3 and x &lt; 6<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-3 &lt; x &lt; 6<\/p>\n<p>e.<br \/>\nWe use &#8220;and&#8221; to connect the two inequalities in parts (a) &#8211; (d)<br \/>\nNow,<br \/>\nFrom (a) &#8211; (d),<br \/>\nWe can observe that,<br \/>\nFor Half-open interval,<br \/>\nWe use \u2265 and &lt;<br \/>\nFor closed interval,<br \/>\nWe use \u2265 and \u2264<br \/>\nFor open interval,<br \/>\nWe use &gt; and &lt;<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Describing Two Infinite Intervals<\/strong><br \/>\n<strong>Work with a partner.<\/strong> In parts (a)\u2013(d), use two inequalities to describe the interval.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-69.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 69\" width=\"503\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-69.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-69-300x141.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\ne. Do you use \u201cand\u201d or \u201cor\u201d to connect the two inequalities in parts (a)\u2013(d)? Explain.<br \/>\nAnswer:<br \/>\nThe given graphs are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-69.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 69\" width=\"503\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-69.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-69-300x141.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\n(a) &#8211; (d):<br \/>\na.<br \/>\nIn the given graph,<br \/>\nThe first marked line starting from -6 including -6 and continued till the end of the left side of the graph<br \/>\nThe second marked line starting from 3 excluding 3 and continued till the end of the right side of the graph<br \/>\nSo,<br \/>\nThe inequality that represents the given intervals are:<br \/>\nx \u2264 -6 and x &gt; 3<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-6 \u2264 x &gt; 3<\/p>\n<p>b.<br \/>\nIn the given graph,<br \/>\nThe first marked line starting from -5 excluding -5 and continued till the end of the left side of the graph<br \/>\nThe second marked line starting from 4 including 4 and continued till the end of the right side of the graph<br \/>\nSo,<br \/>\nThe inequality that represents the given intervals are:<br \/>\nx &lt; -5 and x \u2265 4<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-5 &lt; x \u2265 4<\/p>\n<p>c.<br \/>\nIn the given graph,<br \/>\nThe first marked line starting from -4 including -4 and continued till the end of the left side of the graph<br \/>\nThe second marked line starting from 5 including 5 and continued till the end of the right side of the graph<br \/>\nSo,<br \/>\nThe inequality that represents the given intervals are:<br \/>\nx \u2264 -4 and x \u2265 5<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-4 \u2264 x \u2265 5<\/p>\n<p>d.<br \/>\nIn the given graph,<br \/>\nThe first marked line starting from -3 excluding -3 and continued till the end of the left side of the graph<br \/>\nThe second marked line starting from 6 excluding 6 and continued till the end of the right side of the graph<br \/>\nSo,<br \/>\nThe inequality that represents the given intervals are:<br \/>\nx &lt; -3 and x &gt; 6<br \/>\nHence,<br \/>\nThe compound inequality that represents the given interval is:<br \/>\n-3 &lt; x &gt; 6<\/p>\n<p>e.<br \/>\nWe use &#8220;and&#8221; to connect the two inequalities in parts (a) &#8211; (d)<br \/>\nNow,<br \/>\nFrom (a) &#8211; (d),<br \/>\nWe can observe that,<br \/>\nFor Half-open interval,<br \/>\nWe use \u2265 and &lt;<br \/>\nFor closed interval,<br \/>\nWe use \u2265 and \u2264<br \/>\nFor open interval,<br \/>\nWe use &gt; and &lt;<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use inequalities to describe intervals on the real number line?<br \/>\nAnswer:<br \/>\nAn inequality that includes the boundary point indicated by the \u201cor equal\u201d part of the symbols \u2264 and \u2265 with a closed dot on the number line. The symbol (\u221e) indicates the\u00a0interval\u00a0is unbounded to the right. Express ordering relationships\u00a0using\u00a0the symbol &lt; for \u201cless than\u201d and &gt; for \u201cgreater than.\u201d<\/p>\n<p><strong>2.5 Lesson<\/strong><\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Write the sentence as an inequality. Graph the inequality.<\/strong><\/p>\n<p>Question 1.<br \/>\nA number d is more than 0 and less than 10.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number d is more than 0 and less than 10<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nd &gt; 0 and d &lt; 10<br \/>\nThe representation of the inequalities in the form of compound inequality is:<br \/>\n0 &lt; d &lt; 10<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-91.jpg\" alt=\"\" width=\"680\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-91.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-91-300x42.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 2.<br \/>\nA number a is fewer than -6 or no less than -3.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number a is fewer than -6 or no less than -3<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\na &lt; -6 or a &gt; -3<br \/>\nThe representation of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-92.jpg\" alt=\"\" width=\"680\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-92.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-92-300x43.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 3.<br \/>\n5 \u2264 m + 4 &lt; 10<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n5 \u2264 m + 4 &lt; 10<br \/>\nSubtract by 4 on both sides<br \/>\n5 &#8211; 4 \u2264 m + 4 &#8211; 4 &lt; 10 &#8211; 4<br \/>\n1 \u2264 m &lt; 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the compound inequality for the given inequality is: 1 \u2264 m &lt; 6<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-93.jpg\" alt=\"\" width=\"680\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-93.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-93-300x43.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 4.<br \/>\n-3 &lt; 2k &#8211; 5 &lt; 7<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-3 &lt; 2k &#8211; 5 &lt; 7<br \/>\nAdd 5 on both sides<br \/>\n-3 + 5 &lt; 2k &#8211; 5 + 5 &lt; 7 + 5<br \/>\n2 &lt; 2k &lt; 12<br \/>\nDivide by 2 on both sides<br \/>\n1 &lt; k &lt; 6<br \/>\nHence, from the avove,<br \/>\nWe can conclude that the compound inequality for the given inequality is: 1 &lt; k &lt; 6<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-94.jpg\" alt=\"\" width=\"680\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-94.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-94-300x40.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 5.<br \/>\n4c + 3 \u2264 -5 or c &#8211; 8 &gt; -1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4c + 3 \u2264 -5 or c &#8211; 8 &gt; -1<br \/>\nSo,<br \/>\n4c \u2264 -5 &#8211; 3 or c &gt; -1 + 8<br \/>\n4c \u2264 -8 or c &gt; 7<br \/>\nc \u2264 -8 \/ 4 or c &gt; 7<br \/>\nc \u2264 -2 or c &gt; 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given inequality are: c \u2264 -2 or c &gt; 7<br \/>\nThe representations of the solutions in the graph are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-95.jpg\" alt=\"\" width=\"680\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-95.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-95-300x40.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 6.<br \/>\n2p + 1 &lt; -7 or 3 &#8211; 2p \u2264 -1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2p + 1 &lt; -7 or 3 &#8211; 2p \u2264 -1<br \/>\nSo,<br \/>\n2p &lt; -7 &#8211; 1 or -2p \u2264 -1 &#8211; 3<br \/>\n2p &lt; -8 or -2p \u2264 -4<br \/>\np &lt; -8 \/ 2 or p \u2264 -4 \/ (-2)<br \/>\np &lt; -4 or p \u2264 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given inequality are: p &lt; -4 or p \u2264 2<br \/>\nThe representations of the solutions in the graph are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-96.jpg\" alt=\"\" width=\"680\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-96.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-96-300x44.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 7.<br \/>\nWrite and solve a compound inequality that represents the temperature rating (in degrees Fahrenheit) of the winter boots.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-70.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 70\" width=\"205\" height=\"208\" \/><br \/>\nAnswer:<br \/>\nThe range of the temperature rating ( In \u00b0C ) of the winter boots is: -40\u00b0C to 15\u00b0C<br \/>\nWe know that,<br \/>\n\u00b0F = ( \u00b0C \u00d7 \\(\\frac{9}{5}\\) ) + 32<br \/>\nNow,<br \/>\nTo convert -40\u00b0C into \u00b0F,<br \/>\n\u00b0F = ( -40\u00b0C \u00d7 \\(\\frac{9}{5}\\) ) + 32<br \/>\n\u00b0F = -72\u00a0+ 32<br \/>\n\u00b0F = &#8211; 40\u00b0F<br \/>\nNow,<br \/>\nTo convert 15\u00b0C into \u00b0F,<br \/>\n\u00b0F = ( 15 \u00d7 \\(\\frac{9}{5}\\) ) + 32<br \/>\n\u00b0F = 27 + 32<br \/>\n\u00b0F = 59\u00b0F<br \/>\nLet t be the temperature in \u00b0F<br \/>\nSo,<br \/>\nThe representation of the temperature ranges in the form of inequalities is:<br \/>\nt &gt; -40\u00b0F and t &lt; 59\u00b0F<br \/>\nHence,<br \/>\nThe representation of the temperature ranges in the form of compound inequality is:<br \/>\n-40\u00b0F &lt; t &lt; 59\u00b0F<\/p>\n<h3><a id=\"Solving_Compound_Inequalities_2.5_Exercises\"><\/a>Solving Compound Inequalities 2.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the graph of -6 \u2264 x \u2264 -4 with the graph of x \u2264 -6 or x \u2265 -4.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 1\" width=\"580\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-1.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-1-300x57.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE do DOESN&#8217;T BELONG?<\/strong><br \/>\nWhich compound inequality does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-70.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 70.1\" width=\"566\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-70.1.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-70.1-300x26.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><br \/>\nAnswer:<br \/>\nThe given inequalities are:<br \/>\na. a &gt; 4 or a &lt; -3<br \/>\nb. a&lt; -2 or a &gt; 8<br \/>\nc. a &gt; 7 or a &lt; -5<br \/>\nd. a &lt; 6 or a &gt; -9<br \/>\nNow,<br \/>\nRepresent all the inequalities in the graph<br \/>\nSo,<br \/>\na.<br \/>\nThe given inequality is:<br \/>\na &gt; 4 or a &lt; -3<br \/>\nThe representation of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-97.jpg\" alt=\"\" width=\"680\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-97.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-97-300x42.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><br \/>\nb.<br \/>\nThe given inequality is:<br \/>\na &lt; -2 or a &gt; 8<br \/>\nThe representation of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-98.jpg\" alt=\"\" width=\"680\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-98.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-98-300x43.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><br \/>\nc.<br \/>\nThe given inequality is:<br \/>\na &gt; 7 or a &lt; -5<br \/>\nThe representation of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-99.jpg\" alt=\"\" width=\"680\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-99.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-99-300x41.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><br \/>\nd.<br \/>\nThe given inequality is:<br \/>\na &lt; 6\u00a0 or a &gt; -9<br \/>\nThe representation of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-100.jpg\" alt=\"\" width=\"680\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-100.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-100-300x39.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><br \/>\nFrom the above,<br \/>\nWe can conclude that inequality c) does not belong with the other three inequalities<\/p>\n<p><strong>In Exercises 3\u20136, write a compound inequality that is represented by the graph.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-71.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 71\" width=\"314\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-71.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-71-300x49.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 3\" width=\"284\" height=\"34\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-72.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 72\" width=\"308\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-72.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-72-300x47.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-72.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 72\" width=\"308\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-72.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-72-300x47.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nFrom the above graph,<br \/>\nWe can observe that the marked line started from 7 excluding 7 and continued till 14 excluding 14<br \/>\nHence,<br \/>\nThe representation of the inequalities from the given graph is:<br \/>\nx &gt; 7 and x &lt; 14<br \/>\nThe representation of the inequalities in the form of compound inequality is:<br \/>\n7 &lt; x &lt; 14<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-73.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 73\" width=\"311\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-73.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-73-300x49.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 5\" width=\"172\" height=\"36\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-74.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 74\" width=\"319\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-74.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-74-300x56.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-74.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 74\" width=\"319\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-74.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-74-300x56.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nFrom the above graph,<br \/>\nWe can observe that<br \/>\nThe first marked line started from 4 including 4 and continued till the end of the left end of the graph<br \/>\nThe second marked line started from 6 excluding 6 and continued till the end of the right end of the graph<br \/>\nHence,<br \/>\nThe representation of the given graph in the form of inequality is:<br \/>\nx \u2264 4 or x &gt; 6<\/p>\n<p><b>In Exercises 7\u201310, write the sentence as an inequality. Graph the inequality.<\/b><\/p>\n<p>Question 7.<br \/>\nA number p is less than 6 and greater than 2.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 7\" width=\"423\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-7.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-7-300x120.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Question 8.<br \/>\nA number n is less than or equal to -7 or greater than 12.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number n is less than or equal to -7 or greater than 12<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nn \u2264 -7 or n &gt; 12<br \/>\nThe representation of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-101.jpg\" alt=\"\" width=\"680\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-101.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-101-300x34.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 9.<br \/>\nA number m is more than -7\\(\\frac{2}{3}\\) or at most -10.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 9\" width=\"445\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-9.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-9-300x146.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p>Question 10.<br \/>\nA number r is no less than -1.5 and fewer than 9.5.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number r is no less than -1.5 and fewer than 9.5<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nr &gt; -1.5 and r &lt; 9.5<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of compound inequality is:<br \/>\n-1.5 &lt; r &lt; 9.5<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-102.jpg\" alt=\"\" width=\"348\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-102.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-102-300x45.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 11.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nSlitsnails are large mollusks that live in deep waters. They have been found in the range of elevations shown. Write and graph a compound inequality that represents this range.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-75.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 75\" width=\"110\" height=\"177\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 11\" width=\"374\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-11.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-11-300x112.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/p>\n<p>Question 12.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe life zones on Mount Rainier, a mountain in Washington, can be approximately classified by elevation, as follows.<br \/>\nLow-elevation forest: above 1700 feet to 2500 feet mid-elevation forest: above 2500 feet to 4000 feet Subalpine: above 4000 feet to 6500 feet<br \/>\nAlpine: above 6500 feet to the summit<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-76.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 76\" width=\"230\" height=\"156\" \/><br \/>\nWrite a compound inequality that represents the elevation range for each type of plant life.<br \/>\na. trees in the low-elevation forest zone<br \/>\nb. flowers in the subalpine and alpine zones<br \/>\nAnswer:<br \/>\nIt is given that the elevations of the life zones on Mount Rainier are as follows:<br \/>\nLow-elevation forest: above 1700 feet to 2500 feet<br \/>\nMid-elevation forest: above 2500 feet to 4000 feet<br \/>\nSubalpine: above 4000 feet to 6500 feet<br \/>\nAlpine: above 6500 feet to the summit<br \/>\nLet the elevation range for each type of plant life be x<br \/>\nSo,<br \/>\na.<br \/>\nThe inequality that represents the elevation range of trees in the low-elevation forest zone is:<br \/>\nx &gt; 1700 feet and x &lt; 2500 feet<br \/>\nHence,<br \/>\nThe representation of the elevation range of trees in the low-elevation forest zone in the form of compound inequality is:<br \/>\n1700 feet &lt; x &lt; 2500 feet<br \/>\nb.<br \/>\nThe inequalities that represent the elevation range of trees in the subalpine and alpine zones is:<br \/>\nSubalpine zone: x &gt; 4000 feet and x &lt; 6500 feet<br \/>\nAlpine zone: x &gt; 6500 feet<br \/>\nHence,<br \/>\nThe representation of the elevation range of trees in the Subalpine zone and Alpine zone in the form of compound inequality is:<br \/>\nSubalpine zone: 4000 feet &lt; x &lt; 6500 feet<br \/>\nAlpine zone: x &gt; 6500 feet<\/p>\n<p><b>In Exercises 13\u201320, solve the inequality. Graph the solution.<\/b><\/p>\n<p>Question 13.<br \/>\n6 &lt; x + 5 \u2264 11<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 13\" width=\"242\" height=\"208\" \/><\/p>\n<p>Question 14.<br \/>\n24 &gt; -3r \u2265 -9<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n24 &gt; -3r \u2265 -9<br \/>\nDivide by 3 on both sides<br \/>\n( 24 \/ 3 ) &gt; ( -3r \/ 3 ) \u2265 ( -9 \/ 3 )<br \/>\n8 &gt; -r \u2265 -3<br \/>\nMultiply with &#8216;-&#8216; on both sides<br \/>\n-8 &lt; r \u2264 3 [ Because when we multiply with &#8216;-&#8216;, we have to change the inequality signs also ]<br \/>\nHence,<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-103.jpg\" alt=\"\" width=\"686\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-103.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-103-300x35.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 15.<br \/>\nv + 8 &lt; 3 or -8v &lt; -40<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 15\" width=\"337\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-15.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-15-300x199.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p>Question 16.<br \/>\n-14 &gt; w + 3 or 3w \u2265 -27<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-14 &gt; w + 3 or 3w \u2265 -27<br \/>\nSo,<br \/>\n-14 &#8211; 3 &gt; w or w \u2265 -27 \/ 3<br \/>\n-17 &gt; w or w \u2265 -9<br \/>\nw &lt; -17 or w \u2265 -9<br \/>\nHence,<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-104.jpg\" alt=\"\" width=\"348\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-104.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-104-300x39.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 17.<br \/>\n2r + 3 &lt; 7 or -r + 9 \u2264 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 17\" width=\"378\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-17.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-17-300x240.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 18.<br \/>\n-6 &lt; 3n + 9 &lt; 21<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-6 &lt; 3n + 9 &lt; 21<br \/>\nSubtract with 9 on both sides<br \/>\n-6 &#8211; 9 &lt; 3n + 9 &#8211; 9 &lt; 21 &#8211; 9<br \/>\n-15 &lt; 3n &lt; 12<br \/>\nDivide by 3 on both sides<br \/>\n( -15 \/ 3 ) &lt; ( 3n \/ 3 ) &lt; ( 12 \/ 3 )<br \/>\n-5 &lt; n &lt; 4<br \/>\nHence,<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-105.jpg\" alt=\"\" width=\"686\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-105.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-105-300x35.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 19.<br \/>\n-12 &lt; \\(\\frac{1}{2}\\)(4x + 16) &lt; 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 19\" width=\"342\" height=\"402\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-19.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-19-255x300.png 255w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 20.<br \/>\n35 &lt; 7(2 &#8211; b) or \\(\\frac{1}{3}\\)(15b &#8211; 12) \u2265 21<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n35 &lt; 7 (2 &#8211; b) or \\(\\frac{1}{3}\\) ( 15b &#8211; 12 ) \u2265 21<br \/>\nSo,<br \/>\n35 &lt; 7 (2) &#8211; 7 (b) or 15b &#8211; 12 \u2265 21 (3)<br \/>\n35 &lt; 14 &#8211; 7b or 15b &#8211; 12 \u2265 63<br \/>\n7b &lt; 14 &#8211; 35 or 15b \u2265 63 + 12<br \/>\n7b &lt; -21 or 15b \u2265 75<br \/>\nb &lt; -21 \/ 7 or b \u2265 75 \/ 15<br \/>\nb &lt; -3 or b \u2265 5<br \/>\nHence,<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-106.jpg\" alt=\"\" width=\"686\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-106.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-106-300x34.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 21 and 22, describe and correct the error in solving the inequality or graphing the solution.<\/b><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-77.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 77\" width=\"282\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 21\" width=\"579\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-21.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-21-300x209.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-78.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 78\" width=\"287\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nx &#8211; 2 &gt; 3 or x + 8 &lt; -2<br \/>\nSo,<br \/>\nx &gt; 3 + 2 or x &lt; -2 &#8211; 8<br \/>\nx &gt; 5 or x &lt; -10<br \/>\nHence,<br \/>\nThe representation of the solutions of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-107.jpg\" alt=\"\" width=\"348\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-107.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-107-300x42.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 23.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nWrite and solve a compound inequality that represents the possible temperatures (in degrees Fahrenheit) of the interior of the iceberg.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-79.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 79\" width=\"99\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 23\" width=\"558\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-23.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-23-300x159.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nA ski shop sells skis with lengths ranging from 150 centimeters to 220 centimeters. The shop says the length of the skis should be about 1.16 times a skier\u2019s height (in centimeters). Write and solve a compound inequality that represents the heights of skiers the shop does not provide skis for.<br \/>\nAnswer:<br \/>\nThe compound inequality that represents the heights of skiers the shop does not provide skis for is:<br \/>\n129.3 centimeters &gt; h &gt; 189.7 centimeters<\/p>\n<p>Explanation:<br \/>\nIt is given that a ski shop sells skis with lengths ranging from 150 centimeters to 220 centimeters.<br \/>\nIt is also given that the shop says the length of the skis should be about 1.16 times a skier\u2019s height (in centimeters).<br \/>\nNow,<br \/>\nLet x be the possible length of the skis<br \/>\nLet h be the possible height of the skiers for whom the shop does not provide skis for<br \/>\nSo,<br \/>\nThe inequality that represents the lengths of the skis is:<br \/>\nx &lt; 150 centimeters or x &gt; 220 centimeters<br \/>\nSo,<br \/>\nThe compound inequality that represents the length of the skis is:<br \/>\n150 centimeters &gt; x &gt; 220 centimeters<br \/>\nBut,<br \/>\nx = 1.16h<br \/>\nSo,<br \/>\n150 centimeters &gt; 1.16h &gt; 220 centimeters<br \/>\n(150 \/ 1.16) centimeters &gt; h &gt; (220 \/ 1.16) centimeters<br \/>\n129.3 centimeters &gt; h &gt; 189.7 centimeters<br \/>\nHence, from the above,<br \/>\nWe can conclude that the compound inequality that represents the heights of skiers the shop does not provide skis for is:<br \/>\n129.3 centimeters &gt; h &gt; 189.7 centimeters<\/p>\n<p><b>In Exercises 25\u201330, solve the inequality. Graph the solution, if possible.<\/b><\/p>\n<p>Question 25.<br \/>\n22 &lt; -3c + 4 &lt; 14<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 25\" width=\"564\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-25.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-25-300x158.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 26.<br \/>\n2m &#8211; 1 \u2265 5 or 5m &gt; -25<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2m &#8211; 1\u2265 5 or 5m &gt; -25<br \/>\nSo,<br \/>\n2m \u2265 5 + 1 or m &gt; -25 \/ 5<br \/>\n2m \u2265 6 or m &gt; -5<br \/>\nm \u2265 6 \/ 2 or m &gt; -5<br \/>\nm \u2265 3 or m &gt; -5<br \/>\nHence, from the above<br \/>\nWe can conclude that the solutions to the given inequality are:<br \/>\nm \u2265 3 or m &gt; -5<br \/>\nThe compound inequality of the solutions of the given inequality is:<br \/>\nm &gt; -5<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-108.jpg\" alt=\"\" width=\"686\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-108.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-108-300x37.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 27.<br \/>\n-y + 3 \u2264 8 and y + 2 &gt; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 27\" width=\"568\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-27.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-27-300x176.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 28.<br \/>\nx &#8211; 8 \u2264 4 or 2x + 3 &gt; 9<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nx &#8211; 8 \u2264 4 or 2x + 3 &gt; 9<br \/>\nSo,<br \/>\nx \u2264 4 + 8 or 2x &gt;\u00a0 9 &#8211; 3<br \/>\nx \u2264 12 or 2x &gt; 6<br \/>\nx \u2264 12 or x &gt; 6 \/ 2<br \/>\nx \u2264 12 or x &gt; 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given inequality are:<br \/>\nx \u2264 12 or x &gt; 3<br \/>\nThe compound inequality of the solutions of the given inequality is:<br \/>\n3 &lt; x \u2264 12<br \/>\nThe representation of the solutions of the inequalities in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-109.jpg\" alt=\"\" width=\"686\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-109.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-109-300x37.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 29.<br \/>\n2n + 19 \u2264 10 + n or -3n + 3 &lt; -2n + 33<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 29\" width=\"564\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-29.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-29-300x185.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 30.<br \/>\n3x &#8211; 18 &lt; 4x &#8211; 23 and x &#8211; 16 &lt; -22<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3x &#8211; 18 &lt; 4x &#8211; 23 and x &#8211; 16 &lt; -22<br \/>\nSo,<br \/>\n3x &#8211; 4x &lt; -23 + 18 and x &lt; -22 + 16<br \/>\n-x &lt; -5 and x &lt; &#8211; 6<br \/>\nx &lt; 5 and x &lt; -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given inequality are:<br \/>\nx &lt; 5 and x &lt; -6<br \/>\nThe compound inequality that represents the solutions of the given inequality is:<br \/>\nx &lt; 5<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-110.jpg\" alt=\"\" width=\"686\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-110.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-110-300x37.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 31.<br \/>\n<b>REASONING<\/b><br \/>\nFill in the compound inequality <img loading=\"lazy\" class=\"alignnone size-full wp-image-35164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-110.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 110\" width=\"146\" height=\"23\" \/> and 5(x + 2) \u2265 2(x + 8) with &lt;, \u2264, &gt;, or \u2265 so that the solution is only one value.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 31\" width=\"590\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-31.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-31-300x271.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 32.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nWrite a real-life story that can be modeled by the graph.<br \/>\nAnswer:<br \/>\nThe real-life situation that can be modeled by the graph is:<br \/>\nSuppose we have 100 children in a school. Out of the 100 children, there are 60 boys and the rest are girls.<br \/>\nThe attendance of all the boys in a particular month is 50% and all of the girls is 70%. Mark the percentage attendance that is between the attendance of all the boys and girls?<br \/>\nThe graph representing the above real-life situation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-111.jpg\" alt=\"\" width=\"348\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-111.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-111-300x43.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 33.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nThe sum of the lengths of any two sides of a triangle is greater than the length of the third side. Use the triangle shown to write and solve three inequalities. Your friend claims the value of x can be 1. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-111.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 111\" width=\"122\" height=\"155\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 33\" width=\"516\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-33.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-33-300x83.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe graph shows the annual profits of a company from 2006 to 2013.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-80.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 80\" width=\"331\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-80.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-80-300x163.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\na. Write a compound inequality that represents the annual profits from 2006 to 2013.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-80.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 80\" width=\"331\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-80.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-80-300x163.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that the annual profits from 2006 to 2013<br \/>\nSo,<br \/>\nThe minimum value in the graph is: $65 million<br \/>\nThe highest value in the graph is: $100 million<br \/>\nLet x be the annual profit<br \/>\nHence,<br \/>\nThe inequalities that represent the annual profits from 2006 to 2013 are:<br \/>\nx \u2265 $65 million and x \u2264 $100 million<br \/>\nSo,<br \/>\nThe compound inequality that represents the annual profits from 2006 to 2013 is:<br \/>\n$65 million \u2264 x \u2264 $100 million<\/p>\n<p>b. You can use the formula P = R &#8211; C to find the profit P, where R is the revenue and C is the cost. From 2006 to 2013, the company\u2019s annual cost was about $125 million. Is it possible the company had annual revenue of $160 million from 2006 to 2013? Explain.<br \/>\nAnswer:<br \/>\nYes, it is possible that the company had annual revenue of $160 million from 2006 to 2013<\/p>\n<p>Explanation:<br \/>\nFrom part (a),<br \/>\nThe total profit from 2006 to 2013 is:<br \/>\nP = 65 + 70 + 85 + 50 + 65 + 70 + 90<br \/>\n= $575 million<br \/>\nIt is given that you can use the formula P = R &#8211; C to find the profit P, where R is the revenue and C is the cost.<br \/>\nIt is also given that from 2006 to 2013, the company\u2019s annual cost was about $125 million.<br \/>\nSo,<br \/>\nP = R &#8211; C<br \/>\nR = P + C<br \/>\nR = 575 + 125<br \/>\n= $700 million<br \/>\nHence, from the above,<br \/>\nWe can conclude that it is possible that the company had annual revenue of $160 million from 2006 to 2013<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the equation. Graph the solutions, if possible.<\/b><\/p>\n<p>Question 35.<br \/>\n| \\(\\frac{d}{9}\\) | = 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 35\" width=\"399\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-35.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-35-300x234.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 36.<br \/>\n7 | 5p &#8211; 7 | = -21<br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n7 | 5p &#8211; 7 | = 21<br \/>\nSo,<br \/>\n| 5p &#8211; 7 | = -21 \/ 7<br \/>\n| 5p &#8211; 7 | = -3<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n5p &#8211; 7 = -3 or 5p &#8211; 7 = &#8211; (-3)<br \/>\n5p = -3 + 7 or 5p = 3 + 7<br \/>\n5p = 4 or 5p = 10<br \/>\np = \\(\\frac{4}{5}\\) or p = 2<br \/>\np = 0.8 or p = 2<br \/>\np = 1 [Approx. value] or p = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given absolute value equation are:<br \/>\np = 1 or p = 2<br \/>\nThe representation of the solutions of the given absolute value equation in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-112.jpg\" alt=\"\" width=\"686\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-112.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-112-300x37.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 37.<br \/>\n| r + 2 | = | 3r &#8211; 4 |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-37.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 37.1\" width=\"548\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-37.1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-37.1-300x213.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-37.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 37.2\" width=\"560\" height=\"374\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-37.2.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-37.2-300x200.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-81.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 81\" width=\"137\" height=\"51\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n| \\(\\frac{1}{2}\\)w &#8211; 6 | = | w + 7 |<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\)w &#8211; 6 = w + 7<br \/>\n\\(\\frac{1}{2}\\)w &#8211; w = 7 + 6<br \/>\n&#8211;\\(\\frac{1}{2}\\)w = 13<br \/>\nw = 13 (-2)<br \/>\nw = -26<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given absolute value equation is:<br \/>\nw = -26<br \/>\nThe representation of the solution of the given absolute value equation in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-113.jpg\" alt=\"\" width=\"348\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-113.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-113-300x44.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p><b>Find and interpret the mean absolute deviation of the data.<\/b><\/p>\n<p>Question 39.<br \/>\n1, 1, 2, 5, 6, 8, 10, 12, 12, 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.5 Question 39\" width=\"584\" height=\"345\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-39.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.5-Question-39-300x177.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 40.<br \/>\n24, 26, 28, 28, 30, 30, 32, 32, 34, 36<br \/>\nAnswer:<br \/>\nThe given numbers are:<br \/>\n24, 26, 28, 28, 30, 30, 32, 32, 34, 36<br \/>\nWe know that,<br \/>\nMean = \\(\\frac{The sum of the given numbers}{The total number of numbers}\\)<br \/>\n= \\(\\frac{24 + 26+ 28 + 28 + 30 + 30 + 32 + 32 + 34 + 36}{10}\\)<br \/>\n= \\(\\frac{300}{10}\\)<br \/>\n= 30<br \/>\nNow,<br \/>\nWe know that,<br \/>\nAbsolute deviation = ( The mean ) &#8211; ( Given number )<br \/>\nSo,<br \/>\nAbsolute deviations are:<br \/>\n30 &#8211; 24, 30 &#8211; 26, 30 &#8211; 28, 30 &#8211; 28, 30 &#8211; 30, 30 &#8211; 30, 30 &#8211; 32, 30 &#8211; 32, 30 &#8211; 34, 30 &#8211; 36<br \/>\n= 6, 4, 2, 2, 0, 0, -2, -2, -6, -4<br \/>\nSo,<br \/>\nAbsolute Mean deviation = \\(\\frac{Sum of Absolute deviations}{The numebr of absolute deviations}\\)<br \/>\n= \\(\\frac{6 + 4 + 2 + 2 + 0 + 0 &#8211; 2 &#8211; 2 &#8211; 6 &#8211; 4}{10}\\)<br \/>\n= \\(\\frac{0}{10}\\)<br \/>\n= 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no deviation<\/p>\n<h3><a id=\"Lesson_2.6_Solving_Absolute_Value_Inequalities\"><\/a>Lesson 2.6 Solving Absolute Value Inequalities<\/h3>\n<p><b>Essential Question<br \/>\nHow can you solve an absolute value inequality? Solving an Absolute Value Inequality Algebraically<br \/>\nEXPLORATION 1<br \/>\nSolving an Absolute Value Inequality Algebraically<br \/>\nWork with a partner.<\/b><br \/>\nConsider the absolute value inequality | x + 2 | \u2264 3.<br \/>\na. Describe the values of x + 2 that make the inequality true. Use your description to write two linear inequalities that represent the solutions of the absolute value inequality.<br \/>\nb. Use the linear inequalities you wrote in part (a) to find the solutions of the absolute value inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-82.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 82\" width=\"215\" height=\"192\" \/><br \/>\nc. How can you use linear inequalities to solve an absolute value inequality?<br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n| x + 2 | \u2264 3<br \/>\na.<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 2 \u2264 3 or x + 2 \u2264 -3<br \/>\nx \u2264 3 &#8211; 2 or x \u2264 -3 &#8211; 2<br \/>\nx \u2264 1 or x \u2264 -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given absolute value equation is:<br \/>\nx \u2264 1 or x \u2264 -5<\/p>\n<p>b.<br \/>\nThe given absolute value equation is:<br \/>\n| x + 2 | \u2264 3<br \/>\nFrom part (a),<br \/>\nThe solutions of the given absolute value equation are:<br \/>\nx \u2264 1 or x \u2264 -5<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nNow,<br \/>\nFor x = 1,<br \/>\n| 1 + 2 | \u2264 3<br \/>\n| 3 | \u2264 3<br \/>\n3 \u2264 3<br \/>\nFor x = -5,<br \/>\n| -5 + 2 | \u2264 3<br \/>\n| -3 | \u2264 3<br \/>\n3 \u2264 3<\/p>\n<p>c.<br \/>\nThe following are the steps to solve the absolute value inequality:<br \/>\nA) Isolate the absolute value expression on the left side of the inequality<br \/>\nB) If the number on the other side of the inequality sign is negative, then your equation either has no solution or all real numbers as solutions<br \/>\nC) Remove the absolute value bars by setting up a compound inequality<br \/>\nD) Solve the inequalities<\/p>\n<p><b>EXPLORATION 2<br \/>\nSolving an Absolute Value Inequality Graphically<br \/>\nWork with a partner.<\/b> Consider the absolute value inequality<br \/>\n| x + 2 | \u2264 3.<br \/>\na. On a real number line, locate the point for which | x + 2 | \u2264 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-83.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 83\" width=\"466\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-83.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-83-300x33.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| x + 2 | \u2264 3<br \/>\nFrom Exploration 1,<br \/>\nThe solutions of the absolute value inequality | x + 2 | \u2264 3 are:<br \/>\nx \u2264 1 and x \u2264 -5<br \/>\nThe compound inequality of the solution of the given absolute value inequality is:<br \/>\nx \u2264 1 ( Since the absolute value inequality can never be negative )<br \/>\nNow,<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-83.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 83\" width=\"466\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-83.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-83-300x33.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><br \/>\nHence,<br \/>\nThe representation of the solutions of the absolute value inequality is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-114.jpg\" alt=\"\" width=\"468\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-114.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-114-300x29.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>b. Locate the points that are within 3 units from the point you found in part (a). What do you notice about these points?<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe compound inequality that represents the solution of the given absolute value inequality is:<br \/>\nx \u2264 1<br \/>\nThe points that are within 3 units from the point x \u2264 1, i.e., the given point + 3<br \/>\nSo,<br \/>\n1 + 3 = 4<br \/>\nHence,<br \/>\nThe point we have to locate in the graph is:<br \/>\nx \u2264 4<br \/>\nHence,<br \/>\nThe representation of the compound inequality of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-115.jpg\" alt=\"\" width=\"468\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-115.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-115-300x27.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>c. How can you use a number line to solve an absolute value inequality?<br \/>\nAnswer:<br \/>\nYou begin the marking of the points on the number line by making it into separate equations and then solving them separately. An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound value inequality<\/p>\n<p><b>EXPLORATION 3<\/b><br \/>\n<b>Solving an Absolute Value Inequality Numerically<br \/>\nWork with a partner.<\/b><\/p>\n<p>Solving an Absolute Value Inequality Numerically<br \/>\nWork with a partner. Consider the absolute value inequality | x + 2 | \u2264 3.<br \/>\na. Use a spreadsheet, as shown, to solve the absolute value inequality.<br \/>\nb. Compare the solutions you found using the spreadsheet with those you found in Explorations 1 and 2. What do you notice?<br \/>\nc. How can you use a spreadsheet to solve an absolute value inequality?<br \/>\nAnswer:<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow can you solve an absolute value inequality?<br \/>\nAnswer:<br \/>\nIsolate the\u00a0absolute value\u00a0expression on the left side of the\u00a0inequality. If the number on the other side of the\u00a0inequality\u00a0sign is negative, your equation either has no solution or all real\u00a0numbers\u00a0as solutions. Use the sign of each side of your\u00a0inequality\u00a0to decide which of these cases holds.<\/p>\n<p>Question 5.<br \/>\nWhat do you like or dislike about the algebraic, graphical, and numerical methods for solving an absolute value inequality? Give reasons for your answers.<br \/>\nAnswer:<br \/>\nWe have to use algebraic, graphical, and numerical methods for solving an absolute value inequality depending on the situation<br \/>\nThe algebraic and graphical methods for solving an absolute value inequality are useful when the size of the inequality is small i.e., have only 1 variable<\/p>\n<p><b>2.6 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the inequality. Graph the solution, if possible<\/b><\/p>\n<p>Question 1.<br \/>\n| x | \u2264 3.5<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| x | \u2264 3.5<br \/>\nWe know that,<br \/>\n| x | =x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx \u2264 3.5<br \/>\nx \u2264 4 [Approximate value}<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given absolute value inequality is:<br \/>\nx \u2264 4 [Approximate value]<br \/>\nThe representation of the solution of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-116.jpg\" alt=\"\" width=\"468\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-116.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-116-300x27.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 2.<br \/>\n| k &#8211; 3 | &lt; -1<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| k &#8211; 3 | &lt; -1<br \/>\nWe know that,<br \/>\nIf the number on the other side of the absolute value expression is negative, then the given absolute value equation has no solution or has real numbers as a solution<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value inequality has no solution<\/p>\n<p>Question 3.<br \/>\n| 2w &#8211; 1 | &lt; 11<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| 2w &#8211; 1 | &lt; 11<br \/>\nWe know that,<br \/>\n| x | =x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n2w &#8211; 1 &lt; 11<br \/>\n2w &lt; 11 + 1<br \/>\n2w &lt; 12<br \/>\nw &lt; 12 \/\u00a0 2<br \/>\nw &lt; 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given absolute value inequality is:<br \/>\nw &lt; 6<br \/>\nThe representation of the solution of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-117.jpg\" alt=\"\" width=\"468\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-117.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-117-300x26.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 4.<br \/>\n| x + 3 | &gt; 8<br \/>\nAnswer:<br \/>\nThe given absolute value inquality is:<br \/>\n| x + 3 | &gt; 8<br \/>\nWe know that,<br \/>\n| x | = xfor x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 3 &gt; 8<br \/>\nx &gt; 8 &#8211; 3<br \/>\nx &gt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given absolute value inequality is:<br \/>\nx &gt; 5<br \/>\nThe representation of the solution of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-118.jpg\" alt=\"\" width=\"468\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-118.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-118-300x26.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 5.<br \/>\n| n + 2 | &#8211; 3 \u2265 -6<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| n + 2 | &#8211; 3 \u2265 -6<br \/>\nSo,<br \/>\n| n + 2 | \u2265 -6 + 3<br \/>\n| n + 2 | \u2265 -3<br \/>\nWe know that,<br \/>\nIf the number on the other side of the absolute value expression is negative, then the given absolute value equation has no solution or has real numbers as a solution<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value inequality has no solution<\/p>\n<p>Question 6.<br \/>\n3 | d + 1 | &#8211; 7 \u2265 -1<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n3 | d + 1 | &#8211; 7 \u2265 -1<br \/>\nSo,<br \/>\n3 | d + 1 | \u2265 -1 + 7<br \/>\n3 | d + 1 | \u2265 6<br \/>\n| d + 1 | \u2265 6 \/ 3<br \/>\n| d + 1 | \u2265 2<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nHence,<br \/>\nd + 1 \u2265 2<br \/>\nd \u2265 2 &#8211; 1<br \/>\nd \u2265 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given absolute value inequality is:<br \/>\nd \u2265 1<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-119.jpg\" alt=\"\" width=\"468\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-119.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-119-300x26.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 7.<br \/>\n<b>WHAT IF?<\/b><br \/>\nYou are willing to pay the mean price with an absolute deviation of at most $75. How many of the computer prices meet your condition?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Absolute_Value_Inequalities_2.6_Exercises\"><\/a>Solving Absolute Value Inequalities 2.6 Exercises<\/h3>\n<p>Question 1.<br \/>\n<b>REASONING<br \/>\n<\/b>Can you determine the solution of | 4x &#8211; 2 | \u2265 -6 without solving it? Explain<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 1\" width=\"585\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-1.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-1-300x46.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<br \/>\n<\/b>Describe how solving | w &#8211; 9 | \u2264 2 is different from solving | w &#8211; 9 | \u2265 2.<br \/>\nAnswer:<br \/>\nThe given absolute value inequalities are:<br \/>\n| w &#8211; 9 | \u2264 2 and | w &#8211; 9 | \u2265 2<br \/>\nNow,<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nw &#8211; 9 \u2264 2 and w &#8211; 9 \u2265 2<br \/>\nw \u2264 2 + 9 and w \u2265 2 + 9<br \/>\nw \u2264 11 and w \u2265 11<br \/>\nw &#8211; 9 \u2264 -2 and w &#8211; 9 \u2265 -2<br \/>\nw \u2264 -2 + 9 and w \u2265 -2 + 9<br \/>\nw \u2264 7 and w \u2265 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value inequalities are different by observing the above values for the 2 absolute value inequalities<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics\u00a0<\/b><\/p>\n<p><b>In Exercises 3\u201318, solve the inequality. Graph the solution, if possible.<\/b><\/p>\n<p>Question 3.<br \/>\n| x | &lt; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 3\" width=\"251\" height=\"180\" \/><\/p>\n<p>Question 4.<br \/>\n| y | \u2265 4.<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| y | \u2265 4<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nHence,<br \/>\nThe solutions for the given absolute value inequality is:<br \/>\ny \u2265 4 or y \u2264 -4<br \/>\nThe representation of the compound inequality solution of the given absolute value inequality is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-120.jpg\" alt=\"\" width=\"468\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-120.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-120-300x24.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 5.<br \/>\n| d + 9 | &gt; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 5\" width=\"348\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-5.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-5-300x215.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 6.<br \/>\n| h &#8211; 5 | \u2264 10<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| h &#8211; 5 | \u2264 10<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nh &#8211; 5 \u2264 10<br \/>\nh \u2264 10 + 5 and h \u2265 -10 + 5<br \/>\nh \u2264 15 and h \u2265 -5<br \/>\nHence,<br \/>\nThe compound inequality of the solutions of the given absolute value inequality are:<br \/>\n-5 \u2264\u00a0 h \u2264\u00a0 15<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-121.jpg\" alt=\"\" width=\"680\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-121.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-121-300x33.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 7.<br \/>\n| 2s &#8211; 7 | \u2265 -1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 7\" width=\"509\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-7.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-7-300x118.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 8.<br \/>\n| 4c + 5 | &gt; 7<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| 4c + 5 | &gt; 7<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n4c + 5 &gt; 7 or 4c + 5 &lt; -7<br \/>\n4c &gt; 7 &#8211; 5 or 4c &lt; -7 &#8211; 5<br \/>\n4c &gt; 2 or 4c &lt; -12<br \/>\nc &gt; \\(\\frac{2}{4}\\) or c &lt; &#8211;\\(\\frac{4}{12}\\)<br \/>\nc &gt; \\(\\frac{1}{2}\\) or c &lt; &#8211;\\(\\frac{1}{3}\\)<br \/>\nHence,<br \/>\nThe solutions of the given absolute value equation are:<br \/>\nc &gt; \\(\\frac{1}{2}\\) or c &lt; &#8211;\\(\\frac{1}{3}\\)<br \/>\nc &gt; 1 or c &lt; 0 [ Approximate values of the inequality ]<br \/>\nThe representation of the solutions of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-122.jpg\" alt=\"\" width=\"468\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-122.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-122-300x23.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 9.<br \/>\n| 5p + 2 | &lt; -4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 9\" width=\"565\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-9.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-9-300x66.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 10.<br \/>\n| 9 &#8211; 4n | &lt; 5<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| 9 &#8211; 4n | &lt; 5<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n9 &#8211; 4n &lt; 5 and 9 &#8211; 4n &gt; -5<br \/>\n9 &#8211; 5 &lt; 4n and 9 + 5 &gt; 4n<br \/>\n4 &lt; 4n and 14 &gt; 4n<br \/>\n4n &gt; 4 and 4n &lt; 14<br \/>\nn &gt; 4\/ 4 and n &lt; 14 \/ 4<br \/>\nn &gt; 1 and n &lt; 7 \/ 2<br \/>\nn &gt; 1 and n &lt; 3.5<br \/>\nHence,<br \/>\nThe solutions of the given absolute value inequality are:<br \/>\nn &gt; 1 and n &lt; 3.5<br \/>\nThe compound solution of the solutions of the given absolute value inequality is:<br \/>\n1 &lt; n &lt; 3.5<br \/>\nThe representation of the compound inequality of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-123.jpg\" alt=\"\" width=\"468\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-123.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-123-300x24.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 11.<br \/>\n| 6t &#8211; 7 | &#8211; 8 \u2265 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 11\" width=\"454\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-11.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-11-300x296.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 12.<br \/>\n| 3j &#8211; 1 | + 6 &gt; 0<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| 3j &#8211; 1 | + 6 &gt; 0<br \/>\nSo,<br \/>\n| 3j &#8211; 1 | &gt; 0 &#8211; 6<br \/>\n| 3j &#8211; 1 | &gt; -6<br \/>\nWe know that,<br \/>\nBy definition of absolute values, the absolute value of an expression must be greater than or equal to 0<br \/>\nSo,<br \/>\nThe expression | 3j &#8211; 1 |\u00a0 will always be greater than -6<br \/>\nHence,<br \/>\nFor the given absolute value inequality, all the real numbers are solutions<\/p>\n<p>Question 13.<br \/>\n3 | 14 &#8211; m | &gt; 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 13\" width=\"478\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-13.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-13-300x281.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 14.<br \/>\n-4 | 6b &#8211; 8 | \u2264 12<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n-4 | 6b &#8211; 8 | \u2264 12<br \/>\nSo,<br \/>\n| 6b &#8211; 8 | \u2264 -3<br \/>\nWe know that,<br \/>\nBy definition of absolute values, the absolute value of an expression must be greater than or equal to 0.<br \/>\nSo,<br \/>\nThe expression | 6b &#8211; 8 | must not be less than -3<br \/>\nHence,<br \/>\nFor the given absolute value inequality, there is no solution<\/p>\n<p>Question 15.<br \/>\n2 | 3w + 8 | \u2265 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 15\" width=\"541\" height=\"505\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-15.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-15-300x280.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 16.<br \/>\n3 | 2 &#8211; 4u | + 5 &lt; -13<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n3 | 2 &#8211; 4u | + 5 &lt; -13<br \/>\nSo,<br \/>\n3 | 2 &#8211; 4u | &lt; -13 &#8211; 5<br \/>\n3 | 2 &#8211; 4u | &lt; -18<br \/>\n| 2 &#8211; 4u | &lt; -6<br \/>\nWe know that,<br \/>\nBy definition of absolute values, the absolute value of an expression must be greater than or equal to 0.<br \/>\nSo,<br \/>\nThe expression | 2 &#8211; 4u | must not be less than -6<br \/>\nHence,<br \/>\nFor the given absolute value inequality, there is no solution<\/p>\n<p>Question 17.<br \/>\n6 | -f + 3 | + 7 &gt; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 17\" width=\"545\" height=\"567\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-17.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-17-288x300.png 288w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{2}{3}\\) |4v + 6 | &#8211; 2 \u2264 10<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n\\(\\frac{2}{3}\\) | 4v + 6 | &#8211; 2 \u2264 10<br \/>\n\\(\\frac{2}{3}\\) | 4v + 6 | \u2264 10 + 2<br \/>\n\\(\\frac{2}{3}\\) | 4v + 6 | \u2264 12<br \/>\n| 4v + 6 | \u2264 12 \u00d7 \\(\\frac{3}{2}\\)<br \/>\n| 4v + 6 | \u2264 18<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n4v + 6 \u2264 18 and 4v + 6 \u2265 -18<br \/>\n4v \u2264 18 &#8211; 6 and 4v \u2265 -18 &#8211; 6<br \/>\n4v \u2264 12 and 4v \u2265 -24<br \/>\nv \u2264 12 \/ 4 and v \u2265 -24 \/ 4<br \/>\nv \u2264 3 and v \u2265 -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given absolute value inequality are:<br \/>\nv \u2264 3 and v \u2265 -6<br \/>\nThe representation of the compound inequality of the solutions of the given absolute value inequality is:<br \/>\n-6 \u2264 v \u2264 3<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-54933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-124.jpg\" alt=\"\" width=\"468\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-124.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-124-300x23.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 19.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe rules for an essay contest say that entries can have 500 words with an absolute deviation of at most 30 words. Write and solve an absolute value inequality that represents the acceptable numbers of words.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 19\" width=\"565\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-19.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-19-300x127.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 20.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe normal body temperature of a camel is 37\u00b0C. This temperature varies by up to 3\u00b0C throughout the day. Write and solve an absolute value inequality that represents the range of normal body temperatures (in degrees Celsius) of a camel throughout the day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-84.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 84\" width=\"249\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nThe absolute value inequality that represents the range of normal body temperatures of a camel throughout the day is:<br \/>\n34\u00b0C \u2264 t \u2264 40\u00b0C<\/p>\n<p>Explanation:<br \/>\nIt is given that the normal body temperature of a camel is 37\u00b0C and this temperature varies by up to 3\u00b0C throughout the day.<br \/>\nLet t be the temperature in \u00b0C<br \/>\nSo,<br \/>\nThe absolute value inequality that represents the range of normal body temperatures of a camel throughout the day is:<br \/>\n37 &#8211; 3 \u2264 t \u2264 37 + 3<br \/>\n34\u00b0C \u2264 t \u2264 40\u00b0C<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 21 and 22, describe and correct the error in solving the absolute value inequality.<\/b><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-85.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 85\" width=\"211\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 21\" width=\"588\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-21.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-21-300x132.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-86.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 86\" width=\"308\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-86.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-86-300x129.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| x + 4 | &gt; 13<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 4 &gt; 13 or x + 4 &lt; -13<br \/>\nx &gt; 13 &#8211; 4 or x &lt; -13 &#8211; 4<br \/>\nx &gt; 9 or x &lt; -17<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given absolute value inequality are:<br \/>\nx &gt; 9 or x &lt; -17<\/p>\n<p><b>In Exercises 23\u201326, write the sentence as an absolute value inequality. Then solve the inequality.<\/b><\/p>\n<p>Question 23.<br \/>\nA number is less than 6 units from 0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 23\" width=\"359\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-23.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-23-300x141.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Question 24.<br \/>\nA number is more than 9 units from 3.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number is more than 9 units from 3<br \/>\nLet n be the number<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of absolute value inequality is:<br \/>\n| n &#8211; 3 | &gt; 9<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nn &#8211; 3 &gt; 9 or n &#8211; 3 &lt; -9<br \/>\nn &gt; 9 + 3 or n &lt; -9 + 3<br \/>\nn &gt; 12 or n &lt; -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions o the given absolute value inequality is:<br \/>\nn &gt; 12 or n &lt; -6<\/p>\n<p>Question 25.<br \/>\nHalf of a number is at most 5 units from 14.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 25\" width=\"417\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-25.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-25-300x219.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\n<p>Question 26.<br \/>\nTwice a number is no less than 10 units from -1.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nTwice a number is no less than 10 units from -1<br \/>\nLet x be the number<br \/>\nSo,<br \/>\nThe representation of the given worded form in the form of absolute value inequality is:<br \/>\n| 2x &#8211; (-1) | &gt; 10<br \/>\nSo,<br \/>\n| 2x + 1 | &gt; 10<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nHence,<br \/>\n2x + 1 &gt; 10 or 2x + 1 &lt; -10<br \/>\n2x &gt; 10 &#8211; 1 or 2x &lt; -10 &#8211; 1<br \/>\n2x &gt; 9 or 2x &lt; -11<br \/>\nx &gt; \\(\\frac{9}{2}\\) or x &lt; &#8211;\\(\\frac{11}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given absolute value inequality is:<br \/>\nx &gt; \\(\\frac{9}{2}\\) or x &lt; &#8211;\\(\\frac{11}{2}\\)<\/p>\n<p>Question 27.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nAn auto parts manufacturer throws out gaskets with weights that are not within 0.06 pound of the mean weight of the batch. The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. Which gasket(s) should be thrown out?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 27\" width=\"554\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-27.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-27-300x208.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 28.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nSix students measure the acceleration (in meters per second ) of an object in free fall. The measured values are shown. The students want to state that the absolute deviation of each measured value x from the mean is at most d. Find the value of d.<br \/>\n10.56, 9.52, 9.73, 9.80, 9.78, 10.91<br \/>\nAnswer:<br \/>\nThe value of d is: 0.86<\/p>\n<p>Explanation:<br \/>\nThe given numbers are:<br \/>\n10.56, 9.52, 9.73, 9.80, 9.78, 10.91<br \/>\nWe know that,<br \/>\nMean = \\(\\frac{Sum of the given observations}{Number of observations}\\)<br \/>\n= \\(\\frac{10.56 + 9.52 + 9.73 + 9.80 + 9.78 + 10.91}{6}\\)<br \/>\n= \\(\\frac{60.3}{6}\\)<br \/>\n= 10.05<br \/>\nNow,<br \/>\nWe know that,<br \/>\nAbsolute deviation = Mean &#8211; ( Given observation)<br \/>\nIt is given that that the measured value is x<br \/>\nHence,<br \/>\nThe representation of the absolute deviation in the form of absolute value inequality is:<br \/>\n| x &#8211; 10.05 | \u2264 d<br \/>\nSo,<br \/>\n| 10.56 &#8211; 10.05 | \u2264 d<br \/>\n| 9.52 &#8211; 10.05 | \u2264 d<br \/>\n| 9.73 &#8211; 10.05 | \u2264 d<br \/>\n| 9.80 &#8211; 10.05 | \u2264 d<br \/>\n| 9.78 &#8211; 10.05 | \u2264 d<br \/>\n| 10.91 &#8211; 10.05 | \u2264 d<br \/>\nSo,<br \/>\nd \u2265 0.51<br \/>\nd \u2265 0.53<br \/>\nd \u2265 0.32<br \/>\nd \u2265 0.25<br \/>\nd \u2265 0.27<br \/>\nd \u2265 0.86<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of d will be the highest deviation from the mean value<br \/>\nThe value of d is: 0.86<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 29 and 30, write an absolute value inequality that represents the situation. Then solve the inequality.<\/b><\/p>\n<p>Question 29.<br \/>\nThe difference between the areas of the figures is less than 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-86.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 86.1\" width=\"267\" height=\"166\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 29\" width=\"600\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-29.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-29-300x261.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>Question 30.<br \/>\nThe difference between the perimeters of the figures is less than or equal to 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-87.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 87\" width=\"321\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-87.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-87-300x128.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\nThe given figures are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-87.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 87\" width=\"321\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-87.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-87-300x128.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nFrom the above,<br \/>\nThe given figures are: Rectangle and square<br \/>\nWe know that,<br \/>\nThe perimeter of a rectangle = 2 ( Length + Width )<br \/>\nThe perimeter of a square = 4 ( Side )<br \/>\nSo,<br \/>\nThe perimeter of a rectangle = 2 ( 3 + x + 1 ) = 2 ( x + 4 )<br \/>\nThe perimeter of a square = 4 (x) = 4x<br \/>\nIt is given that the difference of the perimeters of the given figures is less than or equal to 3<br \/>\nSo,<br \/>\n| 2 ( x + 4 ) &#8211; 4x | \u2264 3<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n2 (x + 4) &#8211; 4x \u22643 and 2 ( x + 4 ) &#8211; 4x \u2265 -3<br \/>\n2x + 8 &#8211; 4x \u2264 3 and 2x + 8 &#8211; 4x \u2265 -3<br \/>\n8 &#8211; 2x \u2264 3 and 8- 2x \u2265 -3<br \/>\n-2x \u2264 3 &#8211; 8 and -2x \u2265 -3 &#8211; 8<br \/>\n-2x \u2264 -5 and -2x \u2265 -11<br \/>\n2x \u2264 5 and 2x \u2265 11<br \/>\nx \u2264 \\(\\frac{5}{2}\\) and x \u2265 \\(\\frac{11}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the compound inequality for the solutions of the given absolute value inequality is:<br \/>\n\\(\\frac{11}{2}\\) \u2264 x \u2264 \\(\\frac{5}{2}\\)<\/p>\n<p><b>REASONING<br \/>\nIn Exercises 31\u201334, tell whether the statement is true or false. If it is false, explain why.<\/b><\/p>\n<p>question 31.<br \/>\nIf a is a solution of | x + 3 | \u2264 8, then a is also a solution of x + 3 \u2265 -8.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 31\" width=\"59\" height=\"27\" \/><\/p>\n<p>Question 32.<br \/>\nIf a is a solution of | x + 3 | &gt; 8, then a is also a solution of x + 3 &gt; 8.<br \/>\nAnswer:<br \/>\nThe given statement is true<\/p>\n<p>Explanation:<br \/>\nThe given statement is:<br \/>\nIf a is a solution of | x + 3 | &gt; 8, then a is also a solution of x + 3 &gt; 8<br \/>\nNow,<br \/>\nThe given inequality is:<br \/>\n| x + 3 | &gt; 8<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 3 &gt; 8 or x + 3 &lt; -8<br \/>\nWe know that,<br \/>\nThe value of the absolute value expression must be greater than or equal to 0<br \/>\nSo,<br \/>\nx + 3 &lt; -8 has no solution<br \/>\nSo,<br \/>\na is a solution of x + 3 &gt; 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is true<\/p>\n<p>Question 33.<br \/>\nIf a is a solution of | x + 3 | \u2265 8, then a is also a solution of x + 3 \u2265 -8.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 33\" width=\"582\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-33.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-33-300x60.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 34.<br \/>\nIf a is a solution of x + 3 \u2264\u00a0 -8, then a is also a solution of | x + 3 | \u2265 8.<br \/>\nAnswer:<br \/>\nThe given statement is true<\/p>\n<p>Explanation:<br \/>\nThe given statement is:<br \/>\nIf a is a solution of x + 3 \u2264 -8, then a is a solution of | x + 3 | \u2265 8<br \/>\nNow,<br \/>\nThe given absolute value inequality is:<br \/>\n| x + 3 | \u2265 8<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 3 \u2265 8 or x + 3 \u2264 -8<br \/>\nIf a is a solution of x + 3\u00a0 \u2265 8, then a is also a solution of x + 3 \u2264 -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is true<\/p>\n<p>Question 35.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nOne of your classmates claims that the solution of | n | &gt; 0 is all real numbers. Is your classmate correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 35\" width=\"544\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-35.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-35-300x34.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nDraw and label a geometric figure so that the perimeter P of the figure is a solution to the inequality | P &#8211; 60 | \u2264 12.<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| p &#8211; 60 | \u2264 12<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\np &#8211; 60 \u2264 12 and p &#8211; 60 \u2265 -12<br \/>\np \u2264 12 + 60 and p \u2265 -12 + 60<br \/>\np \u2264 72 and p \u2265 48<br \/>\nHence,<br \/>\nThe representation of the compound inequality of the perimeter of the figure is:<br \/>\n48 \u2264 p \u2264 72<br \/>\nNow, find the value of 4p i.e., the perimeter of the square<br \/>\nSo,<br \/>\n192 \u2264 4p \u2264 288<br \/>\nHence, from the above,<br \/>\nWe can conclude that the perimeter is represented for the perimeter of the square<\/p>\n<p>Question 37.<br \/>\n<b>REASONING<\/b><br \/>\nWhat is the solution of the inequality | ax + b | &lt; c, where c &lt; 0? What is the solution of the inequality | ax + b | &gt; c, where c &lt; 0? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 37\" width=\"586\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-37.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-37-300x119.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nWrite an absolute value inequality for each graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-88.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 88\" width=\"315\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-88.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-88-300x197.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nHow did you decide which inequality symbol to use for each inequality?<br \/>\nAnswer:<br \/>\nThe given graphs are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-88.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 88\" width=\"315\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-88.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-88-300x197.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\na.<br \/>\nFrom the given graph,<br \/>\nThe 1st marked line starts from -1 including -1 and continued till the left end of the number line<br \/>\nThe 2nd marked line starts from 5 including from 5 and continued till the right end of the number line<br \/>\nHence,<br \/>\nThe representation of the marked lines in the form of absolute value inequality is:<br \/>\n| x + 1 | \u2264 3 and | x &#8211; 5 | \u2265 1<\/p>\n<p>b.<br \/>\nFrom the given graph,<br \/>\nThe marked line starts from -1 excluding -1 and continued till 5 on the right end of the number line<br \/>\nHence,<br \/>\nThe representation of the marked line in the form of absolute value inequality is:<br \/>\n| x + 1 | &gt; 6<br \/>\nc.<br \/>\nFrom the given graph,<br \/>\nThe marked line starts from -1 including -1 and continued till 5 on the right end of the number line<br \/>\nHence,<br \/>\nThe representation of the marked line in the form of absolute value inequality is:<br \/>\n| x + 1 | \u2265 6<br \/>\nd.<br \/>\nFro the given graph,<br \/>\nThe 1st marked line starts from -1 excluding -1 and continued till the left end of the number line<br \/>\nThe 2nd marked line starts from 5 excluding 5 and continued till the right end of the number line<br \/>\nHence,<br \/>\nThe representation of the marked lines in the form of absolute value inequality is:<br \/>\n| x + 1 | &lt; 3 and | x &#8211; 5 | &gt; 1<br \/>\nIf the marked point is indicated on the number line and if that marked line continued till the right end of the number line, then we will use \u2265<br \/>\nIf the marked point is not indicated on the number line and if that marked line continued till the right end of the number line, then we will use &gt;<br \/>\nIf the marked point is indicated on the number line and if that marked line continued till the left end of the number line, then we will use \u2264<br \/>\nIf the marked point is not indicated on the number line and if that marked line continued till the left end of the number line, then we will use &lt;<\/p>\n<p>Question 39.<br \/>\n<b>WRITING<\/b><br \/>\nExplain why the solution set of the inequality | x | &lt; 5 is the intersection of two sets, while the solution set of the inequality | x | &gt; 5 is the union of two sets.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 39\" width=\"587\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-39.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-39-300x115.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nSolve the compound inequality below. Describe your steps.<br \/>\n| x &#8211; 3 | &lt; 4 and | x + 2 | &gt; 8<br \/>\nAnswer:<br \/>\nThe given inequalities are:<br \/>\n| x + 3 | &lt; 4 and | x + 2\u00a0 | &gt; 8<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 3 &lt; 4 or x + 3 &gt; -4 and x + 2 &gt; 8 or x + 2 &lt; -8<br \/>\nx &lt; 4 &#8211; 3 or x &gt; -4 &#8211; 3 and x &gt; 8 &#8211; 2 or x &lt; -8 &#8211; 2<br \/>\nx &lt; 1 or x &gt; -7 and x &gt; 6 or x &lt; -10<br \/>\nHence,<br \/>\nThe compound inequality of the solutions of the given absolute value inequalities are:<br \/>\n-7 &lt; x &lt; 1 and -10 &gt; x &gt; 6<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Plot the ordered pair in a coordinate plane. Describe the location of the point.<\/b><\/p>\n<p>Question 41.<br \/>\nA(1, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 41\" width=\"297\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-41.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-41-274x300.png 274w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p>Question 42.<br \/>\nB(0, -3)<br \/>\nAnswer:<br \/>\nIn the graph,<br \/>\nX-axis:<br \/>\nThe right side of the x-axis will be: +ve<br \/>\nThe left side of the x-axis will be: -ve<br \/>\nY-axis:<br \/>\nThe top side of the y-axis will be: +ve<br \/>\nThe downside of the y-axis will be: -ve<br \/>\nWe know that,<br \/>\nThe graph is divided into 4 quadrants. They are:<br \/>\n1st Quadrant: x: +ve and y: -ve<br \/>\n2nd Quadrant: x: -ve and y: +ve<br \/>\n3rd Quadrant: x: -ve and y: -ve<br \/>\n4th Quadrant: x: +ve and y: -ve<br \/>\nHence,<br \/>\nB(0, -3) will be in the 4th Quadrant<br \/>\nThe representation of point B in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-125.jpg\" alt=\"\" width=\"295\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-125.jpg 295w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-125-272x300.jpg 272w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><\/p>\n<p>Question 43.<br \/>\nC(-4, -2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 43\" width=\"296\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-43.png 296w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-43-273x300.png 273w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/p>\n<p>Question 44.<br \/>\nD(-1, 2)<br \/>\nAnswer:<br \/>\nIn the graph,<br \/>\nX-axis:<br \/>\nThe right side of the x-axis will be: +ve<br \/>\nThe left side of the x-axis will be: -ve<br \/>\nY-axis:<br \/>\nThe top side of the y-axis will be: +ve<br \/>\nThe downside of the y-axis will be: -ve<br \/>\nWe know that,<br \/>\nThe graph is divided into 4 quadrants. They are:<br \/>\n1st Quadrant: x: +ve and y: -ve<br \/>\n2nd Quadrant: x: -ve and y: +ve<br \/>\n3rd Quadrant: x: -ve and y: -ve<br \/>\n4th Quadrant: x: +ve and y: -ve<br \/>\nHence,<br \/>\nD(-1, 2) will be in the 2nd Quadrant<br \/>\nThe representation of point D in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-126.jpg\" alt=\"\" width=\"295\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-126.jpg 295w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-126-272x300.jpg 272w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><\/p>\n<p><b>Copy and complete the table.<\/b><\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-89.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 89\" width=\"264\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities 2.6 Question 45\" width=\"562\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-45.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-2-Solving-Linear-Inequalities-2.6-Question-45-300x112.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-90.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 90\" width=\"281\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-127.jpg\" alt=\"\" width=\"594\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-127.jpg 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-127-300x91.jpg 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Performance_Task:_Grading_Calculations\"><\/a>Solving Linear Inequalities Performance Task: Grading Calculations<\/h3>\n<p><b>2.5\u20132.6 <span style=\"font-size: 16px;\">What Did You Learn?<\/span><\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\ncompound inequality, p. 82<br \/>\nabsolute value inequality, p. 88<br \/>\nabsolute deviation, p. 90<\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 2.5<\/b><br \/>\nWriting and Graphing Compound Inequalities, p. 82<br \/>\nSolving Compound Inequalities, p. 83<\/p>\n<p><b>Section 2.6<\/b><br \/>\nSolving Absolute Value Inequalities, p. 88<\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow can you use a diagram to help you solve Exercise 12 on page 85?<br \/>\nAnswer:<br \/>\nIn Exercise 12 on page 85,<br \/>\nThe given diagram represents the maximum elevation of Mount Rainier<br \/>\nIn the diagram,<br \/>\nThe given maximum elevation of Mount Rainier is: 14,410 ft<br \/>\nSo,<br \/>\nThis 14,410 ft is divided into different types of elevation in Exercise 12<\/p>\n<p>Question 2.<br \/>\nIn Exercises 13 and 14 on page 85, how can you use structure to break down the compound inequality into two inequalities?<br \/>\nAnswer:<br \/>\nIn Exercises 13 and 14 on page 85,<br \/>\nFirst, perform the necessary mathematical operations so that only the variable must be present<br \/>\nSo,<br \/>\nAfter performing the necessary mathematical operations, the structure of the compound inequality will be like<br \/>\na &lt; x &lt; b or a &gt; x &gt; b<br \/>\nThe breakdown of the compound inequality a &lt; x &lt; b will be like x &gt;a and x &lt; b<br \/>\nThe breakdown of the compound inequality a &gt; x &gt; b will be like x &lt; a and x &gt; b<br \/>\nWe can put the different types of inequality symbols in the breakdown of inequalities<\/p>\n<p>Question 3.<br \/>\nDescribe the given information and the overall goal of Exercise 27 on page 91.<br \/>\nAnswer:<br \/>\nThe given information is:<br \/>\nAn auto parts manufacturer throws out gaskets with weights that are not within 0.06 pounds of the mean weight of the batch. The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61<br \/>\nThe overall goal of Exercise 27:<br \/>\nFind the mean of the given weights and find the absolute deviation of the gaskets<br \/>\nThe absolute deviation of the gaskets that are less than 0.0 pounds of the man weight should be thrown out<\/p>\n<p>Question 4.<br \/>\nFor false statements in Exercises 31\u201334 on page 92, use examples to show the statements are false.<br \/>\nAnswer:<br \/>\nIn Exercises 31 &#8211; 34 on page 92,<br \/>\nExercises 33 and 34 are false<br \/>\nThe Exercise 33 is: | x + 3 | \u2265 8<br \/>\nThe Exercise 34 is: | x + 3 | \u2265 8<br \/>\nSo,<br \/>\nIn Exercise 33,<br \/>\na is a solution for x + 3 \u2265 8 and x + 3 \u2264 -8<br \/>\nIn Exercise 34,<br \/>\na is a solution of x + 3 \u2265 8 and x + 3 \u2264 -8<\/p>\n<p><b>Performance Task<\/b><\/p>\n<p><b>Grading Calculations<\/b><\/p>\n<p>You are not doing as well as you had hoped in one of your classes. So, you want to figure out the minimum grade you need on the final exam to receive the semester grade that you want. Is it still possible to get an A? How would you explain your calculations to a classmate?<br \/>\nTo explore the answers to this question and more, go to <img loading=\"lazy\" class=\"alignnone size-full wp-image-35119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-91.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 91\" width=\"86\" height=\"80\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-91.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 91.1\" width=\"304\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-91.1.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-91.1-253x300.png 253w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Chapter_Review\"><\/a>Solving Linear Inequalities Chapter Review<\/h3>\n<p><b>2.1 Writing and Graphing Inequalities <\/b>(pp. 53\u201360)<br \/>\na. A number x plus 36 is no more than 40. Write this sentence as an inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-91.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 91.2\" width=\"289\" height=\"103\" \/><br \/>\nb. Graph w &gt; \u22123.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-92.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 92\" width=\"485\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-92.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-92-300x121.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p><b>Write the sentence as an inequality.<\/b><\/p>\n<p>Question 1.<br \/>\nA number d minus 2 is less than -1.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number d minus 2 is less than -1<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nd &#8211; 2 &lt; -1<\/p>\n<p>Question 2.<br \/>\nTen is at least the product of a number h and 5.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nTen is at least the product of a number h and 5<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\n10 \u2265 h(5)<br \/>\n10 \u2265 5h<br \/>\n10 \/ 5 \u2265 h<br \/>\n2 \u2265 h<br \/>\nh \u2264 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the representation of the given worded form in the form of inequality is:<br \/>\nh \u2264 2<\/p>\n<p><b>Graph the inequality.<\/b><\/p>\n<p>Question 3.<br \/>\nx &gt; 4<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nx &gt; 4<br \/>\nHence,<br \/>\nThe representation of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-128.jpg\" alt=\"\" width=\"468\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-128.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-128-300x25.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 4.<br \/>\ny \u2264 2<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\ny \u2264 2<br \/>\nHence,<br \/>\nThe representation of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-129.jpg\" alt=\"\" width=\"468\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-129.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-129-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 5.<br \/>\n-1 \u2265 z<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-1 \u2265 z<br \/>\nz \u2264 -1<br \/>\nHence,<br \/>\nThe representation of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-130.jpg\" alt=\"\" width=\"468\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-130.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-130-300x26.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p><b>2.2 Solving Inequalities Using Addition or Subtraction <\/b>(pp. 61\u201366)<\/p>\n<p><b>Solve x + 2.5 \u2264 \u22126. Graph the solution.<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-93.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 93\" width=\"631\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-93.png 631w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-93-300x83.png 300w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><\/p>\n<p><b>Solve the inequality. Graph the solution.<\/b><\/p>\n<p>Question 6.<br \/>\np + 4 &lt; 10<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\np + 4 &lt; 10<br \/>\nSo,<br \/>\np &lt; 10 &#8211; 4<br \/>\np &lt; 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is p &lt; 6<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-131.jpg\" alt=\"\" width=\"468\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-131.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-131-300x27.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 7.<br \/>\nr &#8211; 4 &lt; -6<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nr &#8211; 4 &lt; -6<br \/>\nSo,<br \/>\nr &lt; -6 + 4<br \/>\nr &lt; -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is r &lt; -2<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-132.jpg\" alt=\"\" width=\"468\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-132.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-132-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 8.<br \/>\n2.1 \u2265 m &#8211; 6.7<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2.1 \u2265 m &#8211; 6.7<br \/>\nSo,<br \/>\n2.1 + 6.7 \u2265 m<br \/>\n8.8 \u2265 m<br \/>\n9 \u2265 m [Approximate value]<br \/>\nm \u2264 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is m \u2264 9<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-133.jpg\" alt=\"\" width=\"468\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-133.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-133-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p><b>2.3 Solving Inequalities. Using Multiplication or Division<\/b><\/p>\n<p>Solve \\(\\frac{n}{-10}\\) &gt; 5. Graph the solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-94.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 94\" width=\"726\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-94.png 726w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-94-300x83.png 300w\" sizes=\"(max-width: 726px) 100vw, 726px\" \/><\/p>\n<p><b>Solve the inequality. Graph the solution.<\/b><\/p>\n<p>Question 9.<br \/>\n3x &gt; -21<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3x &gt; -21<br \/>\nSo,<br \/>\nx &gt; -21 \/ 3<br \/>\nx &gt; -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &gt; -7<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-134.jpg\" alt=\"\" width=\"468\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-134.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-134-300x25.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 10.<br \/>\n-4 \u2264 \\(\\frac{g}{5}\\)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-4 \u2264 \\(\\frac{g}{5}\\)<br \/>\n-4 (5) \u2264 g<br \/>\n-20 \u2264 g<br \/>\ng \u2265 -20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is g \u2265 -20<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-135.jpg\" alt=\"\" width=\"348\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-135.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-135-300x36.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 11.<br \/>\n&#8211;\\(\\frac{3}{4}\\)n \u2264 3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n&#8211;\\(\\frac{3}{4}\\)n \u2264 3<br \/>\nn \u2264 3 \u00d7 &#8211;\\(\\frac{4}{3}\\)<br \/>\nn \u2264 &#8212;\\(\\frac{3 \u00d7 4}{3}\\)<br \/>\nn \u2264 -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is n \u2264 -4<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-136.jpg\" alt=\"\" width=\"468\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-136.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-136-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{s}{-8}\\) \u2265 11<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{s}{-8}\\) \u2265 11<br \/>\ns \u2265 11 (-8)<br \/>\ns \u2265 -88<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is s \u2265 -88<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-137.jpg\" alt=\"\" width=\"348\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-137.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-137-300x37.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 13.<br \/>\n36 &lt; 2q<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n36 &lt; 2q<br \/>\nSo,<br \/>\n36 \/ 2 &lt; q<br \/>\n18 &lt; q<br \/>\nq &gt; 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is q &gt; 18<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-138.jpg\" alt=\"\" width=\"680\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-138.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-138-300x34.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 14.<br \/>\n-1.2k &gt; 6<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-1.2k &gt; 6<br \/>\nSo,<br \/>\nk &gt; 6 \/ -1.2<br \/>\nk &gt; -60 \/ 12<br \/>\nk &gt; -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is k &gt; -5<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-139.jpg\" alt=\"\" width=\"468\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-139.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-139-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p><b>2.4 Solving Multi-step Inequalities<\/b><\/p>\n<p>Solve 22 + 3y \u2265 4. Graph the solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-95.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 2 Solving Linear Inequalities 95\" width=\"509\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-95.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-2-Solving-Linear-Inequalities-95-300x138.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p><b>Solve the inequality. Graph the solution, if possible.<\/b><\/p>\n<p>Question 15.<br \/>\n3x &#8211; 4 &gt; 11<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3x &#8211; 4 &gt; 11<br \/>\nSo,<br \/>\n3x &gt; 11 + 4<br \/>\n3x &gt; 15<br \/>\nx &gt; 15 \/ 3<br \/>\nx &gt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x &gt; 5<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-140.jpg\" alt=\"\" width=\"468\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-140.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-140-300x26.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 16.<br \/>\n-4 &lt; \\(\\frac{b}{2}\\) + 9<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-4 &lt; \\(\\frac{b}{2}\\) + 9<br \/>\n-4 &#8211; 9 &lt; \\(\\frac{b}{2}\\)<br \/>\n-13 &lt; \\(\\frac{b}{2}\\)<br \/>\n-13 (2) &lt; b<br \/>\n-26 &lt; b<br \/>\nb &gt; -26<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given inequality is b &gt; -26<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-141.jpg\" alt=\"\" width=\"348\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-141.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-141-300x38.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 17.<br \/>\n7 &#8211; 3n \u2264 n + 3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n7 &#8211; 3n \u2264 n + 3<br \/>\n-3n &#8211; n \u2264 3 &#8211; 7<br \/>\n-4n \u2264 -4<br \/>\n4n \u2264 4<br \/>\nn \u2264 4 \/ 4<br \/>\nn \u2264 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is n \u2264 1<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-142.jpg\" alt=\"\" width=\"468\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-142.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-142-300x27.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 18.<br \/>\n2(-4s + 2) \u2265 -5s &#8211; 10<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2 (-4s +2) \u2265 -5s &#8211; 10<br \/>\nSo,<br \/>\n2 (-4s) + 2 (2) \u2265 -5s &#8211; 10<br \/>\n-8s + 4 \u2265 -5s &#8211; 10<br \/>\n-8s + 5s \u2265 -10 &#8211;\u00a0 4<br \/>\n-3s \u2265 -14<br \/>\n3s \u2265 14<br \/>\ns \u2265 14 \/ 3<br \/>\ns \u2265 5 [ Approximate value }<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given inequality is s \u2265 5<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-143.jpg\" alt=\"\" width=\"468\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-143.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-143-300x27.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 19.<br \/>\n6(2t + 9) \u2264 12t &#8211; 1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n6(2t + 9) \u2264 12t &#8211; 1<br \/>\nSo,<br \/>\n6 (2t) + 6 (9) \u2264 12t &#8211; 1<br \/>\n12t + 54 \u2264 12t &#8211; 1<br \/>\n1t &#8211; 12t + 54 \u2264 -1<br \/>\n54 \u2264 -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 20.<br \/>\n3r &#8211; 8 &gt; 3(r &#8211; 6)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n3r &#8211; 8 &gt; 3 ( r &#8211; 6 )<br \/>\nSo,<br \/>\n3r &#8211; 8 &gt; 3 (r) &#8211; 3 (6)<br \/>\n3r &#8211; 8 &gt; 3r &#8211; 18<br \/>\n3r &#8211; 8 &#8211; 3r &gt; -18<br \/>\n-8 &gt; -18<br \/>\n8 &gt; 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution to the given inequality<\/p>\n<p><b>2.5 Solving Compound Inequalities<\/b><\/p>\n<p><b>Solve \u22121 \u2264 \u22122d + 7 \u2264 9. Graph the solution.<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-96.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 96\" width=\"479\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-96.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-96-300x128.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 21.<br \/>\nA number x is more than -6 and at most 8. Write this sentence as an inequality. Graph the inequality.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number x is more than -6 and at most 8<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nx &gt; -6 and x \u2264 8<br \/>\nHence,<br \/>\nThe representation of the solutions of the given worded form in the form of compound inequality is:<br \/>\n-6 &lt; x \u2264 8<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-144.jpg\" alt=\"\" width=\"468\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-144.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-144-300x29.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p><b>Solve the inequality. Graph the solution.<\/b><\/p>\n<p>Question 22.<br \/>\n19 \u2265 3z + 1 \u2265 -5<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n19 \u2265 3z + 1 \u2265 -5<br \/>\nSubtract with -1 on both sides<br \/>\nSo,<br \/>\n19 &#8211; 1 \u2265 3z + 1 &#8211; 1 \u2265 -5 &#8211; 1<br \/>\n18 \u2265 3z \u2265 -6<br \/>\nDivide by 3 on both sides<br \/>\nSo,<br \/>\n(18 \/ 3) \u2265 (3z \/ 3) \u2265 (-6 \/ 3)<br \/>\n6 \u2265 z \u2265 -2<br \/>\n-2 \u2264 z \u2264 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the compound inequality solution to the given inequality is:<br \/>\n-2 \u2264 z \u2264 6<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-145.jpg\" alt=\"\" width=\"468\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-145.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-145-300x30.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 23.<br \/>\n\\(\\frac{r}{4}\\) &lt; -5 or -2r &#8211; 7 \u2264 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-97.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 97\" width=\"155\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-97.png 155w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-97-150x39.png 150w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{r}{4}\\) &lt; -5 or -2r &#8211; 7 \u2264 3<br \/>\nr &lt; -5 (4) or -2r \u2264 3 + 7<br \/>\nr &lt; -20 or -2r \u2264 10<br \/>\nr &lt; -20 or r \u2264 -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given inequality are:<br \/>\nr &lt; -20 or r \u2264 -5<br \/>\nThe representations of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-146.jpg\" alt=\"\" width=\"348\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-146.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-146-300x41.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p><strong>2.6 Solving Absolute Value Inequalities<\/strong><\/p>\n<p><b>Solve the inequality. Graph the solution, if possible.<\/b><\/p>\n<p>Question 24.<br \/>\n| m | \u2265 10<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| m | \u2265 10<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nm \u2265 10 or m \u2264 -10<br \/>\nWe know that,<br \/>\nThe value of absolute value expression must be greater than or equal to 0<br \/>\nSo,<br \/>\nm \u2265 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given absolute value inequality is m \u2265 10<br \/>\nThe representation of the solution of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-147.jpg\" alt=\"\" width=\"348\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-147.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-147-300x34.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 25.<br \/>\n| k &#8211; 9 | &lt; -4<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| k &#8211; 9 | &lt; 4<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nk &#8211; 9 &lt; 4 and k &#8211; 9 &gt; -4<br \/>\nk &lt; 4 + 9 and k &gt; -4 + 9<br \/>\nk &lt; 13 and k &gt; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given absolute value inequality are:<br \/>\nk &lt; 13 and k &gt; 5<br \/>\nThe representation of the compound inequality of the solutions of the given absolute inequality is:<br \/>\n5 &lt; k &lt; 13<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-148.jpg\" alt=\"\" width=\"680\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-148.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-148-300x31.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 26.<br \/>\n4 | f &#8211; 6 | \u2264 12<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n4 | f &#8211; 6 | \u2264 12<br \/>\n| f &#8211; 6 | \u2264 3<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| X | = -x for x &lt; 0<br \/>\nSo,<br \/>\nf &#8211; 6 \u2264 3 and f &#8211; 6 \u2265 -3<br \/>\nf \u2264 3 + 6 and f \u2265 -3 + 6<br \/>\nf \u2264 9 and f \u2265 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given absolute value inequality are:<br \/>\nf \u2264 9 and f \u2265 3<br \/>\nThe representation of the compound inequality of the solutions of the given absolute value inequality is:<br \/>\n3 \u2264 f \u2264 9<br \/>\nThe representation of the compound inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-149.jpg\" alt=\"\" width=\"468\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-149.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-149-300x29.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 27.<br \/>\n5 | b + 8 | &#8211; 7 &gt; 13<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n5 | b + 8 | &#8211; 7 &gt; 13<br \/>\n5 | b + 8 | &gt; 13 + 7<br \/>\n5 | b + 8 | &gt; 20<br \/>\n| b + 8 | &gt; 4<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nb + 8\u00a0 &gt; 4 or b + 8 &lt; -4<br \/>\nb &gt; 4 + 8 or b &lt; -4 &#8211; 8<br \/>\nb &gt; 12 or b &lt; -12<br \/>\nWe know that,<br \/>\nThe value of absolute value expression must be greater than or equal to 0<br \/>\nSo,<br \/>\nb &gt; 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given absolute value inequality is b &gt; 12<br \/>\nThe representation of the solution of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-150.jpg\" alt=\"\" width=\"680\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-150.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-150-300x33.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Question 28.<br \/>\n| -3g &#8211; 2 | + 1 &lt; 6<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| -3g &#8211; 2 | + 1 &lt; 6<br \/>\n&#8211; | 3g + 2 | &lt; 6 &#8211; 1<br \/>\n&#8211; | 3g + 2 | &lt; 5<br \/>\n| 3g + 2 | &lt; -5<br \/>\nWe know that,<br \/>\nThe value of absolute value expression must be greater than or equal to 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution to the given absolute value inequality<\/p>\n<p>Question 29.<br \/>\n| 9 &#8211; 2j | + 10 \u2265 2<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| 9 &#8211; 2j | + 10 \u2265\u00a0 2<br \/>\n| 9 &#8211; 2j | \u2265 2 &#8211; 10<br \/>\n| 9 &#8211; 2j | \u2265\u00a0 -8<br \/>\nWe know that,<br \/>\nThe value of absolute value expression must be greater than or equal to 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution to the given absolute value inequality<\/p>\n<p>Question 30.<br \/>\nA safety regulation states that the height of a guardrail should be 106 centimeters with an absolute deviation of no more than 7 centimeters. Write and solve an absolute value inequality that represents the acceptable heights of a guardrail.<br \/>\nAnswer:<br \/>\nThe absolute value inequality that represents the acceptable heights of a guardrail is:<br \/>\n| x &#8211; 106 | \u2264 7 centimeters<\/p>\n<p>Explanation:<br \/>\nIt is given that a safety regulation states that the height of a guardrail should be 106 centimeters with an absolute deviation of no more than 7 centimeters.<br \/>\nNow,<br \/>\nWe know that,<br \/>\nAbsolute deviation = ( Mean ) &#8211; ( The given observation )<br \/>\nLet the Mean be x<br \/>\nSo,<br \/>\nAbsolute deviation = x &#8211; 106<br \/>\nHence,<br \/>\nThe absolute value inequality that represents the acceptable heights of a guardrail is:<br \/>\n| x &#8211; 106 | \u2264 7<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx &#8211; 106 \u2264 7 and x &#8211; 106 \u2265 -7<br \/>\nx \u2264 7 + 106 and x \u2265 -7 + 106<br \/>\nx \u2264 113 and x \u2265 99<br \/>\nHence, from the above,<br \/>\nWe can conclude that the absolute value inequality that represents the acceptable heights of a guardrail is:<br \/>\n| x &#8211; 106 | \u2264 7<\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Chapter_Test\"><\/a>Solving Linear Inequalities Chapter Test<\/h3>\n<p><b>Write the sentence as an inequality.<\/b><\/p>\n<p>Question 1.<br \/>\nThe sum of a number y and 9 is at least -1.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nThe sum of a number y and 9 is at least -1<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\ny + 9 \u2265 -1<\/p>\n<p>Question 2.<br \/>\nA number r is more than 0 or less than or equal to -8.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number r is more than 0 or less than or equal to -8<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nr &gt; 0 or r \u2264 -8<\/p>\n<p>Question 3.<br \/>\nA number k is less than 3 units from 10.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number k is less than 3 units from 10<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\nk &#8211; 10 &lt; 3<\/p>\n<p><b>Solve the inequality. Graph the solution, if possible.<\/b><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{x}{2}\\) &#8211; 5 \u2265 -9<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n\\(\\frac{x}{2}\\) &#8211; 5 \u2265 -9<br \/>\n\\(\\frac{x}{2}\\) \u2265 -9 + 5<br \/>\n\\(\\frac{x}{2}\\) \u2265 -4<br \/>\nx \u2265 -4 (2)<br \/>\nx \u2265 -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is x \u2265 -8<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-151.jpg\" alt=\"\" width=\"468\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-151.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-151-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 5.<br \/>\n-4s &lt; 6s + 1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-4s &lt; 6s + 1<br \/>\nSo,<br \/>\n-4s &#8211; 6s &lt; 1<br \/>\n-10s &lt; 1<br \/>\n10s &lt; -1<br \/>\ns &lt; &#8211;\\(\\frac{1}{10}\\)<br \/>\ns &lt; -0.1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is s &lt; -0.1<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-152.jpg\" alt=\"\" width=\"348\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-152.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-152-300x43.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 6.<br \/>\n4p + 3 \u2265 2(2p + 1)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4p + 3 \u2265 2 (2p + 1)<br \/>\nSo,<br \/>\n4p + 3 \u2265 2 (2p) + 2 (1)<br \/>\n4p + 3 \u2265 4p + 2<br \/>\n4p &#8211; 4p + 3 \u2265 2<br \/>\n3 \u2265 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no solution for the given inequality<\/p>\n<p>Question 7.<br \/>\n-7 &lt; 2c &#8211; 1 &lt; 10<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-7 &lt; 2c &#8211; 1 &lt; 10<br \/>\nAdd 1 on both sides<br \/>\nSo,<br \/>\n-7 + 1 &lt; 2c &#8211; 1 + 1 &lt; 10 + 1<br \/>\n-6 &lt; 2c &lt; 11<br \/>\nDivide by 3 on both sides<br \/>\n(-6 \/ 2) &lt; (2c \/ 2) &lt; (11 \/ 2)<br \/>\n-3 &lt; c &lt; 5.5<br \/>\n-3 &lt; c &lt; 6 [Approximate inequality]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is -3 &lt; c &lt; 6<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-153.jpg\" alt=\"\" width=\"468\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-153.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-153-300x26.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 8.<br \/>\n-2 \u2264 4 &#8211; 3a \u2264 13<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-2 \u2264 4 &#8211; 3a \u2264 13<br \/>\nSubtract 4 on both sides<br \/>\n-2 &#8211; 4 \u2264 4 &#8211; 4 &#8211; 3a \u2264 13 &#8211; 4<br \/>\n-6 \u2264 -3a \u2264 9<br \/>\nDivide by &#8211; on both sides<br \/>\n6 \u2265 3a \u2265 -9<br \/>\nDivide by 3 on both sides<br \/>\n(6 \/ 3) \u2265 (3a \/ 3) \u2265 (-9 \/ 3)<br \/>\n2 \u2265 a \u2265 -3<br \/>\n-3 \u2264 a \u2264 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is -3 \u2264 a \u2264 2<br \/>\nThe representation of the solution of the inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-154.jpg\" alt=\"\" width=\"468\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-154.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-154-300x27.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 9.<br \/>\n-5 &lt; 2 &#8211; h or 6h + 5 &gt; 71<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n-5 &lt; 2 &#8211; h or 6h + 5 &gt; 71<br \/>\n-5 &#8211; 2 &lt; h or 6h &gt; 71 &#8211; 5<br \/>\n-7 &lt; -h or 6h &gt; 66<br \/>\n7 &lt; h or h &gt; 66 \/ 6<br \/>\nh &gt; 7 or h &gt; 11<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is h &gt; 7 [Since h &gt; 11 is before\u00a0 h &gt; 7]<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-155.jpg\" alt=\"\" width=\"686\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-155.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-155-300x33.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 10.<br \/>\n| 2q + 8 | &gt; 4<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| 2q + 8 | &gt; 4<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n2q + 8 &gt; 4 or 2q + 8 &lt; -4<br \/>\n2q &gt; 4 &#8211; 8 or 2q &lt; -4 &#8211; 8<br \/>\n2q &gt; -4 or 2q &lt; -12<br \/>\nWe know that,<br \/>\nThe value of the absolute value expression must be greater than or equal to 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value inequality has no solution<\/p>\n<p>Question 11.<br \/>\n-2 | y &#8211; 3 | &#8211; 5 \u2265 -4<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n-2 | y &#8211; 3 | &#8211; 5 \u2265 -4<br \/>\nSo,<br \/>\n-2 | y &#8211; 3 | \u2265 -4 + 5<br \/>\n-2 | y &#8211; 3 | \u22651<br \/>\n| y &#8211; 3 | \u2265 &#8211;\\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\nThe value of the absolute value expression must be greater than or equal to 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute inequality has no solution<\/p>\n<p>Question 12.<br \/>\n4 | -3b + 5 | &#8211; 9 &lt; 7<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n4 | -3b + 5 | &#8211; 9 &lt; 7<br \/>\nSo,<br \/>\n4 | -3b + 5 | &lt; 7 + 9<br \/>\n4 | -3b + 5 | &lt; 16<br \/>\n| -3b + 5 | &lt; 16 \/ 4<br \/>\n| -3b + 5 | &lt; 4<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n-3b + 5 &lt; 4 and -3b + 5 &gt; -4<br \/>\n-3b &lt; 4 &#8211; 5 and -3b &gt; -4 &#8211; 5<br \/>\n-3b &lt; -1 and -3b &gt; -9<br \/>\n3b &lt; 1 and b &gt; 3<br \/>\nb &lt; \\(\\frac{1}{3}\\) and b &gt; 3<br \/>\nb &lt; 0 and b &gt; 3 [ Approximate value of inequality ]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given inequality are b &lt; 0 and b &gt; 3<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-156.jpg\" alt=\"\" width=\"468\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-156.jpg 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-2-156-300x28.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 13.<br \/>\nYou start a small baking business, and you want to earn a profit of at least $250 in the first month. The expenses in the first month are $155. What are the possible revenues that you need to earn to meet the profit goal?<br \/>\nAnswer:<br \/>\nThe possible revenues that you need to earn to meet the profit goal is:<br \/>\nR \u2265 $405<\/p>\n<p>Explanation:<br \/>\nIt is given that you start a small baking business, and you want to earn a profit of at least $250 in the first month. The expenses in the first month are $155.<br \/>\nNow,<br \/>\nLet<br \/>\nP is the profit<br \/>\nR is the Revenue<br \/>\nE is the expenses<br \/>\nWe know that,<br \/>\nP = R &#8211; E<br \/>\nIt is given that P \u2265 $250<br \/>\nSo,<br \/>\nR &#8211; E \u2265250<br \/>\nR &#8211; 155 \u2265 250<br \/>\nR \u2265 250 + 155<br \/>\nR \u2265 405<br \/>\nHence, from the above,<br \/>\nWe can conclude that the possible revenues that you need to earn to meet the profit goal is:<br \/>\nR \u2265 $405<\/p>\n<p>Question 14.<br \/>\nA manufacturer of bicycle parts requires that a bicycle chain have a width of 0.3 inches with an absolute deviation of at most 0.0003 inches. Write and solve an absolute value inequality that represents the acceptable widths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-96.1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 96.1\" width=\"197\" height=\"185\" \/><br \/>\nAnswer:<br \/>\nThe absolute value inequality that represents the acceptable widths is:<br \/>\n0.2997 inches \u2264 w \u22640.3003 inches<\/p>\n<p>Explanation:<br \/>\nIt is given that a manufacturer of bicycle parts requires that a bicycle chain have a width of 0.3 inches with an absolute deviation of at most 0.0003 inches.<br \/>\nWe know that,<br \/>\nAbsolute deviation = Mean &#8211; Observation<br \/>\nLet the Mean be x<br \/>\nSo,<br \/>\nx &#8211; 0.3 \u2264 0.0003<br \/>\nHence,<br \/>\nThe absolute value inequality that represents the acceptable widths is:<br \/>\n| x &#8211; 0.3 | \u2264 0.0003<br \/>\n-0.0003 \u2264 x &#8211; 0.3 \u2264 0.0003<br \/>\nAdd with 0.3 on both sides<br \/>\n-0.0003 + 0.3 \u2264 x &#8211; 0.3 + 0.3 \u2264 0.0003 + 0.3<br \/>\n0.2997 \u2264 x \u2264 0.3003<br \/>\nHence, from the above,<br \/>\nWe can conclude that the absolute value inequality that represents the acceptable widths is:<br \/>\n0.2997 inches \u2264 w \u22640.3003 inches<\/p>\n<p>Question 15.<br \/>\nLet a, b, c, and d be constants. Describe the possible solution sets of the inequality ax + b &lt; cx + d.<br \/>\nAnswer:<\/p>\n<p><b>Write and graph a compound inequality that represents the numbers that are not solutions to the inequality represented by the graph shown. Explain your reasoning.<\/b><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-97.1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 97.1\" width=\"239\" height=\"54\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-97.1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 97.1\" width=\"239\" height=\"54\" \/><br \/>\nFrom the graph,<br \/>\nThe 1st marked line starts from -3 including -3 and continued till the left end of the number line<br \/>\nThe 2nd marked line starts from 2 excluding 2 and continued till the right end of the number line<br \/>\nHence,<br \/>\nThe representation of the inequalities from the graph is:<br \/>\nx \u2264 -3 and x &gt; 2<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-98.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 98\" width=\"231\" height=\"55\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-98.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 98\" width=\"231\" height=\"55\" \/><br \/>\nFrom the graph,<br \/>\nThe marked line starts from -4 including -4 and continued till -1 including -1 to the right end of the number line<br \/>\nHence,<br \/>\nThe representation of the inequality from the graph is:<br \/>\nx \u2265 -4 and x \u2264 -1<br \/>\nHence,<br \/>\nThe representation of the inequalities in the form of compound inequality is:<br \/>\n&#8211;4 \u2264 x \u2264 -1<\/p>\n<p>Question 18.<br \/>\nA state imposes a sales tax on items of clothing that cost more than $175. The tax applies only to the difference in the price of the item and $175.<br \/>\na. Use the receipt shown to find the tax rate (as a percent).<br \/>\nb. A shopper has $430 to spend on a winter coat. Write and solve an inequality to find the prices p of coats that the shopper can afford. Assume that p \u2265 175.<br \/>\nc. Another state imposes a 5% sales tax on the entire price of an item of clothing. For which prices would paying the 5% tax to be cheaper than paying the tax described above? Write and solve an inequality to find your answer and list three prices that are solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-99.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 99\" width=\"223\" height=\"194\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\nFrom the given receipt,<br \/>\nThe price is: $295<br \/>\nThe total price is: $302.50<br \/>\nIt is given that<br \/>\nTax = Product price &#8211; $175<br \/>\nNow,<br \/>\nLet R be the tax rate<br \/>\nSo,<br \/>\nR (product price &#8211; 175) = 7.5<br \/>\nR ( 295 &#8211; 175 ) = 7.5<br \/>\nR ( 120 ) = 7.5<br \/>\n%R = \\(\\frac{7.5}{120}\\) \u00d7 100<br \/>\n%R = \\(\\frac{75}{1200}\\) \u00d7 100<br \/>\n%R = 0.0625 \u00d7 100<br \/>\n%R = 6.25%<br \/>\nHence, from the above,<br \/>\nWe can conclude that the tax rate using the receipt is: 6.25%<\/p>\n<p>b.<br \/>\nIt is given that a shopper has $430 to spend on a winter coat<br \/>\nLet p be the number of coats<br \/>\nIt is also given that to assume p \u2265 175<br \/>\nWe know that,<br \/>\nThe total price = The given price + Tax<br \/>\nSo,<br \/>\nThe representation of the inequality that represents the price of coats is:<br \/>\np + R ( p &#8211; 175 ) \u2264 430<br \/>\np + 0.0625 (p &#8211; 175)\u00a0 \u2264 430<br \/>\n1.0625p &#8211; 10.9375 \u2264 430<br \/>\n1.0625p \u2264 430 + 10.9375<br \/>\n1.0625p \u2264 440.9375<br \/>\np \u2264 440.9375 \/ 1.0625<br \/>\np \u2264 415<br \/>\nHence, from the above,<br \/>\nWe can conclude that the prices of the coats that the shopper can afford are:<br \/>\np \u2264 $415<\/p>\n<p>c.<br \/>\nIt is given that another state imposes a 5% sales tax on the entire price of an item of clothing.<br \/>\nNow,<br \/>\nLet t be the tax rate that another state-imposed<br \/>\nLet x be the price<br \/>\nSo,<br \/>\n(1+0.05) \u00d7 t \u2264 t + 0.0625 (t &#8211; 175)<br \/>\n1.05t \u2264 1.0625t &#8211; 10.9375<br \/>\n10.9375 \u2264 1.0625t &#8211; 1.05t<br \/>\n10.9375 \u2264 0.0125t<br \/>\n10.9375 \/ 0.0125 \u2264 t<br \/>\n875 \u2264 t<br \/>\nt \u2265 875<br \/>\nhence, from the above,<br \/>\nWe can conclude that $875 is cheaper<\/p>\n<h3><a id=\"Solving_Linear_Inequalities_Maintaining_Cumulative_Assessment\"><\/a>Solving Linear Inequalities Maintaining Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nThe expected attendance at a school event is 65 people. The actual attendance can vary by up to 30 people. Which equation can you use to find the minimum and maximum attendances?<br \/>\nA. | x &#8211; 65 | = 30<br \/>\nB. | x + 65 | = 30<br \/>\nC. | x &#8211; 30 | = 65<br \/>\nD. | x + 30 | = 65<br \/>\nAnswer:<br \/>\nIt is given that the expected attendance at a school event is 65 people. The actual attendance can vary by up to 30 people.<br \/>\nSo,<br \/>\nThe absolute value equation that represents the maximum and minimum attendances are:<br \/>\n| x &#8211; Expected maximum attendance | \u2264 30<br \/>\nHence,<br \/>\n| x &#8211; 65 | \u2264 30<br \/>\n| x &#8211; 65 | = 30<br \/>\nHence, from the above,<br \/>\nWe can conclude that option A represents the minimum and maximum attendances at a school event<\/p>\n<p>Question 2.<br \/>\nFill in values for a and b so that each statement is true for the inequality ax + 4 \u2264 3x + b.<br \/>\na. When a = 5 and b = _____, x \u2264 -3.<br \/>\nb. When a = _____ and b = _____, the solution of the inequality is all real numbers.<br \/>\nc. When a = _____ and b = _____, the inequality has no solution.<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\nax + 4\u00a0 \u2264 3x + b<br \/>\na.<br \/>\nWhen a = 5,<br \/>\n5x + 4 \u2264 3x + b<br \/>\n5x &#8211; 3x + 4 \u2264 b<br \/>\n2x + 4 \u2264 b<br \/>\n2x \u2264 b &#8211; 4<br \/>\nx \u2264 ( b &#8211; 4 ) \/ 2<br \/>\nSo,<br \/>\nThe solution x \u2264 -3 will be possible only if b = -2<\/p>\n<p>b.<br \/>\nThe given inequality is:<br \/>\nax + 4 \u2264 3x + b<br \/>\nCompare the like coefficients<br \/>\nHence,<br \/>\nThe values of a and b so that the solution of an inequality is all real numbers are:<br \/>\na = 3, b \u2265 4<\/p>\n<p>c.<br \/>\nThe given inequality is:<br \/>\nax + 4 \u2264 3x + b<br \/>\nHence,<br \/>\nThe values of a and b so that the inequality has no solution are:<br \/>\na = 3 and b &lt; 4<\/p>\n<p>Question 3.<br \/>\nPlace each inequality into one of the two categories.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-101.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 2 Solving Linear Inequalities 101\" width=\"527\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-101.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-2-Solving-Linear-Inequalities-101-300x157.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\nAnswer:<br \/>\nThe inequalities that have at least one integer solution must have x variable<br \/>\nThe inequalities that have no integer solution must not have x variable<br \/>\nSo,<br \/>\nThe given inequalities are:<br \/>\na. 5x &#8211; 6 + x \u2265 2x &#8211; 8<br \/>\nb. x &#8211; 8 + 4x \u2264 3 (x &#8211; 3) + 2x<br \/>\nc. 2 (3x + 8) &gt; 3 (2x + 6)<br \/>\nd. 9x &#8211; 3 &lt; 12 or 6x + 2 &gt; -10<br \/>\ne. 17 &lt; 4x + 5 &lt; 21<br \/>\nf. 5 (x &#8211; 1) \u2264 5x &#8211; 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe inequalities that have at least one integer solution are: a, d, e<br \/>\nThe inequalities that have no integer solution are: b, c, f<\/p>\n<p>Question 4.<br \/>\nAdmission to a play costs $25. A season pass costs $180.<br \/>\na. Write an inequality that represents the number x of plays you must attend for the season pass to be a better deal.<br \/>\nb. Select the number of plays for which the season pass is not a better deal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-104.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 104\" width=\"325\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-104.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-104-300x140.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that admission to a play costs $25 and a season pass costs $180<br \/>\nLet the number of plays be x<br \/>\nSo,<br \/>\nThe total number of pays = 25x<br \/>\nHence,<br \/>\nThe inequality that represents the number x of plays you must attend for the season pass to be a\u00a0 better deal is:<br \/>\n25x &gt; 180<br \/>\nx &gt; 180 \/ 25<br \/>\nx &gt; 7.2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the inequality that represents the number x of plays you must attend for the season pass to be a better deal is:<br \/>\nx &gt; 7.2<\/p>\n<p>b.<br \/>\nFrom part (a),<br \/>\nThe inequality that represents the season pas to be a better deal is:<br \/>\nx &gt; 7.2<br \/>\nSo,<br \/>\nThe inequality that represents the season pass not to be a better deal is:<br \/>\nx &lt; 7.2<br \/>\nHence, from the given numbers,<br \/>\nThe number of plays that the season pass is not a better deal is: 0, 1, 2, 3, 4, 5, 6, and 7<\/p>\n<p>Question 5.<br \/>\nSelect the values of a that make the solution of the equation 3(2x &#8211; 4) = 4(ax &#8211; 2) positive.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-105.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 105\" width=\"517\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-105.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-105-300x37.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3 (2x &#8211; 4) = 4 (ax &#8211; 2)<br \/>\nSo,<br \/>\n3 (2x) &#8211; 3 (4) = 4 (ax) &#8211; 4 (2)<br \/>\n6x &#8211; 12 = 4ax &#8211; 8<br \/>\n6x &#8211; 12 + 8 = 4ax<br \/>\n6x &#8211; 4 = 4ax<br \/>\n6x &#8211; 4ax = 4<br \/>\nx (6 &#8211; 4a) = 4<br \/>\nNow,<br \/>\nThe given numbers are: -2, -1, 0, 1, 2, 3, 4, 5<br \/>\nSo,<br \/>\nx (6 &#8211; 4(-2) ) = 4<br \/>\nx ( 6 &#8211; 4 ( -1) ) = 4<br \/>\nx ( 6 &#8211; 4(0) ) = 4<br \/>\nx ( 6 &#8211; 4(1) ) = 4<br \/>\nx ( 6 &#8211; 4 (2) ) = 4<br \/>\nx ( 6 &#8211; 4 (3) ) = 4<br \/>\nx ( 6 &#8211; 4 (4) ) = 4<br \/>\nx ( 6 &#8211; 4 (5) ) = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of a so that the solution is positive are: -2, -1, 0, 1<\/p>\n<p>Question 6.<br \/>\nFill in the compound inequality with &lt;, \u2264, \ue004, \u2265, or &gt; so the solution is shown in the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-107.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 107\" width=\"415\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-107.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-107-300x80.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\nAnswer:<br \/>\nFrom the graph,<br \/>\nThe representation of the inequality is:<br \/>\n-2 \u2264 x &lt; 3<br \/>\nNow,<br \/>\nThe given inequality is:<br \/>\n4x &#8211; 18 ____ -x &#8211; 3 and -3x &#8211; 9 _____ -3<br \/>\n4x + x ____ -3 + 18 and -3x ___ -3 + 9<br \/>\n5x ____ 15 and -3x ___ 6<br \/>\nx ____ 15 \/ 5 and x ____ -3 \/ 6<br \/>\nx ____ 3 and x ____ -2<br \/>\nHence,<br \/>\nThe blanks that can fill the inequality are:<br \/>\nx &lt; 3 and x \u2265 -2<\/p>\n<p>Question 7.<br \/>\nYou have a $250 gift card to use at a sporting goods store.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-108.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 108\" width=\"449\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-108.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-108-300x130.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><br \/>\na. Write an inequality that represents the possible numbers x of pairs of socks you can buy when you buy 2 pairs of sneakers. Can you buy 8 pairs of socks? Explain.<br \/>\nb. Describe what the inequality 60 + 80x \u2264 250 represents in this context.<br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that<br \/>\nThe cost of a pair of sneakers is: $80<br \/>\nThe cost of a pair of socks is: $12<br \/>\nIt is given that there are 2 pairs of sneakers and x pairs of socks<br \/>\nHence,<br \/>\nThe inequality that represents the possible number of x pairs of socks you can buy when you buy 2 pairs of sneakers is:<br \/>\n2 (80) + 12x \u2264 250<br \/>\n160 + 12x \u2264 250<br \/>\n12x \u2264 250 &#8211; 160<br \/>\n12x \u2264 90<br \/>\nx \u2264 90 \/ 12<br \/>\nx \u2264 7.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that you can buy only 7 pairs of socks<\/p>\n<p>b.<br \/>\nThe given inequality is:<br \/>\n60 + 8x \u2264 250<br \/>\n12 (5) + 8x \u2264 250<br \/>\nHence, from the above,<br \/>\nWe can conclude that you can buy 5 pairs of sneakers in this context<\/p>\n<p>Question 8.<br \/>\nConsider the equation shown, where a, b, c, and d are integers.<br \/>\nax + b = cx + d<br \/>\nStudent A claims the equation will always have one solution. Student B claims the equation will always have no solution. Use the numbers shown to answer parts (a)\u2013(c).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-109.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 2 Solving Linear Inequalities 109\" width=\"508\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-109.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-2-Solving-Linear-Inequalities-109-300x45.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\na. Select values for a, b, c, and d to create an equation that supports Student A\u2019s claim.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nax + b = cx + d<br \/>\nStudent A claims the equation will have always one solution<br \/>\nHence,<br \/>\nFrom the given numbers,<br \/>\nThe values of a, b, c, and d are:<br \/>\na = -1, b = 2, c = -1, d = 4<br \/>\nSo,<br \/>\nThe value of x is:<br \/>\n-x + 2 = x + 4<br \/>\n-x &#8211; x = 4 &#8211; 2<br \/>\n-2x = 2<br \/>\nx = -2 \/2<br \/>\nx = -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that according to Student A&#8217;s claim,<br \/>\nThe values of a, b, c, and d are:<br \/>\na = -1, b = 2, c = 1, d = 4<\/p>\n<p>b. Select values for a, b, c, and d to create an equation that supports Student B\u2019s claim.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nax + b = cx + d<br \/>\nStudent B claims that the equation will have no solution<br \/>\nSo,<br \/>\nThe value of x must be equal to 0<br \/>\nSo,<br \/>\na must be equal to c<br \/>\nHence,<br \/>\nThe values of a, b, c, and d are: a = c and the values of b and d will be any number from the given numbers<\/p>\n<p>c. Select values for a, b, c, and d to create an equation that shows both Student A and Student B are incorrect.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nax + b = cx + d<br \/>\nFor the claims of both Student A and Student B to be false,<br \/>\nThe given equation must have the real numbers as a solution<br \/>\nSo,<br \/>\nTo have the real numbers as a solution, the values of a and b will be arbitrary from the given numbers<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Clearing the math queries of algebra 1 concepts can be tricky for educators but we have shared an excellent guide for resolving all student&#8217;s issues while learning the concepts. 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