{"id":30687,"date":"2022-04-01T16:30:51","date_gmt":"2022-04-01T11:00:51","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=30687"},"modified":"2022-04-07T10:57:10","modified_gmt":"2022-04-07T05:27:10","slug":"big-ideas-math-answers-grade-7-chapter-4","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-4\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities"},"content":{"rendered":"<p>Hey guys!! Are you in search of the concept of Equations and Inequalities? If yes, then here is the quick material for the candidates. With the help of <strong>Big Ideas Math Grade 7 Answer Key for Chapter 4 Equations and Inequalities<\/strong>, you will get diverse opportunities, and also it provides problem-solving skills. Here, we are providing the fun learning way to Big Ideas 7th Grade Math Chapter 4 Equations and Inequalities Answer Key.<\/p>\n<p>You can also get various mathematical practices through engaging activities like literature-based exercises, games, and many others. Refer to<a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7\/\"> Big Ideas Math Answers Grade 7 <\/a>Chapter 4 Equations and Inequalities Answer Key and clear all your doubts while practicing the various concepts. Check the below sections to know the various concepts<\/p>\n<h2>Big Ideas Math Book 7th Grade Answer Key Chapter 4 Equations and Inequalities<\/h2>\n<p>The user-friendly and free edition of <em>Big Ideas Math Book Grade 7 Answer Key Chapter 4 Equations and Inequalities<\/em> are given in the below pdf links. You can find the various problems and solutions of concepts like Solving Equations Using Addition or Subtraction, Solving Equations Using Multiplication or Division, Solving Two-Step Equations, Writing and Graphing Inequalities, Solving Two-Step Inequalities, etc.<\/p>\n<p>You can improve the math and problem-solving techniques concerning chapter-wise Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities. It helps the candidates to get perfection in the topic of the Equations and Inequalities concept. <strong>Big Ideas Math Book 7th Grade Chapter 4 Equations and Inequalities Answer Key<\/strong> helps you to solve homework and assignments properly. Know the solved examples and answer keys and start your preparation.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Equations_and_Inequalities_STEAM_Video\/Performance\">Equations and Inequalities STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Equations_and_Inequalities_Getting_Ready_for_Chapter_4\">Equations and Inequalities Getting Ready for Chapter 4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Solving Equations Using Addition or Subtraction<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.1_Solving_Equations_Using_Addition_or_Subtraction\">Lesson 4.1 Solving Equations Using Addition or Subtraction<\/a><\/li>\n<li><a href=\"#Solving_Equations_Using_Addition_or_Subtraction_Homework_&amp;_Practice_4.1\">Solving Equations Using Addition or Subtraction Homework &amp; Practice 4.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Solving Equations Using Multiplication or Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.2_Solving_Equations_Using_Multiplication_or_Division\">Lesson 4.2 Solving Equations Using Multiplication or Division<\/a><\/li>\n<li><a href=\"#Solving_Equations_Using_Multiplication_or_Division_Homework_&amp;_Practice_4.2\">Solving Equations Using Multiplication or Division Homework &amp; Practice 4.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Solving Two-Step Equations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.3_Solving_Two_Step_Equations\">Lesson 4.3 Solving Two-Step Equations<\/a><\/li>\n<li><a href=\"#Solving_Two_Step_Equations_Homework_&amp;_Practice_4.3\">Solving Two-Step Equations Homework &amp; Practice 4.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Writing and Graphing Inequalities<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.4_Writing_and_Graphing_Inequalities\">Lesson 4.4 Writing and Graphing Inequalities<\/a><\/li>\n<li><a href=\"#Writing_and_Graphing_Inequalities_Homework_&amp;_Practice_4.4\">Writing and Graphing Inequalities Homework &amp; Practice 4.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Solving Inequalities Using Addition or Subtraction<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.5_Solving_Inequalities_Using_Addition_or_Subtraction\">Lesson 4.5 Solving Inequalities Using Addition or Subtraction<\/a><\/li>\n<li><a href=\"#Solving_Inequalities_Using_Addition_or_Subtraction_Homework_&amp;_Practice_4.5\">Solving Inequalities Using Addition or Subtraction Homework &amp; Practice 4.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Solving Inequalities Using Multiplication or Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.6_Solving_Inequalities_Using_Multiplication_or_Division\">Lesson 4.6 Solving Inequalities Using Multiplication or Division<\/a><\/li>\n<li><a href=\"#Solving_Inequalities_Using_Multiplication_or_Division_Homework_&amp;_Practice_4.6\">Solving Inequalities Using Multiplication or Division Homework &amp; Practice 4.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Solving Two-Step Inequalities<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.7_Solving_Two_Step_Inequalities\">Lesson 4.7 Solving Two-Step Inequalities<\/a><\/li>\n<li><a href=\"#Solving_Two_Step_Inequalities_Homework_&amp;_Practice_4.7\">Solving Two-Step Inequalities Homework &amp; Practice 4.7<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 4 &#8211; Equations and Inequalities<\/strong><\/p>\n<ul>\n<li><a href=\"#Equations_and_Inequalities_Connecting_Concepts\">Equations and Inequalities Connecting Concepts<\/a><\/li>\n<li><a href=\"#Equations_and_Inequalities_Chapter_Review\">Equations and Inequalities Chapter Review<\/a><\/li>\n<li><a href=\"#Equations_and_Inequalities_Practice_Test\">Equations and Inequalities Practice Test<\/a><\/li>\n<li><a href=\"#Equations_and_Inequalities_Cumulative_Practice\">Equations and Inequalities Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Equations_and_Inequalities_STEAM_Video\/Performance\"><\/a>Equations and Inequalities STEAM Video\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p><strong>Space Cadets<\/strong><\/p>\n<p>Inequalities can be used to help determine whether someone is quali\ufb01ed to be an astronaut. Can you think of any other real-life situations where inequalities are useful?<\/p>\n<p><strong>Watch the STEAM Video \u201cSpace Cadets.\u201d Then answer the following questions. Tori and Robert use the inequalities below to represent requirements for applying to be an astronaut, where height is measured in inches and age is measured in years.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 1\" width=\"231\" height=\"221\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-1.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 1.1\" width=\"405\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-1.1.png 405w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-1.1-300x78.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/p>\n<p>Question 1.<br \/>\nCan you use equations to correctly describe the requirements? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nYes, we can use equations to correctly describe the requirements.<\/p>\n<p>Explanation:<br \/>\nYou can take the requirements as variables and their limit as constants. So that you can use equations to correctly describe the requirements.<\/p>\n<p>Question 2.<br \/>\nThe graph shows when a person who recently had vision correction surgery can apply to be an astronaut. Explain how you can determine when they had the surgery.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 2\" width=\"369\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-2.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-2-300x41.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/p>\n<p>Answer:<br \/>\nThe person had surgery exactly 4 months ago.<\/p>\n<p>Explanation:<br \/>\nWe can say that he had eye vision correction surgery 4 months from now because the point on the graph is at 4 and the line represents months.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Distance and Brightness of the Stars<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in STEAM Video Performance Task. You will be given information about the celestial bodies below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 3\" width=\"185\" height=\"66\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 4\" width=\"290\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-4.png 290w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-4-236x300.png 236w\" sizes=\"(max-width: 290px) 100vw, 290px\" \/><br \/>\nYou will use inequalities to calculate the distances of stars from Earth and to calculate the brightnesses, or apparent magnitudes, of several stars. How do you think you can use one value to describe the brightnesses of all the stars that can be seen from Earth? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nI can take the value of brightness of all the stars that can be seen from Earth as variables. And each start brightness is assigned to that variable. Based on those stars brightness you will put an inequality symbol in between those variables.<\/p>\n<h3><a id=\"Equations_and_Inequalities_Getting_Ready_for_Chapter_4\"><\/a>Equations and Inequalities Getting Ready for Chapter 4<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>Question 1.<br \/>\nWork with a partner. Use algebra tiles to model and solve each equation. <img loading=\"lazy\" class=\"alignnone size-full wp-image-30979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 5\" width=\"102\" height=\"99\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 6\" width=\"566\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-6.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-6-300x263.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34589 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-5.png\" alt=\"big-ideas-math-answers-grade-7-chapter-4\" width=\"566\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-5.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-5-300x263.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITE GUIDELINES<\/strong><br \/>\nWork with a partner. Use your models in Exercise 1 to summarize the algebraic steps that you use to solve an equation.<\/p>\n<p>Answer:<br \/>\nThe + symbol in the yellow box represents adding 1, &#8211; symbol in the red box represents subtracting 1, + in the green box represents the variable. So, you have to represent the given equation in the form of these symbols and do calculations to get the answer.<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p><strong>The following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 7\" width=\"501\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-7.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-7-300x27.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<h3><a id=\"Lesson_4.1_Solving_Equations_Using_Addition_or_Subtraction\"><\/a>Lesson 4.1 Solving Equations Using Addition or Subtraction<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using Algebra Tiles to Solve Equations<\/strong><\/p>\n<p><strong>Work with a partner.<\/strong><br \/>\na. Use the examples to explain the meaning of each property.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 8\" width=\"420\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-8.png 420w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-8-300x93.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><br \/>\nAre these properties true for equations involving negative numbers? Explain your reasoning.<br \/>\nb. Write the four equations modeled by the algebra tiles. Explain how you can use algebra tiles to solve each equation. Then \ufb01nd the solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 9\" width=\"245\" height=\"297\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 10\" width=\"159\" height=\"195\" \/><br \/>\nc. How can you solve each equation in part(b) without using algebra tiles?<\/p>\n<p>Answer:<br \/>\na. x = -1<br \/>\nYes, algebraic properties are true for equations involving negative numbers.<br \/>\nb. x = -1, x = -7, x = 6, x = 7<\/p>\n<p>Explanation:<br \/>\na. x = 1 &#8211; 2<br \/>\nx = -1<br \/>\nb. x &#8211; 3 = -4<br \/>\nx = -4 + 3 = -1<br \/>\n-5 = x + 2<br \/>\nx = -5 &#8211; 2 = -7<br \/>\nx &#8211; 3 = 3<br \/>\nx = 3 + 3 = 6<br \/>\n5 = x &#8211; 2<br \/>\nx = 5 + 2 = 7<\/p>\n<p><strong>4.1 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\np &#8211; 5 = -2<\/p>\n<p>Answer:<br \/>\np = 3<\/p>\n<p>Explanation:<br \/>\np &#8211; 5 = -2<br \/>\nAdd 5 to both sides<br \/>\np &#8211; 5 + 5 = -2 + 5<br \/>\np = 3<br \/>\nSubstitute p = 3 in p &#8211; 5 = -2<br \/>\n3 &#8211; 5 = -2<\/p>\n<p>Question 2.<br \/>\nw + 13.2 = 10.4<\/p>\n<p>Answer:<br \/>\nw = -2.8<\/p>\n<p>Explanation:<br \/>\nw + 13.2 = 10.4<br \/>\nSubtract 13.2 from both sides<br \/>\nw + 13.2 &#8211; 13.2 = 10.4 &#8211; 13.2<br \/>\nw = -2.8<br \/>\nPutting w = -2.8 in w + 13.2 = 10.4<br \/>\n-2.8 + 13.2 = 10.4<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 11\" width=\"95\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\nx = 4\/6<\/p>\n<p>Explanation:<br \/>\nAdding 5\/6 to both sides<br \/>\nx &#8211; 5\/6 + 5\/6 = -1\/6 + 5\/6<br \/>\nx = (-1 + 5)\/6<br \/>\nx = 4\/6<br \/>\nPutting x = 4\/6 in x &#8211; 5\/6 = -1\/6<br \/>\n4\/6 &#8211; 5\/6 = -1\/6<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 4.<br \/>\nA bakery has a pro\ufb01t of $120.50 today. This pro\ufb01t is $145.25 less than the pro\ufb01t P yesterday. Write an equation that can be used to \ufb01nd P.<\/p>\n<p>Answer:<br \/>\nP = $120.50 + $145.25<br \/>\nP = $265.75<\/p>\n<p>Explanation:<br \/>\nToday profit = $120.50<br \/>\n$120.50 = &#8211; $145.25 + yesterday profit<br \/>\n$120.50 = -$145.25 + P<br \/>\nP = $120.50 + $145.25<br \/>\nP = $265.75<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 5.<br \/>\nc &#8211; 12 = -4<\/p>\n<p>Answer:<br \/>\nc = 8<\/p>\n<p>Explanation:<br \/>\nAdd 12 to both sides<br \/>\nc &#8211; 12 + 12 = -4 + 12<br \/>\nc = 8<br \/>\n8 &#8211; 12 = -4<\/p>\n<p>Question 6.<br \/>\nk + 8.4 = -6.3<\/p>\n<p>Answer:<br \/>\nk = -14.7<\/p>\n<p>Explanation:<br \/>\nSubtracting 8.4 from both sides<br \/>\nk + 8.4 &#8211; 8.4 = -6.3 &#8211; 8.4<br \/>\nk = -14.7<br \/>\n-14.7 + 8.4 = -6.3<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 12\" width=\"107\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\nw = 5\/3<\/p>\n<p>Explanation:<br \/>\nAdding 7\/3 on both sides<br \/>\n-2\/3 + 7\/3 = w &#8211; 7\/3 + 7\/3<br \/>\n(-2 + 7)\/3 = w<br \/>\nw = 5\/3<br \/>\n-2\/3 = 5\/3 &#8211; 7\/3<\/p>\n<p>Question 8.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the equations m + 3 = -5 and m &#8211; 4 = -12 equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nYes, both equations are equivalent.<\/p>\n<p>Explanation:<br \/>\nm + 3 = -5 and m &#8211; 4 = -12<br \/>\nm = -5 &#8211; 3 and m = -12 + 4<br \/>\nm = -8 and m = -8<\/p>\n<p>Question 9.<br \/>\n<strong>WHICH ONE DOESN&#8217;T BELONG?<\/strong><br \/>\nWhich equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 13\" width=\"247\" height=\"94\" \/><\/p>\n<p>Answer:<br \/>\nx + 1 = -5<\/p>\n<p>Explanation:<br \/>\nx + 3 = -1<br \/>\nx = -1 &#8211; 3 = -4<br \/>\nx + 1 = -5<br \/>\nx = -5 &#8211; 1 = -6<br \/>\nx &#8211; 2 = -6<br \/>\nx = -6 + 2 = -4<br \/>\nx &#8211; 9 = -13<br \/>\nx = -13 + 9 = -4<br \/>\nBy solving all equations, we get solution as -4, but for x + 1 = -5, we get solution as -6.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\nYou have $512.50. You earn additional money by shoveling snow. Then you purchase a new cell phone for $249.95 and have $482.55 left. How much money do you earn shoveling snow?<\/p>\n<p>Answer:<br \/>\nYou earn $220 by shoveling snow.<\/p>\n<p>Explanation:<br \/>\nLet us take additional money earned by shoveling snow as x.<br \/>\nThe total money you spend = $249.95<br \/>\n$512.50 + x &#8211; $249.95 = $482.55<br \/>\n$262.55 + x = $482.55<br \/>\nx = $482.55 &#8211; $262.55<br \/>\nx = $220<br \/>\nSo, the money earned at shoveling snow is $220<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 14\" width=\"180\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\n1.26 seconds faster is my third length than the previous record holder.<\/p>\n<p>Explanation:<br \/>\nLet us take the record at the third length as x.<br \/>\nSo, -0.23 + 0.11 + x &#8211; 0.42 = 0.72<br \/>\n-0.54 + x = 0.72<br \/>\nx = 0.72 + 0.54<br \/>\nx = 1.26<br \/>\nSo, the record at third length is 1.26 seconds.<\/p>\n<h3><a id=\"Solving_Equations_Using_Addition_or_Subtraction_Homework_&amp;_Practice_4.1\"><\/a>Solving Equations Using Addition or Subtraction Homework &amp; Practice 4.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Factor out the coefficient of the variable term.<\/strong><\/p>\n<p>Question 1.<br \/>\n4x &#8211; 20<\/p>\n<p>Answer:<br \/>\n4(x &#8211; 5)<\/p>\n<p>Explanation:<br \/>\nTake 4 as common factor out.<br \/>\n4x &#8211; 20 = 4(x &#8211; 5)<\/p>\n<p>Question 2.<br \/>\n-6y &#8211; 18<\/p>\n<p>Answer:<br \/>\n-6y &#8211; 18 = -6(y + 3)<\/p>\n<p>Explanation:<br \/>\nTake -6 as common factor out.<br \/>\n-6y &#8211; 18 = -6(y + 3)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 15\" width=\"86\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n-2\/5 w + 4\/5 = 2\/5(-w + 2)<\/p>\n<p>Explanation:<br \/>\nTake 2\/5 as common factor<br \/>\n-2\/5 w + 4\/5 = 2\/5(-w + 2)<\/p>\n<p>Question 4.<br \/>\n0.75z &#8211; 6.75<\/p>\n<p>Answer:<br \/>\n0.75z &#8211; 6.75 = 0.75(z &#8211; 6)<\/p>\n<p>Explanation:<br \/>\nTake 0.75 as common factor<br \/>\n0.75z &#8211; 6.75 = 0.75(z &#8211; 6)<\/p>\n<p><strong>Multiply or divide.<\/strong><\/p>\n<p>Question 5.<br \/>\n-7 \u00d7 8<\/p>\n<p>Answer:<br \/>\n-7 \u00d7 8 = -56<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34584 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-1.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.1-2\" width=\"139\" height=\"194\" \/><\/p>\n<p>Question 6.<br \/>\n6 \u00d7 (-12)<\/p>\n<p>Answer:<br \/>\n6 \u00d7 (-12) = -72<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34585 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-2.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.1-3\" width=\"139\" height=\"240\" \/><\/p>\n<p>Question 7.<br \/>\n18 \u00f7 (-2)<\/p>\n<p>Answer:<br \/>\n18 \u00f7 (-2) = -9<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34586 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-3.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.1-4\" width=\"108\" height=\"263\" \/><\/p>\n<p>Question 8.<br \/>\n-26 \u00f7 4<\/p>\n<p>Answer:<br \/>\n-26 \u00f7 4 = -6.5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34587 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4-4.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.1-5\" width=\"104\" height=\"261\" \/><\/p>\n<p>Question 9.<br \/>\nA class of 144 students voted for a class president. Three-fourths of the students voted for you. Of the students who voted for you, \\(\\frac{5}{9}\\) are female. How many female students voted for you?<br \/>\nA. 50<br \/>\nB. 60<br \/>\nC. 80<br \/>\nD. 108<\/p>\n<p>Answer:<br \/>\nThe number of female students voted for you is 60<\/p>\n<p>Explanation:<br \/>\nThe total number of students in class = 144<br \/>\nThree-fourths of the students voted for you = 3\/4 x 144 = 36 x 3 = 108<br \/>\nOut of 108, 5\/9 are female = 5\/9 x 108 = 12 x 5 = 60<br \/>\nTherefore, the number of female students voted for you is 60.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING ALGEBRA TILES<\/strong><br \/>\n<strong>Solve the equation using algebra tiles. Explain your reasoning.<\/strong> (See Exploration 1, p. 127.)<\/p>\n<p>Question 10.<br \/>\n6 + x = 4<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\n6 + x = 4<br \/>\nSubtract 6 from both sides<br \/>\n6 + x &#8211; 6 = 4 &#8211; 6<br \/>\nx = -2<\/p>\n<p>Question 11.<br \/>\nx &#8211; 3 = = -5<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\nAdd 3 to both sides<br \/>\nx &#8211; 3 + 3 = -5 + 3<br \/>\nx = -2<\/p>\n<p>Question 12.<br \/>\n-7 + x = -9<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\nAdd 7 to both sides<br \/>\n-7 + x + 7 = -9 + 7<br \/>\nx = -2<\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 13.<br \/>\na &#8211; 6 = 13<\/p>\n<p>Answer:<br \/>\na = 19<\/p>\n<p>Explanation:<br \/>\nAdd 6 to both sides<br \/>\na &#8211; 6 + 6 = 13 + 6<br \/>\na = 19<br \/>\nSubstituting a= 19 in a &#8211; 6 = 13<br \/>\n19 &#8211; 6 = 13<\/p>\n<p>Question 14.<br \/>\n-3 = z &#8211; 8<\/p>\n<p>Answer:<br \/>\nz = 5<\/p>\n<p>Explanation:<br \/>\nAdd 8 to both sides.<br \/>\n-3 + 8 = z &#8211; 8 + 8<br \/>\n5 = z<br \/>\nSubstituting z = 5 in -3 = z &#8211; 8<br \/>\n-3 = 5 &#8211; 8<\/p>\n<p>Question 15.<br \/>\n-14 = k + 6<\/p>\n<p>Answer:<br \/>\nk = -20<\/p>\n<p>Explanation:<br \/>\nSubtract 6 from both sides<br \/>\n-14 &#8211; 6 = k + 6 &#8211; 6<br \/>\n-20 = k<br \/>\nSubstituting k = -20 in -14 = k + 6<br \/>\n-14 = -20 + 6<\/p>\n<p>Question 16.<br \/>\nx + 4 = -14<\/p>\n<p>Answer:<br \/>\nx = -18<\/p>\n<p>Explanation:<br \/>\nSubtract 4 from both sides<br \/>\nx + 4 &#8211; 4 = -14 &#8211; 4<br \/>\nx = -18<br \/>\nSubstituting x = -18 in x + 4 = -14<br \/>\n-18 + 4 = -14<\/p>\n<p>Question 17.<br \/>\ng &#8211; 9 = -19<\/p>\n<p>Answer:<br \/>\ng = -10<\/p>\n<p>Explanation:<br \/>\nAdd 9 to both sides.<br \/>\ng &#8211; 9 + 9 = -19 + 9<br \/>\ng = -10<br \/>\nSubstituting g = -10 in g &#8211; 9 = -19<br \/>\n-10 &#8211; 9 = -19<\/p>\n<p>Question 18.<br \/>\nc &#8211; 7.6 = -4<\/p>\n<p>Answer:<br \/>\nc = 3.6<\/p>\n<p>Explanation:<br \/>\nAdd 7.6 to both sides<br \/>\nc &#8211; 7.6 + 7.6 = -4 + 7.6<br \/>\nc = 3.6<br \/>\nSubstituting c = 3.6 in c &#8211; 7.6 = -4<br \/>\n3.6 &#8211; 7.6 = -4<\/p>\n<p>Question 19.<br \/>\n-10.1 = w + 5.3<\/p>\n<p>Answer:<br \/>\nw = -15.4<\/p>\n<p>Explanation:<br \/>\nSubtract 5.3 from both sides<br \/>\n-10.1 &#8211; 5.3 = w + 5.3 &#8211; 5.3<br \/>\n-15.4 = w<br \/>\nSubstituting w = -15.4 in -10.1 = w + 5.3<br \/>\n-10.1 = -15.4 + 5.3<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 16\" width=\"94\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\nq = -1\/6<\/p>\n<p>Explanation:<br \/>\nSubtract 2\/3 from both sides<br \/>\n1\/2 &#8211; 2\/3 = q + 2\/3 &#8211; 2\/3<br \/>\n(3 &#8211; 4)\/6 = q<br \/>\nq = -1\/6<br \/>\nSubstituting q = -1\/6 in 1\/2 &#8211; 2\/3 = q + 2\/3 &#8211; 2\/3<br \/>\n1\/2 = -1\/6 + 2\/3<br \/>\n= (-1 + 4)\/6 = 3\/6 = 1\/2<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 17\" width=\"122\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\np = 4\/6<\/p>\n<p>Explanation:<br \/>\np &#8211; 19\/6 = -5\/2<br \/>\nAdding 19\/6 to both sides<br \/>\np &#8211; 19\/6 + 19\/6 = -5\/2 + 19\/6<br \/>\np = (-15 + 19)\/6<br \/>\np = 4\/6<br \/>\nSubstituting p = 4\/6 in p &#8211; 19\/6 = -5\/2<br \/>\n4\/6 &#8211; 19\/6 = -5\/2<br \/>\n(-15\/6) = -\/2<\/p>\n<p>Question 22.<br \/>\n-9.3 = d &#8211; 3.4<\/p>\n<p>Answer:<br \/>\nd = -5.9<\/p>\n<p>Explanation:<br \/>\nAdd 3.4 to both sides<br \/>\n-9.3 + 3.4 = d &#8211; 3.4 + 3.4<br \/>\nd = -5.9<br \/>\nSubstituting d = -5.9 in -9.3 = d &#8211; 3.4<br \/>\n-9.3 = -5.9 &#8211; 3.4<\/p>\n<p>Question 23.<br \/>\n4.58 + y = 2.5<\/p>\n<p>Answer:<br \/>\ny = -2.08<\/p>\n<p>Explanation:<br \/>\nSubtract 4.58 from both sides<br \/>\n4.58 + y &#8211; 4.58 = 2.5 &#8211; 4.58<br \/>\ny = -2.08<br \/>\nPutting y = -2.08 in 4.58 + y = 2.5<br \/>\n4.58 &#8211; 2.08 = 2.5<\/p>\n<p>Question 24.<br \/>\nx &#8211; 5.2 = -18.73<\/p>\n<p>Answer:<br \/>\nx = -13.53<\/p>\n<p>Explanation:<br \/>\nAdd 5.2 to both sides<br \/>\nx &#8211; 5.2 + 5.2 = -18.73 + 5.2<br \/>\nx = -13.53<br \/>\nPutting x = -13.53 in x &#8211; 5.2 = -18.73<br \/>\n-13.53 &#8211; 5.2 = -18.73<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 18\" width=\"85\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\nq = 10\/9<\/p>\n<p>Explanation:<br \/>\nSubtract 5\/9 from both sides<br \/>\nq + 5\/9 &#8211; 5\/9 = 5\/6 &#8211; 5\/9<br \/>\nq = (15 &#8211; 5)\/9 = 10\/9<br \/>\nSubstituting q = 10\/9 in q + 5\/9 = 5\/6<br \/>\n10\/9 + 5\/9 = 15\/9 = 5\/6<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 19\" width=\"106\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\nr = -19\/20<\/p>\n<p>Explanation:<br \/>\n-7\/4 = r &#8211; 4\/5<br \/>\nAdding 4\/5 to both sides<br \/>\n-7\/4 + 4\/5 = r &#8211; 4\/5 + 4\/5<br \/>\n(-35 + 16)\/20 = r<br \/>\nr = -19\/20<br \/>\nPutting r = -19\/20 in -7\/4 = r &#8211; 4\/5<br \/>\n-7\/4 = -19\/20 &#8211; 4\/5<br \/>\n= (-19 &#8211; 16)\/20 = -35\/20 = -7\/4<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 20\" width=\"111\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\nw = -74\/48<\/p>\n<p>Explanation:<br \/>\nw + 27\/8 = 11\/6<br \/>\nSubtract 27\/8 from both sides<br \/>\nw + 27\/8 &#8211; 27\/8 = 11\/6 &#8211; 27\/8<br \/>\nw = (88 &#8211; 162)\/48<br \/>\nw = -74\/48<br \/>\nPutting w = -74\/48 in w + 27\/8 = 11\/6<br \/>\n-74\/48 + 27\/8<br \/>\n(-74 + 162)\/48 = 88\/48 = 11\/6<\/p>\n<p>Question 28.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the equation x + 8 = 10. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 21\" width=\"185\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is not correct.<\/p>\n<p>Explanation:<br \/>\nx + 8 = 10<br \/>\nx = 10 &#8211; 8<br \/>\nx = 2<br \/>\nThe above mentioned is the correct solution. As my friend taken x + 8 = -10, there she did mistake.<\/p>\n<p><strong>WRITING AND SOLVING AN EQUATION<\/strong><br \/>\n<strong>Write the word sentence as an equation. Then solve the equation.<\/strong><\/p>\n<p>Question 29.<br \/>\n4 less than a number n is -15.<\/p>\n<p>Answer:<br \/>\n4 &#8211; n = -15<br \/>\nn = 19<\/p>\n<p>Explanation:<br \/>\nAs 4 is less than a number n subtract 4 from n.<br \/>\n4 &#8211; n = -15<br \/>\nAdd n to sides of the equation<br \/>\n4 &#8211; n + n = -15 + n<br \/>\n4 = -15 + n<br \/>\nAdd 15 to both sides<br \/>\n4 + 15 = -15 + n + 15<br \/>\nn = 19<\/p>\n<p>Question 30.<br \/>\n10 more than a number c is 3.<\/p>\n<p>Answer:<br \/>\n10 + c = 3<br \/>\nc = -7<\/p>\n<p>Explanation:<br \/>\nAs 10 is more than c add 10 to c<br \/>\n10 + c = 3<br \/>\nSubtract 10 from both sides<br \/>\n10 + c &#8211; 10 = 3 &#8211; 10<br \/>\nc = -7<\/p>\n<p>Question 31.<br \/>\nThe sum of a number y and -3 is -8.<\/p>\n<p>Answer:<br \/>\ny &#8211; 3 = -8<br \/>\ny = -5<\/p>\n<p>Explanation:<br \/>\ny + (-3) = -8<br \/>\ny &#8211; 3 = -8<br \/>\ny &#8211; 3 + 3 = -8 + 3<br \/>\ny = -5<\/p>\n<p>Question 32.<br \/>\nThe difference of a number p and 6 is 14.<\/p>\n<p>Answer:<br \/>\np &#8211; 6 = 14<br \/>\np = 20<\/p>\n<p>Explanation:<br \/>\np &#8211; 6 = 14<br \/>\np &#8211; 6 + 6 = 14 + 6<br \/>\np = 20<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe temperature of dry ice is -109.3\u00b0F. This is 184.9\u00b0F less than the outside temperature. Write and solve an equation to \ufb01nd the outside temperature.<\/p>\n<p>Answer:<br \/>\n-109.3\u00b0F = x &#8211; 184.9\u00b0F<br \/>\nOutside temperature is -24.4\u00b0F.<\/p>\n<p>Explanation:<br \/>\nThe temperature of dry ice = -109.3\u00b0F<br \/>\nLet us take the outside temperature as x.<br \/>\ndry ice is 84.9\u00b0F less than the outside temperature<br \/>\n-109.3\u00b0F = x &#8211; 184.9\u00b0F<br \/>\nx = -109.3\u00b0F + 184.9\u00b0F<br \/>\nx = 75.6\u00b0F<br \/>\nTherefore, Outside temperature is -24.4\u00b0F<\/p>\n<p>Question 34.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA company makes a pro\ufb01t of $1.38 million. This is $2.54 million more than last year. What was the pro\ufb01t last year? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe last year company got $1.16 millions loss.<\/p>\n<p>Explanation:<br \/>\nA company makes a pro\ufb01t of $1.38 million<br \/>\nLet us take last year profit as p.<br \/>\np + $2.54 = $1.38<br \/>\np = $1.38 &#8211; $2.54<br \/>\np = -$1.16<br \/>\nThe last year company was at a loss of $1.16 million.<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe difference in elevation of a helicopter and a submarine is 18\\(\\frac{1}{2}\\) meters. The elevation of the submarine is -7\\(\\frac{3}{4}\\) meters. What is the elevation of the helicopter? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe elevation of the helicopter is 49\/4 meters.<\/p>\n<p>Explanation:<br \/>\nLet us take the elevation of the helicopter as x.<br \/>\nThe elevation of the submarine = -7(3\/4) = -25\/4<br \/>\nx &#8211; 18(1\/2) = -25\/4<br \/>\nx &#8211; 37\/2 = -25\/4<br \/>\nx = -25\/4 + 37\/2<br \/>\nx = (-25 + 74)\/4 = 49\/4<br \/>\nSo, the elevation of the helicopter is 49\/4<\/p>\n<p><strong>GEOMETRY<\/strong><br \/>\n<strong>What is the unknown side length?<\/strong><\/p>\n<p>Question 36.<br \/>\nPerimeter = 12 cm<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-21.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 21.1\" width=\"144\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown side length is 4 cm.<\/p>\n<p>Explanation:<br \/>\nLet us take the unknown side length as x cm.<br \/>\nPerimeter = 12 cm<br \/>\nx + 3 + 5 = 12<br \/>\nx + 8 = 12<br \/>\nx = 12 &#8211; 8<br \/>\nx = 4 cm<\/p>\n<p>Question 37.<br \/>\nPerimeter = 24.2 in.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-21.2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 21.2\" width=\"185\" height=\"94\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown side length is 3.8 in.<\/p>\n<p>Explanation:<br \/>\nLet us take the unknown side length as x inches<br \/>\nPerimeter = 24.2 in.<br \/>\nx + 8.3 + 3.8 + 8.3 = 24.2<br \/>\nx + 20.4 = 24.2<br \/>\nx = 24.2 &#8211; 20.4<br \/>\nx = 3.8 in<\/p>\n<p>Question 38.<br \/>\nPerimeter = 34.6 ft<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 22\" width=\"199\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown side length is 11.9 ft<\/p>\n<p>Explanation:<br \/>\nLet us take the unknown side length as x ft.<br \/>\nPerimeter = 34.6 ft<br \/>\n5.2 + 11.1 + 6.4 + x = 34.6<br \/>\n22.7 + x = 34.6<br \/>\nx = 34.6 &#8211; 22.7<br \/>\nx = 11.9 ft<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe total height of the Statue of Liberty and its pedestal is 153 feet more than the height of the statue. What is the height of the statue? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 23\" width=\"136\" height=\"275\" \/><\/p>\n<p>Answer:<br \/>\nThe height of statue is 152 feet.<\/p>\n<p>Explanation:<br \/>\nLet us take the height of the statue as x feet.<br \/>\nThe total height of the Statue of Liberty and its pedestal = x + 153<br \/>\n305 = x + 153<br \/>\nx = 305 &#8211; 153<br \/>\nx = 152 feet<br \/>\nSo, the height of statue is 152 feet.<\/p>\n<p>Question 40.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWhen bungee jumping, you reach a positive elevation on your \ufb01rst jump that is 50\\(\\frac{1}{6}\\) feet greater than the elevation you reach on your second jump. Your change in elevation on the \ufb01rst jump is -200\\(\\frac{2}{3}\\)feet. What is your change in elevation on the second jump?<\/p>\n<p>Answer:<br \/>\nThe height of second jump is 301\/2 feet.<\/p>\n<p>Explanation:<br \/>\nThe height of the first jump = 200(2\/3) = 602\/3<br \/>\nThe height of second jump = The height of the first jump &#8211; 50(1\/6)<br \/>\n= -602\/3 &#8211; 301\/6<br \/>\n= (1204 &#8211; 301)\/6 = 903\/6 = 301\/2<br \/>\nThe height of second jump is 301\/2 feet.<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nBoatesville is a 65\\(\\frac{3}{5}\\)-kilometer drive from Stanton. A bus traveling from Stanton to Boatesville is 24 \\(\\frac{1}{3}\\) kilometers from Boatesville. How far has the bus traveled? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe bus travelled 619\/5 km from Boatesville.<\/p>\n<p>Explanation:<br \/>\nThe distance between Boatesville and stanton = 65(3\/5) = 328\/5<br \/>\nThe distance between Stanton and bus = 24(1\/3) = 73\/3<br \/>\nThe bus travelled = 328\/5 &#8211; 73\/3 = (984 &#8211; 365)\/15<br \/>\n= 619\/15<\/p>\n<p>Question 42.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe sum of the measures of the angles of a triangle equals 180\u00b0. What is the missing angle measure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 24\" width=\"216\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nMissing angle is 108.9\u00b0.<\/p>\n<p>Explanation:<br \/>\nThe sum of the measures of the angles of a triangle equals 180\u00b0<br \/>\n30.3 + m + 40.8 = 180<br \/>\n71.1 + m = 180<br \/>\nm = 180 &#8211; 71.1 = 108.9\u00b0<\/p>\n<p>Question 43.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows your scores in a skateboarding competition. The \ufb01rst-place \ufb01nisher scores 311.62 total points, which is 4.72 more points than you score. What is your score in the fourth round?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 25\" width=\"286\" height=\"66\" \/><\/p>\n<p>Answer:<br \/>\nYour score in the fourth round is 74.36 points.<\/p>\n<p>Explanation:<br \/>\nThe \ufb01rst-place \ufb01nisher scores 311.62 total points, which is 4.72 more points than you score<br \/>\n63.43 + 87.15 + 81.96 + x + 4.72 = 311.62<br \/>\nx + 237.26 = 311.62<br \/>\nx = 311.62 &#8211; 237.26<br \/>\nx = 74.36<\/p>\n<p>Question 44.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nFind the value of 2x &#8211; 1 when x + 6 = -2.<\/p>\n<p>Answer:<br \/>\n2x &#8211; 1 = -17<\/p>\n<p>Explanation:<br \/>\nx + 6 = -2<br \/>\nx = -2 &#8211; 6<br \/>\nx = -8<br \/>\nputting x = -8 in 2x &#8211; 1<br \/>\n2(-8) &#8211; 1 = -16 &#8211; 1 = -17<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\n<strong>Solve the equation.<\/strong><\/p>\n<p>Question 45.<br \/>\n| x | = 2<\/p>\n<p>Answer:<br \/>\nx = \u00b1 2<\/p>\n<p>Explanation:<br \/>\nWhen mod x is 2, then x is plus or minus 2.<\/p>\n<p>Question 46.<br \/>\n| x | &#8211; 2 = -2<\/p>\n<p>Answer:<br \/>\nx = 0<\/p>\n<p>Explanation:<br \/>\n| x | = -2 + 2<br \/>\n| x | = 0<\/p>\n<p>Question 47.<br \/>\n| x | + 5 = 18<\/p>\n<p>Answer:<br \/>\nx = \u00b1 13<\/p>\n<p>Explanation:<br \/>\n| x | = 18 &#8211; 5<br \/>\n| x | = 13<br \/>\nx = \u00b1 13<\/p>\n<h3><a id=\"Lesson_4.2_Solving_Equations_Using_Multiplication_or_Division\"><\/a>Lesson 4.2 Solving Equations Using Multiplication or Division<\/h3>\n<p><strong>EXPLORATION 1<br \/>\nUsing Algebra Tiles to Solve Equations<\/strong><\/p>\n<p><strong>Work with a partner.<\/strong><br \/>\na. Use the examples to explain the meaning of each property.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 26\" width=\"393\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-26.png 393w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-26-300x115.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><br \/>\nAre these properties true for equations involving negative numbers? Explain your reasoning.<br \/>\nb. Write the three equations modeled by the algebra tiles. Explain how you can use algebra tiles to solve each equation. Then \ufb01nd the solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-27.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 27\" width=\"230\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-27.png 230w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-27-214x300.png 214w\" sizes=\"(max-width: 230px) 100vw, 230px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-28.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 28\" width=\"163\" height=\"178\" \/><br \/>\nc. How can you solve each equation in part(b) without using algebra tiles?<\/p>\n<p><strong>4.2 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{x}{5}\\) = -2<\/p>\n<p>Answer:<br \/>\nx = -10<\/p>\n<p>Explanation:<br \/>\nx\/5 = -2<br \/>\nx = -2 x 5<br \/>\nx = -10<br \/>\nPutting x = -10 in x\/5 = -2<br \/>\n-10\/5 = -2<\/p>\n<p>Question 2.<br \/>\n-a = -24<\/p>\n<p>Answer:<br \/>\na = 24<\/p>\n<p>Explanation:<br \/>\na = 24<\/p>\n<p>Question 3.<br \/>\n3 = -1.5n<\/p>\n<p>Answer:<br \/>\nn = -2<\/p>\n<p>Explanation:<br \/>\nn = -3\/1.5<br \/>\nn = -2<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n&#8211;\\(\\frac{8}{5}\\)b = 5<\/p>\n<p>Answer:<br \/>\nb = -25\/8<\/p>\n<p>Explanation:<br \/>\n-8\/5 b = 5<br \/>\n-b = 5 x (5\/8)<br \/>\n-b = 25\/8<br \/>\nb = -25\/8<br \/>\nSubstituting b = -25\/8 in -8\/5 b = 5<br \/>\n-8\/5 (-25\/8) = (25 x 8)\/(8 x 5) = 5<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{3}{8}\\)h = -9<\/p>\n<p>Answer:<br \/>\nh = -24<\/p>\n<p>Explanation:<br \/>\n3\/8 h = -9<br \/>\nh = -9 x (8\/3)<br \/>\nh = -3 x 8 = -24<br \/>\nSubstituting h = -24 in 3\/8 h = -9<br \/>\n3\/8 (-24) = 3 x -3 = -9<\/p>\n<p>Question 6.<br \/>\n-14 = \\(\\frac{2}{3}\\)x<\/p>\n<p>Answer:<br \/>\nx = -21<\/p>\n<p>Explanation:<br \/>\n-14 = (2\/3) x<br \/>\nx = -14 x (3\/2)<br \/>\nx = -7 x 3 = -21<br \/>\nSubstituting x = -21 in -14 = (2\/3) x<br \/>\n-14 = (2\/3) -21 = 2 x -7<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 7.<br \/>\n6d = 24<\/p>\n<p>Answer:<br \/>\nd = 4<\/p>\n<p>Explanation:<br \/>\n6d = 24<br \/>\nd = 24\/6<br \/>\nd = 4<br \/>\nPutting d = 4 in 6d = 24<br \/>\n6 x 4 = 24<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{t}{3}\\) = -4<\/p>\n<p>Answer:<br \/>\nt = -12<\/p>\n<p>Explanation:<br \/>\nt\/3 = -4<br \/>\nt = -4 x 3<br \/>\nt = -12<br \/>\nPutting t = -12 in t\/3 = -4<br \/>\n-12\/3 = -4<\/p>\n<p>Question 9.<br \/>\n&#8211;\\(\\frac{2}{5}\\)p = -6<\/p>\n<p>Answer:<br \/>\np = 15<\/p>\n<p>Explanation:<br \/>\n(-2\/5) p = -6<br \/>\np = -6 x (-5\/2)<br \/>\np = 3 x 5 = 15<br \/>\nPutting p = 15 in (-2\/5) p = -6<br \/>\n(-2\/5) 15 = -2 x 3 = -6<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why you can use multiplication to solve equations involving division.<\/p>\n<p>Answer:<br \/>\nMultiplication is the inverse of division. So it can easily undo the operation.<\/p>\n<p>Question 11.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the equations \\(\\frac{2}{3}\\)m = -4 and -4m = 24 equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nBoth the given equations are equivalent.<\/p>\n<p>Explanation:<br \/>\n(2\/3)m = -4 and -4m = 24<br \/>\nm = -4 x (3\/2) and m = -24\/4<br \/>\nm = -2 x 3 and m = -6<br \/>\nm = -6 and m = -6<br \/>\nYes both the equations are equivalent.<\/p>\n<p>Question 11.<br \/>\n<strong>REASONING<\/strong><br \/>\nDescribe the inverse operation that will undo the given operation.<\/p>\n<p>Answer:<br \/>\nThe inverse operation of division is the multiplication and they are opposite. When dividing a number by a, the multiplication by a will undo the operation.<\/p>\n<p>Question 12.<br \/>\nsubtracting 12<\/p>\n<p>Answer:<br \/>\nAdding 12.<\/p>\n<p>Explanation:<br \/>\nThe inverse operation of subtraction is addition.<\/p>\n<p>Question 13.<br \/>\nmultiplying by &#8211;\\(\\frac{1}{8}\\)<\/p>\n<p>Answer:<br \/>\nDividing by (-8)<\/p>\n<p>Explanation:<br \/>\nThe inverse operation of multiplication is division. So, dividing by (-8)<\/p>\n<p>Question 14.<br \/>\nadding -6<\/p>\n<p>Answer:<br \/>\nSubtracting -6<\/p>\n<p>Explanation:<br \/>\nThe inverse operation for addition is subtraction. So, subtracting -6.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 15.<br \/>\nThe elevation of the surface of a lake is 315 feet. During a drought, the water level of the lake changes -3\\(\\frac{1}{5}\\) feet per week. Find how long it takes for the surface of the lake to reach an elevation of 299 feet. Justify your answer.<\/p>\n<p>Answer:<br \/>\nIt takes 5 weeks for the surface of the lake to reach an elevation of 299 feet<\/p>\n<p>Explanation:<br \/>\nLet us take the number of weeks as x.<br \/>\nThe lake reduced = 315 &#8211; 299 = 16 feet<br \/>\n-3(1\/5)x = 16<br \/>\n-16\/5 x = 16<br \/>\nx = -16 (5\/16)<br \/>\nx = 5<br \/>\nIt takes 5 weeks for the surface of the lake to reach an elevation of 299 feet<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe patio shown has an area of 116 square feet. What is the value of h? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-29.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 29\" width=\"256\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nh = 8<\/p>\n<p>Explanation:<br \/>\nTotal area = 116<br \/>\nTriangle 1 + rectangle + triangle2 = 116<br \/>\n1\/2 x 4.5 x h + 10 x h + 1\/2 x 4.5 x h = 116<br \/>\n10h + 4.5h = 116<br \/>\n14.5h = 116<br \/>\nh = 116\/14.5 = 8<\/p>\n<h3><a id=\"Solving_Equations_Using_Multiplication_or_Division_Homework_&amp;_Practice_4.2\"><\/a>Solving Equations Using Multiplication or Division Homework &amp; Practice 4.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\nn &#8211; 9 = -12<\/p>\n<p>Answer:<br \/>\nn = -3<\/p>\n<p>Explanation:<br \/>\nn = -12 + 9<br \/>\nn = -3<br \/>\nPutting n = -3 in n &#8211; 9 = -12<br \/>\n-3 &#8211; 9 = -12<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-30.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 30\" width=\"100\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\nm = 5\/4<\/p>\n<p>Explanation:<br \/>\n-1\/2 = m &#8211; (7\/4)<br \/>\nm = -1\/2 + 7\/4<br \/>\nm = (-2 + 7)\/4 = 5\/4<br \/>\nPutting m = 5\/4 in -1\/2 = m &#8211; (7\/4)<br \/>\n-1\/2 = 5\/4 &#8211; (7\/4) = (5 &#8211; 7)\/4<br \/>\n= -2\/4 = -1\/2<\/p>\n<p>Question 3.<br \/>\n-6.4h = h + 8.7<\/p>\n<p>Answer:<br \/>\nh = -1.75<\/p>\n<p>Explanation:<br \/>\n-6.4h = h + 8.7<br \/>\nh + 6.4h = -8.7<br \/>\n7.4h = -8.7<br \/>\nh = -8.7\/7.4<br \/>\nh = -1.75<br \/>\nPutting h = -1.175 in -6.4h = h + 8.7<br \/>\n-6.4 x -1.175 = -1.175 + 8.7<br \/>\n7.52 = 7.52<\/p>\n<p><strong>Find the difference.<\/strong><\/p>\n<p>Question 4.<br \/>\n5 &#8211; 12<\/p>\n<p>Answer:<br \/>\n-7<\/p>\n<p>Explanation:<br \/>\n5 &#8211; 12 = -7<\/p>\n<p>Question 5.<br \/>\n-7 &#8211; 2<\/p>\n<p>Answer:<br \/>\n-9<\/p>\n<p>Explanation:<br \/>\n-7 &#8211; 2 = -9<\/p>\n<p>Question 6.<br \/>\n4 &#8211; (-8)<\/p>\n<p>Answer:<br \/>\n12<\/p>\n<p>Explanation:<br \/>\n4 &#8211; (-8) = 4 + 8 = 12<\/p>\n<p>Question 7.<br \/>\n-14 &#8211; (-5)<\/p>\n<p>Answer:<br \/>\n-9<\/p>\n<p>Explanation:<br \/>\n-14 &#8211; (-5) = -14 + 5 = -9<\/p>\n<p>Question 8.<br \/>\nOf the 120 apartments in a building, 75 have been scheduled to receive new carpet. What percent of the apartments have not been scheduled to receive new carpet?<br \/>\nA. 25%<br \/>\nB. 37.5%<br \/>\nC. 62.5%<br \/>\nD. 75%<\/p>\n<p>Answer:<br \/>\nB<\/p>\n<p>Explanation:<br \/>\nTotal number of apartments = 120<br \/>\nThe number of apartments has not been scheduled to receive new carpet = 120 &#8211; 75 = 45<br \/>\nPercentage = (45\/120) x 100 = 37.5%<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>USING ALGEBRA TILES<\/strong><br \/>\n<strong>Solve the equation using algebra tiles. Explain your reasoning.<\/strong> (See Exploration 1, p. 133.)<\/p>\n<p>Question 9.<br \/>\n4x = -16<\/p>\n<p>Answer:<br \/>\nx = -4<\/p>\n<p>Explanation:<br \/>\n4x = -16<br \/>\nx = -16\/4 = -4<\/p>\n<p>Question 10.<br \/>\n2x = -6<\/p>\n<p>Answer:<br \/>\nx = -3<\/p>\n<p>Explanation:<br \/>\n2x = -6<br \/>\nx = -6\/2 = -3<\/p>\n<p>Question 11.<br \/>\n-5x = -20<\/p>\n<p>Answer:<br \/>\nx = 4<\/p>\n<p>Explanation:<br \/>\n-5x = -20<br \/>\n5x = 20<br \/>\nx = 20\/5 = 4<\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 12.<br \/>\n4x = -16<\/p>\n<p>Answer:<br \/>\nx = -4<\/p>\n<p>Explanation:<br \/>\n4x = -16<br \/>\nx = -16\/4 = -4<br \/>\nPutting x = -4 in 4x = -16<br \/>\n4(-4) = -16<\/p>\n<p>Question 13.<br \/>\n2x = -6<\/p>\n<p>Answer:<br \/>\nx = -3<\/p>\n<p>Explanation:<br \/>\n2x = -6<br \/>\nx = -6\/2 = -3<br \/>\nPutting x = -3 in 2x = -6<br \/>\n2(-3) = -6<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{n}{2}\\) = -7<\/p>\n<p>Answer:<br \/>\nn = -14<\/p>\n<p>Explanation:<br \/>\nn\/2 = -7<br \/>\nn = -7 x 2 = -14<br \/>\nPutting n = -14 in n\/2 = -7<br \/>\n-14\/2 = -7<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{k}{-3}\\) = 9<\/p>\n<p>Answer:<br \/>\nk = -27<\/p>\n<p>Explanation:<br \/>\nk\/-3 = 9<br \/>\nk = 9 x -3 = -27<br \/>\nPutting k = -27 in k\/-3 = 9<br \/>\n-27\/-3 = 9<\/p>\n<p>Question 16.<br \/>\n5m = -10<\/p>\n<p>Answer:<br \/>\nm = -2<\/p>\n<p>Explanation:<br \/>\nm = -10\/5<br \/>\nm = -2<br \/>\nPutting m = -2 in 5m = -10<br \/>\n5(-2) = -10<\/p>\n<p>Question 17.<br \/>\n8t = -32<\/p>\n<p>Answer:<br \/>\nt = -4<\/p>\n<p>Explanation:<br \/>\nt = -32\/8 = -4<br \/>\nPutting t = -4 in 8t = -32<br \/>\n8(-4) = -32<\/p>\n<p>Question 18.<br \/>\n-0.2x = 1.6<\/p>\n<p>Answer:<br \/>\nx = -8<\/p>\n<p>Explanation:<br \/>\n-0.2x = 1.6<br \/>\nx = -1.6\/0.2<br \/>\nx = -8<br \/>\nPutting x = -8 in -0.2x = 1.6<br \/>\n-0.2 (-8) = 1.6<\/p>\n<p>Question 19.<br \/>\n-10 = &#8211;\\(\\frac{b}{4}\\)<\/p>\n<p>Answer:<br \/>\nb = 40<\/p>\n<p>Explanation:<br \/>\n-10 = -(b\/4)<br \/>\nb\/4 = 10<br \/>\nb = 10 x 4 = 40<br \/>\nPutting b = 40 in -10 = -(b\/4)<br \/>\n-10 = -(40\/4) = -10<\/p>\n<p>Question 20.<br \/>\n-6p = 48<\/p>\n<p>Answer:<br \/>\np = -8<\/p>\n<p>Explanation:<br \/>\n-6p = 48<br \/>\np = -48\/6 = -8<br \/>\nPutting p = -8 in -6p = 48<br \/>\n-6(-8) = 48<\/p>\n<p>Question 21.<br \/>\n-72 = 8d<\/p>\n<p>Answer:<br \/>\nd = -9<\/p>\n<p>Explanation:<br \/>\n-72 = 8d<br \/>\nd = -72\/8<br \/>\nd = -9<br \/>\nPutting d = -9 in -72 = 8d<br \/>\n-72 = 8 (-9)<\/p>\n<p>Question 22.<br \/>\n\\(\\frac{n}{1.6}\\) = 5<\/p>\n<p>Answer:<br \/>\nn = 8<\/p>\n<p>Explanation:<br \/>\nn\/1.6 = 5<br \/>\nn = 1.6 x 5<br \/>\nn = 8<br \/>\nPutting n = 8 in n\/1.6 = 5<br \/>\n8\/1.6 = 80\/16 = 5<\/p>\n<p>Question 23.<br \/>\n-14.4 = -0.6p<\/p>\n<p>Answer:<br \/>\np = 24<\/p>\n<p>Explanation:<br \/>\n-14.4 = -0.6p<br \/>\n0.6p = 14.4<br \/>\np = 14.4\/0.6<br \/>\np = 144\/6 = 24<br \/>\nPutting p = 24 in -14.4 = -0.6p<br \/>\n-14.4 = -0.6 x 24<\/p>\n<p>Question 24.<br \/>\n\\(\\frac{3}{4}\\)g = -12<\/p>\n<p>Answer:<br \/>\ng = -16<\/p>\n<p>Explanation:<br \/>\n(3\/4)g = -12<br \/>\n3g = -12 x 4<br \/>\n3g = -48<br \/>\ng = -48\/3<br \/>\ng = -16<br \/>\nPutting g = -16 in (3\/4)g = -12<br \/>\n(3\/4) x (-16) = 3 x -4 = -12<\/p>\n<p>Question 25.<br \/>\n8 = &#8211;\\(\\frac{2}{5}\\)c<\/p>\n<p>Answer:<br \/>\nc = -20<\/p>\n<p>Explanation:<br \/>\n8 = -(2\/5)c<br \/>\n-2c = 8 x 5 = 40<br \/>\n2c = -40<br \/>\nc = -40\/2 = -20<br \/>\nPutting c = -20 in 8 = -(2\/5)c<br \/>\n8 = -(2\/5) x -20 = (2\/5)20 = 2 x 4<br \/>\n= 8<\/p>\n<p>Question 26.<br \/>\n&#8211;\\(\\frac{4}{9}\\)f = -3<\/p>\n<p>Answer:<br \/>\nf = 27\/4<\/p>\n<p>Explanation:<br \/>\n-(4\/9)f = -3<br \/>\n(4\/9)f = 3<br \/>\n4f = 3 x 9 = 27<br \/>\nf = 27\/4<br \/>\nPutting f = 27\/4 in -(4\/9)f = -3<br \/>\n-(4\/9) x (27\/4) = -27\/9 = -3<\/p>\n<p>Question 27.<br \/>\n26 = &#8211;\\(\\frac{8}{5}\\)y<\/p>\n<p>Answer:<br \/>\ny = -130\/8<\/p>\n<p>Explanation:<br \/>\n26 = -(8\/5)y<br \/>\n-8y = 26 x 5 = 130<br \/>\ny = -130\/8<br \/>\nPutting y = -65\/4 in 26 = -(8\/5)y<br \/>\n26 = -(8\/5) x (-130\/8) = 130\/5 = 26<\/p>\n<p>Question 28.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the equation -4.2x = 21. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-31.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 31\" width=\"156\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is wrong.<\/p>\n<p>Explanation:<br \/>\n-4.2x = 21<br \/>\n-x = 21\/4.1<br \/>\nx = -5.12<\/p>\n<p><strong>WRITING AND SOLVING AN EQUATION<\/strong><br \/>\n<strong>Write the word sentence as an equation. Then solve the equation.<\/strong><\/p>\n<p>Question 29.<br \/>\nA number multiplied by -9 is -16.<\/p>\n<p>Answer:<br \/>\n9n = 16<br \/>\nn = 16\/9<\/p>\n<p>Explanation:<br \/>\nn x -9 = -16<br \/>\n9n = 16<br \/>\nn = 16\/9<\/p>\n<p>Question 30.<br \/>\nA number multiplied by \\(\\frac{2}{5}\\) is \\(\\frac{3}{20}\\).<\/p>\n<p>Answer:<br \/>\n(2\/5)n = 3\/20<br \/>\nn = 15\/40<\/p>\n<p>Explanation:<br \/>\nn x (2\/5) = 3\/20<br \/>\n(2\/5)n = 3\/20<br \/>\nn = (3\/20) x (5\/2)<br \/>\n= 15\/40<\/p>\n<p>Question 31.<br \/>\nThe product of 15 and a number is -75.<\/p>\n<p>Answer:<br \/>\n15n = -75<br \/>\nn = -5<\/p>\n<p>Explanation:<br \/>\n15 x n = -75<br \/>\n15n = -75<br \/>\nn = -75\/15<br \/>\nn = -5<\/p>\n<p>Question 32.<br \/>\nThe quotient of a number and -1.5 is 21.<\/p>\n<p>Answer:<br \/>\nn\/-1.5 = 21<br \/>\nn = -31.5<\/p>\n<p>Explanation:<br \/>\nn\/-1.5 = 21<br \/>\n-n\/1.5 = 21<br \/>\n-n = 21 x 1.5<br \/>\n-n = 31.5<br \/>\nn = -31.5<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou make a pro\ufb01t of $0.75 for every bracelet you sell. Write and solve an equation to determine how many bracelets you must sell to earn enough money to buy the soccer cleats shown.<\/p>\n<p>Answer:<br \/>\nI need to sell 48 bracelets to earn enough money to buy the soccer cleats shown.<\/p>\n<p>Explanation:<br \/>\nLet us take a number of bracelets as x.<br \/>\n0.75x = 36<br \/>\nx = 36\/0.75<br \/>\nx = 48<\/p>\n<p>Question 34.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA rock climber averages 12\\(\\frac{3}{5}\\) feet climbed per minute. How many feet does the rock climber climb in 30 minutes? Justify your answer.<\/p>\n<p>Answer:<br \/>\nClimber climbs 378 feet in 30 minutes.<\/p>\n<p>Explanation:<br \/>\nA rock climber averages 63\/5 feet climbed per minute<br \/>\nLet us take he climb x feet in 30 minutes<br \/>\nx\/30 = 63\/5<br \/>\nx = (63\/5) x 30<br \/>\nx = 63 x 6<br \/>\nx = 378 feet<\/p>\n<p><strong>OPEN-ENDED<\/strong><br \/>\n<strong>Write (a) a multiplication equation and (b) a division equation that has the given solution.<\/strong><\/p>\n<p>Question 35.<br \/>\n-3<\/p>\n<p>Answer:<br \/>\n(a) 3x = -9<br \/>\n(b) x\/3 = -1<\/p>\n<p>Explanation:<br \/>\n(a) 3x = -9<br \/>\nx = -9\/3 = -3<br \/>\nx\/3 = -1<br \/>\nx = -1 x 3 = -3<\/p>\n<p>Question 36.<br \/>\n-2.2<\/p>\n<p>Answer:<br \/>\n(a) -5x = 11<br \/>\n(b) x\/2 = -1.1<\/p>\n<p>Explanation:<br \/>\n(a) -5x = 11<br \/>\nx = -11\/5<br \/>\nx = -2.2<br \/>\n(b) x\/2 = -1.1<br \/>\nx = 2 x -1.1<br \/>\nx = -2.2<\/p>\n<p>Question 37.<br \/>\n&#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Answer:<br \/>\n(a) 6x = -3<br \/>\n(b) -x\/4 = 0.125<\/p>\n<p>Explanation:<br \/>\n(a) 6x = -3<br \/>\nx = -3\/6 = -1\/2<br \/>\n(b) -x\/4 = 0.125<br \/>\n-x = 0.125 x 4 = 0.5<br \/>\nx = -0.5<\/p>\n<p>Question 38.<br \/>\n-1\\(\\frac{1}{4}\\)<\/p>\n<p>Answer:<br \/>\n(a) 4x = 5<br \/>\n(b) x\/2 = 10\/16<\/p>\n<p>Explanation:<br \/>\n(a) 4x = 5<br \/>\nx = 5\/4 = 1(1\/4)<br \/>\n(b) x\/2 = 10\/16<br \/>\nx = 2(10\/16)<br \/>\nx = 10\/8 = 5\/4<\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich method(s) can you use to solve &#8211;\\(\\frac{2}{3}\\)c = 16?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-31.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 31.1\" width=\"450\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-31.1.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-31.1-300x89.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Answer:<br \/>\nMultiply each side by -3\/2.<\/p>\n<p>Explanation:<br \/>\n-(2\/3)c = 16<br \/>\nMultiply both sides by -(3\/2)<br \/>\n-(2\/3)c x (-3\/2) = 16 x (-3\/2)<br \/>\nc = -8 x 3 = -24<\/p>\n<p>Question 40.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA stock has a return of -$1.26 per day. Find the number of days until the total return is -$10.08. Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe number of days required is 8 days.<\/p>\n<p>Explanation:<br \/>\nLet us take the number of days as x.<br \/>\nMultiply number of days by one day return to get a total return<br \/>\n-$1.26 * x = -$10.08<br \/>\nx = 10.08\/1.26<br \/>\nx = 8<\/p>\n<p>Question 41.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nIn a school election, \\(\\frac{3}{4}\\) of the students vote. There are 1464 votes. Find the number of students. Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe number of students who voted is 1098 and the number of students who not voted is 366.<\/p>\n<p>Explanation:<br \/>\nThe number of students voted = (3\/4) x 1464<br \/>\n= 366 x 3 = 1098<br \/>\nSo, 75% of students are 1098<br \/>\nRemaining 25% = 1098 x (25\/75)<br \/>\n= 1098 x (1\/3) = 366<br \/>\nThe number of students voted is 1098 and number of students not voted is 366.<\/p>\n<p>Question 42.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe diagram shows Aquarius, an underwater ocean laboratory located in the Florida Keys National Marine Sanctuary. The equation \\(\\frac{31}{25}\\)x = -62 can be used to calculate the depth of Aquarius. Interpret the equation. Then \ufb01nd the depth of Aquarius. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-32.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 32\" width=\"207\" height=\"280\" \/><\/p>\n<p>Answer:<br \/>\nThe depth of the aquarius is -50 feet<\/p>\n<p>Explanation:<br \/>\n(31\/25)x = -62<br \/>\nMultiply both sides by (25\/31)<br \/>\n(31\/25)x . (25\/31) = -62 . (25\/31)<br \/>\nx = (-2) x 25<br \/>\nx = -50<br \/>\nThe depth of the aquarius is -50 feet<\/p>\n<p>Question 43<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe price of a bike at Store A is \\(\\frac{5}{6}\\) the price at Store B. The price at Store A is $150.60. Find how much you save by buying the bike at Store A. Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe amount saved is $30.12<\/p>\n<p>Explanation:<br \/>\nLet us take the price of the bike at store b as x.<br \/>\n$150.60 = (5\/6)x<br \/>\n150.6 * (6\/5) = x<br \/>\nx = 30.12 * 6 = 180.72<br \/>\nThe amount saved is $180.72 &#8211; $150.60 = $30.12<\/p>\n<p>Question 44.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSolve -2| m | = -10.<\/p>\n<p>Answer:<br \/>\nm = 5<\/p>\n<p>Explanation:<br \/>\n-2m = -10<br \/>\n2m = 10<br \/>\nm = 10\/2 = 5<\/p>\n<p>Question 45.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nIn 4 days, your family drives \\(\\frac{5}{7}\\) of the total distance of a trip. The total distance is 1250 miles. At this rate, how many more days will it take to reach your destination? Justify your answer.<\/p>\n<p>Answer:<br \/>\nIt took 1(1\/2) day to reach the destination.<\/p>\n<p>Explanation:<br \/>\nThe distance travelled in 4 days = 1250 * (5\/7)<br \/>\n= 892.857 miles<br \/>\nThe distance travelled in 1 day = 892.857\/4 = 223.214<br \/>\nRemaining distance = 1250 &#8211; 892.57 = 357.14<br \/>\n357.14 = 223.214x<br \/>\nx = 357.14\/223.214 = 1.59<br \/>\nSo, it took 1(1\/2) day to reach the destination.<\/p>\n<h3><a id=\"Lesson_4.3_Solving_Two_Step_Equations\"><\/a>Lesson 4.3 Solving Two-Step Equations<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Using Algebra Tiles to Solve Equations<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. What is being modeled by the algebra tiles below? What is the solution?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-33.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 33\" width=\"334\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-33.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-33-300x220.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nb. Use properties of equality to solve the original equation in part(a). How do your steps compare to the steps performed with algebra tiles?<br \/>\nc. Write the three equations modeled by the algebra tiles below. Then solve each equation using algebra tiles. Check your answers using properties of equality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-34.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 34\" width=\"524\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-34.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-34-300x142.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nd. Explain how to solve an equation of the form ax + b = c for x.<\/p>\n<p><strong>4.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\n2x + 12 = 4<\/p>\n<p>Answer:<br \/>\nx = -4<\/p>\n<p>Explanation:<br \/>\n2x = 4 &#8211; 12 = -8<br \/>\nx = -8\/2<br \/>\nx = -4<br \/>\nPutting x = -4 in 2x + 12 = 4<br \/>\n2(-4) + 12 = -8 + 12 = 4<\/p>\n<p>Question 2.<br \/>\n-5c + 9 = -16<\/p>\n<p>Answer:<br \/>\nc = 5<\/p>\n<p>Explanation:<br \/>\n9 + 16 = 5c<br \/>\n5c = 25<br \/>\nc = 25\/5<br \/>\nc = 5<br \/>\nPutting c = 5 in -5c + 9 = -16<br \/>\n-5(5) + 9 = -25 + 9 = -16<\/p>\n<p>Question 3.<br \/>\n9 = 3x &#8211; 12<\/p>\n<p>Answer:<br \/>\nx = 7<\/p>\n<p>Explanation:<br \/>\n3x = 9 + 12<br \/>\n3x = 21<br \/>\nx = 21\/3 = 7<br \/>\nPutting x = 7 in 9 = 3x &#8211; 12<br \/>\n9 = 3(7) &#8211; 12 = 21 &#8211; 12 = 9<\/p>\n<p><strong>4.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-35.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 35\" width=\"92\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\nm = 8<\/p>\n<p>Explanation:<br \/>\nm\/2 = 10 &#8211; 6<br \/>\nm\/2 = 4<br \/>\nm = 2 x 4<br \/>\nm = 8<br \/>\nputting m = 8 in m\/2 + 6 = 10<br \/>\n8\/2 + 6 = 4 + 6 = 10<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-36.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 36\" width=\"88\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nz = -12<\/p>\n<p>Explanation:<br \/>\n5 &#8211; 9 = z\/3<br \/>\nz\/3 = -4<br \/>\nz = -4 x 3<br \/>\nz = -12<br \/>\nPutting z = -12 in -z\/3 + 5 = 9<br \/>\n-(-12)\/3 + 5 = 12\/3 + 5 = 4 + 5 = 9<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-37.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 37\" width=\"99\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\na = -2\/5<\/p>\n<p>Explanation:<br \/>\n2\/5 + 4a =-6\/5<br \/>\n4a = -6\/5 &#8211; 2\/5<br \/>\n4a = -8\/5<br \/>\na = (-8\/5) x (1\/4)<br \/>\na = -2\/5<br \/>\nPutting a = -2\/5 in 2\/5 + 4a =-6\/5<br \/>\n2\/5 + 4(-2\/5) = 2\/5 &#8211; 8\/5 = (2 &#8211; 8)\/5 = -6\/5<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 7.<br \/>\n4 &#8211; 2y + 3 = -9<\/p>\n<p>Answer:<br \/>\ny = 8<\/p>\n<p>Explanation:<br \/>\n7 &#8211; 2y = -9<br \/>\n7 + 9 = 2y<br \/>\n16 = 2y<br \/>\ny = 16\/2<br \/>\ny = 8<br \/>\nPuuting y = 8 in 4 &#8211; 2y + 3 = -9<br \/>\n4 &#8211; 2(8) + 3 = 7 &#8211; 16 = -9<\/p>\n<p>Question 8.<br \/>\n7x &#8211; 10x = 15<\/p>\n<p>Answer:<br \/>\nx = -5<\/p>\n<p>Explanation:<br \/>\n-3x = 15<br \/>\nx = -15\/3<br \/>\nx = -5<br \/>\nPutting x = -5 in 7x &#8211; 10x = 15<br \/>\n7(-5) &#8211; 10(-5) = -35 + 50 = 15<\/p>\n<p>Question 9.<br \/>\n-8 = 1.3m &#8211; 2.1m<\/p>\n<p>Answer:<br \/>\nm = 10<\/p>\n<p>Explanation:<br \/>\n-8 = -0.8m<br \/>\nm = 8\/0.8<br \/>\nm = 10<br \/>\nPutting m = 10 in -8 = 1.3m &#8211; 2.1m<br \/>\n-8 = 1.3(10) &#8211; 2.1(10)<br \/>\n= 13 &#8211; 21<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>MATCHING<\/strong><br \/>\n<strong>Match the equation with the step(s) to solve it.<\/strong><\/p>\n<p>Question 10.<br \/>\n4 + 4n = 12<\/p>\n<p>Answer:<br \/>\nn = 2<\/p>\n<p>Explanation:<br \/>\n4n = 12 &#8211; 4<br \/>\n4n = 8<br \/>\nn = 8\/4<br \/>\nn = 2<\/p>\n<p>Question 11.<br \/>\n4n = 12<\/p>\n<p>Answer:<br \/>\nn = 3<\/p>\n<p>Explanation:<br \/>\nn = 12\/4<br \/>\nn = 3<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{n}{4}\\) = 12<\/p>\n<p>Answer:<br \/>\nn = 48<\/p>\n<p>Explanation:<br \/>\nn\/4 = 12<br \/>\nn = 12 x 4<br \/>\nn = 48<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{n}{4}\\) &#8211; 4 = 12<\/p>\n<p>A. Add 4 to each side. Then multiply each side by 4.<br \/>\nB. Subtract 4 from each side. Then divide each side by 4.<br \/>\nC. Multiply each side by 4.<br \/>\nD. Divide each side by 4.<\/p>\n<p>Answer:<br \/>\nAdd 4 to each side. Then multiply each side by 4.<\/p>\n<p>Explanation:<br \/>\nn\/4 &#8211; 4 = 12<br \/>\nAdd 4 to each side<br \/>\nn\/4 &#8211; 4 + 4 = 12 + 4<br \/>\nn\/4 = 16<br \/>\nMultiply each side by 4<br \/>\nn\/4 x 4 = 16 x 4<br \/>\nn = 64<\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 14.<br \/>\n4p + 5 = 3<\/p>\n<p>Answer:<br \/>\np = -1\/2<\/p>\n<p>Explanation:<br \/>\n4p = 3 &#8211; 5<br \/>\n4p = -2<br \/>\np = -2\/4<br \/>\np = -1\/2<br \/>\nputting p = -1\/2 in 4p + 5 = 3<br \/>\n4(-1\/2) + 5 = -2 + 5 = 3<\/p>\n<p>Question 15.<br \/>\n&#8211;\\(\\frac{d}{5}\\) &#8211; 1 = -6<\/p>\n<p>Answer:<br \/>\nd = 25<\/p>\n<p>Explanation:<br \/>\n-1 + 6 = d\/5<br \/>\n5 = d\/5<br \/>\nd = 5 x 5<br \/>\nd = 25<br \/>\nPutting d = 25 in -d\/5 &#8211; 1 = -6<br \/>\n-25\/5 &#8211; 1 = -5 &#8211; 1 = -6<\/p>\n<p>Question 16.<br \/>\n3.6g = 21.6<\/p>\n<p>Answer:<br \/>\ng = 6<\/p>\n<p>Explanation:<br \/>\ng = 21.6 \/ 6.3<br \/>\ng = 6<br \/>\nPutting g = 6 in 3.6g = 21.6<br \/>\n3.6(6) = 21.6<\/p>\n<p>Question 17.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the equations 3x + 12 = 6 and -2 = 4 &#8211; 3x equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nEquations are not equivalent<\/p>\n<p>Explanation:<br \/>\n3x + 12 = 6 and -2 = 4 &#8211; 3x<br \/>\n3x = 6 &#8211; 12 and 3x = 4 + 2<br \/>\n3x = -6 and 3x = 6<br \/>\nx = -6\/3 and x = 6\/3<br \/>\nx = -2 and x = 2<br \/>\nEquations are not equivalent<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 18.<br \/>\nYou must scuba dive to the entrance of your room at Jules\u2019 Undersea Lodge in Key Largo, Florida. The diver is 1 foot deeper than \\(\\frac{2}{3}\\) of the elevation of the entrance. What is the elevation of the entrance?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-38.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 38\" width=\"196\" height=\"189\" \/><\/p>\n<p>Answer:<br \/>\nThe elevation of entrance is 21 feet<\/p>\n<p>Explanation:<br \/>\n2\/3 rd of elevation = -15 foot + 1 feet<br \/>\n(2\/3) * x = 14<br \/>\nx = 14 * (3\/2)<br \/>\nx = 7 * 3 = 21 foot<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA car drives east along a road at a constant speed of 46 miles per hour. At 4:00 P.M., a truck is 264 miles away, driving west along the same road at a constant speed. The vehicles pass each other at 7:00 P.M. What is the speed of the truck?<\/p>\n<p>Answer:<br \/>\nThe speed of truck is 42 miles per hour<\/p>\n<p>Explanation:<br \/>\nSpeed = distance\/time<br \/>\nThe time taken is 3 hours<br \/>\n46 + x = 264\/3<br \/>\n46 + x = 88<br \/>\nx = 88 &#8211; 46 = 42<\/p>\n<h3><a id=\"Solving_Two_Step_Equations_Homework_&amp;_Practice_4.3\"><\/a>Solving Two-Step Equations Homework &amp; Practice 4.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the equation.<\/strong><\/p>\n<p>Question 1.<br \/>\n3z = 18<\/p>\n<p>Answer:<br \/>\nz = 6<\/p>\n<p>Explanation:<br \/>\nz = 18\/3<br \/>\nz = 6<\/p>\n<p>Question 2.<br \/>\n-8p = 40<\/p>\n<p>Answer:<br \/>\np = -5<\/p>\n<p>Explanation:<br \/>\n-p = 40\/8<br \/>\n-p = 5<br \/>\np = -5<\/p>\n<p>Question 3.<br \/>\n&#8211;\\(\\frac{m}{4}\\) = 5<\/p>\n<p>Answer:<br \/>\nm = -20<\/p>\n<p>Explanation:<br \/>\n-m\/4 = 5<br \/>\n-m = 5 x 4<br \/>\n-m = 20<br \/>\nm = -20<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{5}{6}\\)k = -10<\/p>\n<p>Answer:<br \/>\nk = -12<\/p>\n<p>Explanation:<br \/>\n(5\/6)k = -10<br \/>\nk = -10(6\/5)<br \/>\nk = -2(6)<br \/>\nk = -12<\/p>\n<p><strong>Multiply or divide.<\/strong><\/p>\n<p>Question 5.<br \/>\n-6.2 \u00d7 5.6<\/p>\n<p>Answer:<br \/>\n-6.2 \u00d7 5.6 = -34.72<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34667 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.3-1.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.3-1\" width=\"206\" height=\"244\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-39.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 39\" width=\"91\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n-40\/6<\/p>\n<p>Explanation:<br \/>\n(8\/3) x (-5\/2) = -40\/6<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-40.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 40\" width=\"86\" height=\"64\" \/><\/p>\n<p>Answer:<br \/>\n-25\/8<\/p>\n<p>Explanation:<br \/>\n(5\/2) \/ (-4\/5) = (5 x 5) \/ (2 x &#8211; 4)<br \/>\n= -25\/8<\/p>\n<p>Question 8.<br \/>\n-18.6 \u00f7 (-3)<\/p>\n<p>Answer:<br \/>\n6.2<\/p>\n<p>Explanation:<br \/>\n-18.6 \u00f7 (-3) = 186\/30<br \/>\n= 6.2<\/p>\n<p>Question 9.<br \/>\nWhich fraction is not equivalent to 0.75?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-41.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 41\" width=\"478\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-41.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-41-300x35.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Answer:<br \/>\n6\/9 is not equivalent to 0.75<\/p>\n<p>Explanation:<br \/>\n15\/20 = 3\/4 = 0.75<br \/>\n9\/12 = 3\/4 = 0.75<br \/>\n6\/9 = 2\/3 = 0.66<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING ALGEBRA TILES<\/strong><br \/>\n<strong>Write the equation modeled by the algebra tiles. Then solve the equation using algebra tiles. Check your answer using properties of equality.<\/strong> (See Exploration 1, p. 139.)<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-42.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 42\" width=\"215\" height=\"64\" \/><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-43.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 43\" width=\"215\" height=\"84\" \/><\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 12.<br \/>\n2v + 7 = 3<\/p>\n<p>Answer:<br \/>\nv = -2<\/p>\n<p>Explanation:<br \/>\n2v = 3 &#8211; 7<br \/>\n2v = -4<br \/>\nv = -4\/2<br \/>\nv = -2<br \/>\nPutting v = -2 in 2v + 7 = 3<br \/>\n2(-2) + 7 = -4 + 7 = 3<\/p>\n<p>Question 13.<br \/>\n4b + 3 = -9<\/p>\n<p>Answer:<br \/>\nb = -3<\/p>\n<p>Explanation:<br \/>\n4b = -9 &#8211; 3<br \/>\n4b = -12<br \/>\nb = -12\/4<br \/>\nb = -3<br \/>\nPutting b = -3 in 4b + 3 = -9<br \/>\n4(-3) + 3 = -12 + 3 = -9<\/p>\n<p>Question 14.<br \/>\n17 = 5k &#8211; 2<\/p>\n<p>Answer:<br \/>\nk = 19\/5<\/p>\n<p>Explanation:<br \/>\n5k = 17 + 2<br \/>\n5k = 19<br \/>\nk = 19\/5<br \/>\nPutting k = 19\/5 in 5k = 17 + 2<br \/>\n5(19\/5) &#8211; 2 = 19 &#8211; 2 = 17<\/p>\n<p>Question 15.<br \/>\n-6t &#8211; 7 = 17<\/p>\n<p>Answer:<br \/>\nt = -4<\/p>\n<p>Explanation:<br \/>\n-6t = 17 + 7<br \/>\n-6t = 24<br \/>\nt = -24\/6<br \/>\nt = -4<br \/>\nPutting t = -4 in -6t &#8211; 7 = 17<br \/>\n-6(-4) &#8211; 7 = 24 &#8211; 7 = 17<\/p>\n<p>Question 16.<br \/>\n8n + 16.2 = 1.6<\/p>\n<p>Answer:<br \/>\nn = -1.825<\/p>\n<p>Explanation:<br \/>\n8n = 1.6 &#8211; 16.2<br \/>\n8n = -14.6<br \/>\nn = -14.6\/8<br \/>\nn = -1.825<br \/>\nPutting n = -1.825 in 8n + 16.2 = 1.6<br \/>\n8(-1.825) + 16.2 = -14.6 + 16.2 = 1.6<\/p>\n<p>Question 17.<br \/>\n-5g + 2.3 = -18.8<\/p>\n<p>Answer:<br \/>\ng = 4.22<\/p>\n<p>Explanation:<br \/>\n2.3 + 18.8 = 5g<br \/>\n5g = 21.1<br \/>\ng = 21.1\/5<br \/>\ng = 4.22<br \/>\nputting g = 4.22 in -5g + 2.3 = -18.8<br \/>\n-5(4.22) + 2.3 = -21.1 + 2.3 = -18.8<\/p>\n<p>Question 18.<br \/>\n2t + 8 = -10<\/p>\n<p>Answer:<br \/>\nt = -9<\/p>\n<p>Explanation:<br \/>\n2t = -10 &#8211; 8<br \/>\n2t = -18<br \/>\nt = -18\/2<br \/>\nt = -9<br \/>\nPutting t = -9 in 2t + 8 = -10<br \/>\n2(-9) + 8 = -18 + 8 = -10<\/p>\n<p>Question 19.<br \/>\n-4p + 9 = -5<\/p>\n<p>Answer:<br \/>\np = 3.5<\/p>\n<p>Explanation:<br \/>\n4p = 9 + 5<br \/>\n4p = 14<br \/>\np = 14\/4<br \/>\np = 3.5<br \/>\nPutting p = 3.5 in -4p + 9 = -5<br \/>\n-4(3.5) + 9 = -14 + 9 = -5<\/p>\n<p>Question 20.<br \/>\n15 = -5x + 10<\/p>\n<p>Answer:<br \/>\nx = -1<\/p>\n<p>Explanation:<br \/>\n15 &#8211; 10 = -5x<br \/>\n-5x = 5<br \/>\nx = -5\/5<br \/>\nx = -1<br \/>\nPutting x = -1 in 15 = -5x + 10<br \/>\n15 = -5(-1) + 10 = 5 + 10<br \/>\n= 15<\/p>\n<p>Question 21.<br \/>\n10.35 + 2.3h = -9.2<\/p>\n<p>Answer:<br \/>\nh = -8.5<\/p>\n<p>Explanation:<br \/>\n2.3h = -9.2 &#8211; 10.35<br \/>\n2.3h = -19.55<br \/>\nh = -19.55\/2.3<br \/>\nh = -8.5<br \/>\nPutting h = -8.5 in 10.35 + 2.3h = -9.2<br \/>\n10.35 + 2.3(-8.5) = 10.35 &#8211; 19.55 = -9.2<\/p>\n<p>Question 22.<br \/>\n-4.8f + 6.4 = -8.48<\/p>\n<p>Answer:<br \/>\nf = 3.1<\/p>\n<p>Explanation:<br \/>\n-4.8f = -8.48 &#8211; 6.4<br \/>\n-4.8f = -14.88<br \/>\n4.8f = 14.88<br \/>\nf = 14.88\/4.8<br \/>\nf = 3.1<br \/>\nPutting f = 3.1 in -4.8f + 6.4 = -8.48<br \/>\n-4.8(3.1) + 6.4 = -14.88 + 6.4 = -8.48<\/p>\n<p>Question 23.<br \/>\n7.3y &#8211; 5.18 = -51.9<\/p>\n<p>Answer:<br \/>\ny = -6.4<\/p>\n<p>Explanation:<br \/>\n7.3y = -51.9 + 5.18<br \/>\n7.3y = -46.72<br \/>\ny = -46.72\/7.3<br \/>\ny = -6.4<br \/>\nPutting y = -6.4 in 7.3y &#8211; 5.18 = -51.9<br \/>\n7.3(-6.4) &#8211; 5.18 = -46.72 &#8211; 5.18 = -51.9<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend solves the equation. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-44.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 44\" width=\"178\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is wrong.<\/p>\n<p>Explanation:<br \/>\n-6x + 2x = -10<br \/>\n-4x = -10<br \/>\nx = 10\/4<br \/>\nx = 5\/2<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-45.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 45\" width=\"167\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is wrong.<\/p>\n<p>Explanation:<br \/>\n-3(x + 6) = 12<br \/>\nx + 6 = -12\/3<br \/>\nx + 6 = -4<br \/>\nx = -4 &#8211; 6<br \/>\nx = -10<\/p>\n<p><strong>SOLVING AN EQUATION<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-46.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 46\" width=\"118\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\ng = -5<\/p>\n<p>Explanation:<br \/>\n(3\/5)g = -10\/3 + 1\/3<br \/>\n(3\/5)g = (-10 + 1)\/3<br \/>\n= -9\/3 = -3<br \/>\n(3\/5)g = -3<br \/>\ng = -3 x (5\/3)<br \/>\ng = -5<br \/>\nPutting g = -5 in (3\/5)g -1\/3 = -10\/3<br \/>\n(3\/5)(-5) -1\/3 = -3 &#8211; 1\/3 = (-9 &#8211; 1)\/3<br \/>\n= -10\/3<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-47.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 47\" width=\"91\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\na = 4\/3<\/p>\n<p>Explanation:<br \/>\na\/4 = -1\/2 + 5\/6<br \/>\na\/4 = (-3 + 5)\/6<br \/>\na\/4 = 2\/6<br \/>\na = (2\/6) x 4<br \/>\na = 4\/3 = 1.33<br \/>\nPutting a = 4\/3 in a\/4 &#8211; 5\/6 = -1\/2<br \/>\n(1.33)\/4 &#8211; 5\/6 = (4 &#8211; 10)\/12 = -6\/12 = -1\/2<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-48.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 48\" width=\"128\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\nz = -3\/2<\/p>\n<p>Explanation:<br \/>\n(4 + z) = -5\/6 x -3<br \/>\n4 + z = 5\/2<br \/>\nz = 5\/2 &#8211; 4<br \/>\nz = (5 &#8211; 8)\/2<br \/>\nz = -3\/2<br \/>\nputting z = -3\/2 in -1\/3(4 + z) = -5\/6<br \/>\n-1\/3(4 + (-3\/2)) = -1\/3(4 &#8211; 3\/2)<br \/>\n= -1\/3(8-3)\/2 = -1\/6 x (5)<br \/>\n= -5\/6<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-49.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 49\" width=\"92\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nb = 27\/2<\/p>\n<p>Explanation:<br \/>\n2 + 5\/2 = b\/3<br \/>\n(4 + 5)\/2 = b\/3<br \/>\nb\/3 = 9\/2<br \/>\nb = 9\/2 x 3<br \/>\nb = 27\/2<br \/>\nPutting b = 27\/2 in 2 &#8211; b\/3 = &#8211; 5\/2<br \/>\n2 &#8211; (27\/2)\/3 = 2 &#8211; 27\/6<br \/>\n= (12 &#8211; 27)\/6 = -15\/6 = &#8211; 5\/2<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-50.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 50\" width=\"116\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nx = -27\/20<\/p>\n<p>Explanation:<br \/>\n(x + 3\/5) = 1\/2 x (-3\/2)<br \/>\nx + 3\/5 = -3\/4<br \/>\nx = -3\/4 &#8211; 3\/5<br \/>\nx = (-15 &#8211; 12)\/20<br \/>\nx = -27\/20<br \/>\nPutting x = -27\/20\u00a0in -2\/3(x + 3\/5) = 1\/2<br \/>\n-2\/3(-27\/20 + 3\/5) = -2\/3(-27 + 12)\/20<br \/>\n= -2\/3(-15\/20) = (2 x 15)\/(3 x 20)<br \/>\n= 30\/60 = 1\/2<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-51.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 51\" width=\"97\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\nv = -1\/30<\/p>\n<p>Explanation:<br \/>\n-9\/4 v = 7\/8 &#8211; 4\/5<br \/>\n-9\/4 v = (35 &#8211; 32)\/40 = 3\/40<br \/>\nv = -3\/40 x 4\/9<br \/>\nv = -1\/30<br \/>\nPutting v = -1\/30 in -9\/4 v + 4\/5 = 7\/8<br \/>\n-9\/4 v + 4\/5 = -9\/4 (-1\/30) + 4\/5<br \/>\n= 3\/40 + 4\/5 = (3 + 32)\/40<br \/>\n= 35\/40 = 7\/8<\/p>\n<p>Question 32.<br \/>\n<strong>PRECISION<\/strong><br \/>\nStarting at 1:00 P.M., the temperature changes -4\u00b0F per hour. Write and solve an equation to determine how long it will take for the temperature to reach -1\u00b0F.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-52.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 52\" width=\"131\" height=\"196\" \/><\/p>\n<p>Answer:<br \/>\nIit takes 8 hours 30 minutes.<\/p>\n<p>Explanation:<br \/>\nStarting at 1:00 P.M., the temperature changes -4\u00b0F per hour.<br \/>\nThe temperature change is 35 &#8211; 1 = 34\u00b0F<br \/>\nSo, the equation is 4x = 34<br \/>\nx = 34\/4<br \/>\nx = 8.5<br \/>\nS,o, it takes 8 hours 30 minutes.<\/p>\n<p><strong>COMBINING LIKE TERMS<\/strong><br \/>\n<strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 33.<br \/>\n3v &#8211; 9v = 30<\/p>\n<p>Answer:<br \/>\nv = -5<\/p>\n<p>Explanation:<br \/>\n-6v = 30<br \/>\nv = -30\/6<br \/>\nv = -5<br \/>\nPutting v = -5 in 3v &#8211; 9v = 30<br \/>\n3(-5) &#8211; 9(-5) = -15 + 45 = 30<\/p>\n<p>Question 34.<br \/>\n12t &#8211; 8t = -52<\/p>\n<p>Answer:<br \/>\nt = -13<\/p>\n<p>Explanation:<br \/>\n4t = -52<br \/>\nt = -52\/4<br \/>\nt = -13<br \/>\nPutting t = -13 in 12t &#8211; 8t = -52<br \/>\n12(-13) &#8211; 8(-13) = -156 + 104 = -52<\/p>\n<p>Question 35.<br \/>\n-8d &#8211; 5d + 7d = 72<\/p>\n<p>Answer:<br \/>\nd = -12<\/p>\n<p>Explanation:<br \/>\n-13d + 7d = 72<br \/>\n-6d = 72<br \/>\nd = -72\/6<br \/>\nd = -12<br \/>\nPutting d = -12 in -8d &#8211; 5d + 7d = 72<br \/>\n-8(-12) &#8211; 5(-12) + 7(-12) = 96 + 60 &#8211; 84<br \/>\n= 156 &#8211; 84 = 72<\/p>\n<p>Question 36.<br \/>\n-3.8g + 5 + 2.7g = 12.7<\/p>\n<p>Answer:<br \/>\ng = -7<\/p>\n<p>Explanation:<br \/>\n-1.1g + 5 = 12.7<br \/>\n-1.1g = 12.7-5<br \/>\n-1.1g = 7.7<br \/>\ng = -7.7\/1.1<br \/>\ng = -7<br \/>\nPutting g = -7 in -3.8g + 5 + 2.7g = 12.7<br \/>\n-3.8(-7) + 5 + 2.7(-7) = 26.6 + 5 &#8211; 18.9 = 12.7<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou have $9.25. How many games can you bowl if you rent bowling shoes? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-4-Equations-and-Inequalities-53.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 4 Equations and Inequalities 53\" width=\"243\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\n3 games can be played<\/p>\n<p>Explanation:<br \/>\nThe amount you have is $9.25<br \/>\nAfter renting $9.25 &#8211; $2.50 = $6.75<br \/>\nBowling per game = $2.25<br \/>\nAfter one game,<br \/>\n$2.25 gone out of $6.75<br \/>\nAfter two games,<br \/>\n$4.50 gone<br \/>\nAfter three games,<br \/>\n$6.75 gone<br \/>\nTotal is $6.75, after three games it will cost you $6.75<br \/>\nSo, 3 games can be played<\/p>\n<p>Question 38.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cell phone company charges a monthly fee plus $0.25 for each text message you send. The monthly fee is $30.00. You owe $59.50. How many text messages did you send? Justify your answer.<\/p>\n<p>Answer:<br \/>\nYou have sent 118 text messages.<\/p>\n<p>Explanation:<br \/>\nSince the total cost of $59.50 is comprised of the monthly fee of $30 plus $0.25 for each text message, we can write<br \/>\n$59.50 = $30 + $0.25x<br \/>\n$0.25x = $59.50 &#8211; $30<br \/>\n$29.50 = $0.25x<br \/>\nx = 29.5\/0.25<br \/>\nx = 118<br \/>\nSo, you have sent 118 text messages<\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe height at the top of a roller coaster hill is 10 times the height h of the starting point. The height decreases 100 feet from the top to the bottom of the hill. The height at the bottom of the hill is -10 feet. Find h.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-54.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 54\" width=\"330\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-54.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-54-300x170.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/p>\n<p>Answer:<br \/>\nh = -9<\/p>\n<p>Explanation:<br \/>\nFrom the image, we can write the equation as,<br \/>\n-10 + 10h = -100<br \/>\n10h = -100 + 10<br \/>\n10h = -90<br \/>\nh = -90\/10<br \/>\nh = -9<\/p>\n<p>Question 40.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nOn a given day, the coldest surface temperature on the Moon, -280\u00b0F, is 53.6\u00b0F colder than twice the coldest surface temperature on Earth. What is the coldest surface temperature on Earth that day? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe coldest surface temperature on Earth is 166.8\u00b0F<\/p>\n<p>Explanation:<br \/>\nthe coldest surface temperature on the Moon = -280\u00b0F<br \/>\n2E + 53.6 = -280<br \/>\n2E = -280 &#8211; 53.6<br \/>\n2E = 333.6<br \/>\nE = 166.8\u00b0F<br \/>\nThe coldest surface temperature on Earth is 166.8\u00b0F<\/p>\n<p>Question 41.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOn Saturday, you catch insects for your science class. Five of the insects escape. The remaining insects are divided into three groups to share in class. Each group has nine insects.<br \/>\na. Write and solve an equation to \ufb01nd the number of insects you catch on Saturday.<br \/>\nb. Find the number of insects you catch on Saturday without using an equation. Compare the steps used to solve the equation in part (a) with the steps used to solve the problem in part (b).<br \/>\nc. Describe a problem that is more convenient to solve using an equation. Then describe a problem that is more convenient to solve without using an equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-56.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 56\" width=\"196\" height=\"245\" \/><\/p>\n<p>Answer:<br \/>\na. You catch 32 insects on Saturday.<br \/>\nb.<\/p>\n<p>Explanation:<\/p>\n<p>a.<br \/>\n(x &#8211; 5)\/3 = 9<br \/>\n(x &#8211; 5) = 27<br \/>\nx = 27 + 5 = 32<br \/>\nYou catch 32 insects on saturday.<br \/>\nb. The only number which is divisible by 3 and obtained after subtracting 5 insects from it is 5. so, you caught 32 insects.<br \/>\nc. Equation is more convenient to solve the problem.<\/p>\n<p>Question 42.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nHow can you change the dimensions of the rectangle so that the ratio of the length to the width stays the same, but the perimeter is 185 centimeters? Write an equation that shows how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-57.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 57\" width=\"186\" height=\"95\" \/><\/p>\n<p>Answer:<br \/>\nThe required dimensions are 52.75, 52.75, 39.75.<\/p>\n<p>Explanation:<br \/>\nThe perimeter for given dimensions = 2(25 + 12) = 50 + 24 = 74<br \/>\nGiven perimeter = 185<br \/>\nChange in perimeter = 185 &#8211; 74 = 111<br \/>\nDivide the perimeter by 4 = 111\/4 = 27.75<br \/>\nAdd 27.75 to each dimension to get the perimeter 185<br \/>\nSo, the required dimensions are 52.75, 52.75, 39.75<\/p>\n<h3><a id=\"Lesson_4.4_Writing_and_Graphing_Inequalities\"><\/a>Lesson 4.4 Writing and Graphing Inequalities<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Understanding Inequality Statements<\/strong><br \/>\n<strong>Work with a partner. Create a number line on the \ufb02oor with both positive and negative numbers.<\/strong><br \/>\na. For each statement, stand at a number on your number line that could represent the situation. On what other numbers can you stand?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-58.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 58\" width=\"170\" height=\"177\" \/><br \/>\n\u2022 Atleast 3 students from our school are in a chess tournament.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-59.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 59\" width=\"234\" height=\"197\" \/><br \/>\n\u2022 Your ring size is less than 7.5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-60.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 60\" width=\"133\" height=\"206\" \/><br \/>\n\u2022 The temperature is no more than -1 degree Fahrenheit.<br \/>\n\u2022 The elevation of a frog\ufb01sh is greater 1 than -8\\(\\frac{1}{2}\\) meters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-61.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 61\" width=\"222\" height=\"197\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-62.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 62\" width=\"156\" height=\"147\" \/><br \/>\nb. How can you represent all of the solutions for each statement in part(a) on a number line?<\/p>\n<p><strong>4.4 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the word sentence as an inequality.<\/strong><\/p>\n<p>Question 1.<br \/>\nA number is at least -10.<\/p>\n<p>Answer:<br \/>\nn \u2265 -10<\/p>\n<p>Explanation:<br \/>\nThe symbol for at least is \u2265.<br \/>\nSo, n \u2265 -10<\/p>\n<p>Question 2.<br \/>\nTwice a number y is more than &#8211;\\(\\frac{5}{2}\\).<\/p>\n<p>Answer:<br \/>\n2y &gt; -5\/2<\/p>\n<p>Explanation:<br \/>\nmore than symbol is &gt;.<br \/>\n2y &gt; -5\/2<\/p>\n<p>A solution of an inequality is a value that makes the inequality true. An inequality can have more than one solution. The set of all solutions of an inequality is called the solution set.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-63.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 63\" width=\"673\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-63.png 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-63-300x112.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether -5 is a solution of the inequality.<\/strong><\/p>\n<p>Question 3.<br \/>\nx + 12 &gt; 7<\/p>\n<p>Answer:<br \/>\n-5 is not soution.<\/p>\n<p>Explanation:<br \/>\nx + 12 &gt; 7<br \/>\n-5 + 12 &gt; 7<br \/>\n7 &gt; 7<\/p>\n<p>Question 4.<br \/>\n1 &#8211; 2p \u2264 -9<\/p>\n<p>Answer:<br \/>\n-5 is not the solution.<\/p>\n<p>Explanation:<br \/>\n1 &#8211; 2p \u2264 -9<br \/>\n1 &#8211; 2(-5) \u2264 -9<br \/>\n1 + 10 \u2264 -9<br \/>\n11 \u2264 -9<\/p>\n<p>Question 5.<br \/>\nn \u00f7 2.5 \u2265 -3<\/p>\n<p>Answer:<br \/>\n-5 is solution.<\/p>\n<p>Explanation:<br \/>\n-5 \u00f7 2.5 \u2265 -3<br \/>\n-2\u00a0\u2265 -3<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\n<strong>REASONING<\/strong><br \/>\nDo x &lt; 5 and 5 &lt; x represent the same inequality? Explain.<\/p>\n<p>Answer:<br \/>\nNo, both inequalities do not represent the same.<\/p>\n<p>Explanation:<br \/>\nNo, both inequalities do not represent the same.<br \/>\nThe reason is the first one x &lt; 5 means all numbers that are less than 5.<br \/>\nSecond one 5 &lt; x, all numbers that are greater than 5.<\/p>\n<p>Question 7.<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-31040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-64.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 64\" width=\"454\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-64.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-64-300x99.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Answer:<br \/>\nA number k is no more than -3 is different.<\/p>\n<p>Explanation:<br \/>\nA number k is less than or equal to -3<br \/>\nk \u2264 -3<br \/>\nA number k is at least -3<br \/>\nk \u2265 &#8211; 3<br \/>\na number k is at most -3<br \/>\nk \u2264 -3<br \/>\nA number k is no more than -3<br \/>\nk &lt; -3<\/p>\n<p><strong>CHECKING SOLUTIONS <\/strong><br \/>\n<strong>Tell whether -4 is a solution of the inequality.<\/strong><\/p>\n<p>Question 8.<br \/>\nc + 6 \u2264 3<\/p>\n<p>Answer:<br \/>\nYes, -4 is a solution of the inequality.<\/p>\n<p>Explanation:<br \/>\nc + 6 \u2264 3<br \/>\n-4 + 6 \u2264 3<br \/>\n2 \u2264 3<\/p>\n<p>Question 9.<br \/>\n6 &gt; p \u00f7 (-0.5)<\/p>\n<p>Answer:<br \/>\nNo, -4 is not a solution of the inequality.<\/p>\n<p>Explanation:<br \/>\n6 &gt; p \u00f7 (-0.5)<br \/>\n6 &gt; -4 \u00f7 (-0.5)<br \/>\n6 &gt; 4 \u00f7 (0.5)<br \/>\n6 &gt; 8<\/p>\n<p>Question 10.<br \/>\n-7 &lt; 2g + 1<\/p>\n<p>Answer:<br \/>\nNo, -4 is not a solution of the inequality.<\/p>\n<p>Explanation:<br \/>\n-7 &lt; 2g + 1<br \/>\n-7 &lt; 2(-4) + 1<br \/>\n-7 &lt; -8 + 1<br \/>\n-7 &lt; -7<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 11.<br \/>\nThe three requirements to pass a \ufb01tness test are shown. Write and graph three inequalities that represent the requirements. Then give a set of possible values for a person who passes the test.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-65.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 65\" width=\"213\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-65.png 213w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-65-150x150.png 150w\" sizes=\"(max-width: 213px) 100vw, 213px\" \/><\/p>\n<p>Answer:<br \/>\nx \u2265 2 kilometers<br \/>\nx \u2265 25 pushups<br \/>\nx \u2265 10 pullups<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34855 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-1.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-1\" width=\"1071\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-1.jpg 1071w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-1-300x44.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-1-1024x149.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-1-768x112.jpg 768w\" sizes=\"(max-width: 1071px) 100vw, 1071px\" \/><\/p>\n<p>Explanation:<br \/>\nJog at least 2 kilometers<br \/>\nx \u2265 2 kilometers<br \/>\nPerform 25 or more pushups<br \/>\nx \u2265 25 pushups<br \/>\nPerform at least 10 pull-ups<br \/>\nx \u2265 10 pullups<\/p>\n<p>Question 12.<br \/>\nTo set a depth record, a submersible vehicle must reach a water depth less than -715 feet. A vehicle breaks the record by more than 10 feet. Write and graph an inequality that represents the possible depths reached by the vehicle.<\/p>\n<p>Answer:<br \/>\n-705 &lt; x &lt; -175<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34902 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-2.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-2\" width=\"1059\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-2.jpg 1059w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-2-300x44.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-2-1024x151.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-2-768x113.jpg 768w\" sizes=\"(max-width: 1059px) 100vw, 1059px\" \/><\/p>\n<p>Explanation:<br \/>\nSubmersible vehicle must reach a water depth less than -715 feet<br \/>\nx &lt; &#8211; 175<br \/>\nA vehicle breaks the record by more than 10 feet.<br \/>\nSo, -175 + 10 &lt; x &lt; -175<br \/>\n-705 &lt; x &lt; -175<\/p>\n<h3><a id=\"Writing_and_Graphing_Inequalities_Homework_&amp;_Practice_4.4\"><\/a>Writing and Graphing Inequalities Homework &amp; Practice 4.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Solve the equation. Check your solution.<\/p>\n<p>Question 1.<br \/>\np &#8211; 8 = 3<\/p>\n<p>Answer:<br \/>\np = 11<\/p>\n<p>Explanation:<br \/>\np &#8211; 8 = 3<br \/>\np = 8 + 3<br \/>\np = 11<br \/>\nPutting p = 11 in p &#8211; 8 = 3<br \/>\n11 &#8211; 8 = 3<\/p>\n<p>Question 2.<br \/>\n8.7 + w = 5.1<\/p>\n<p>Answer:<br \/>\nw = -3.6<\/p>\n<p>Explanation:<br \/>\n8.7 + w = 5.1<br \/>\nw = 5.1 &#8211; 8.7<br \/>\nw = -3.6<br \/>\nPutting w = -3.6 in 8.7 + w = 5.1<br \/>\n8.7 + (-3.6) = 8.7 &#8211; 3.6 = 5.1<\/p>\n<p>Question 3.<br \/>\nx &#8211; 2 = -9<\/p>\n<p>Answer:<br \/>\nx = -7<\/p>\n<p>Explanation:<br \/>\nx &#8211; 2 = -9<br \/>\nx = -9 + 2<br \/>\nx = -7<br \/>\nPutting x = -7 in x &#8211; 2 = -9<br \/>\n-7 &#8211; 2 = -9<\/p>\n<p>Question 4.<br \/>\n8v + 5 = 1<\/p>\n<p>Answer:<br \/>\nv = -1\/2<\/p>\n<p>Explanation:<br \/>\n8v + 5 = 1<br \/>\n8v = 1 &#8211; 5<br \/>\n8v = -4<br \/>\nv = -4\/8<br \/>\nv = -1\/2<br \/>\nPutting v = -1\/2 in 8v + 5 = 1<br \/>\n8(-1\/2) + 5 = -4 + 5 = 1<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-66.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 66\" width=\"116\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nn = 5<\/p>\n<p>Explanation:<br \/>\n7\/8 &#8211; (1\/4)n = -3\/8<br \/>\n7\/8 + 3\/8 = 1\/4 n<br \/>\n1\/4 n = (7 + 3)\/8<br \/>\n1\/4 n = 10\/8<br \/>\nn = (10\/8) x (4)<br \/>\nn = 10\/2<br \/>\nn = 5<br \/>\nPutting n = 5 in 7\/8 &#8211; (1\/4)n = -3\/8<br \/>\n7\/8 &#8211; (1\/4)5 = 7\/8 &#8211; 5\/4<br \/>\n= (7-10)\/8 = -3\/8<\/p>\n<p>Question 6.<br \/>\n1.8 = 2.1h &#8211; 5.7 &#8211; 4.6h<\/p>\n<p>Answer:<br \/>\nh = -3<\/p>\n<p>Explanation:<br \/>\n1.8 = 2.1h &#8211; 5.7 &#8211; 4.6h<br \/>\n1.8 + 5.7 = 2.1h &#8211; 4.6h<br \/>\n-2.5h = 7.5<br \/>\nh = -7.5\/2.5<br \/>\nh = -3<br \/>\nPutting h = -3 in 1.8 = 2.1h &#8211; 5.7 &#8211; 4.6h<br \/>\n1.8 = 2.1(-3) &#8211; 5.7 &#8211; 4.6(-3)<br \/>\n= -6.3 &#8211; 5.7 + 13.8<br \/>\n= -12 + 13.8<\/p>\n<p>Question 7.<br \/>\nWhich expression has a value less than -5?<br \/>\nA. 5 + 8<br \/>\nB. -9 + 5<br \/>\nC. 1 + (-8)<br \/>\nD. 7 + (-2)<\/p>\n<p>Answer:<br \/>\nB has a value less than -5.<\/p>\n<p>Explanation:<br \/>\nA. 5 + 8 = 13<br \/>\nB. -9 + 5 = -4<br \/>\nC. 1 + (-8) = -7<br \/>\nD. 7 + (-2) = 5<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>UNDERSTANDING INEQUALITY STATEMENTS<\/strong><br \/>\n<strong>Choose a number that could represent the situation. What other numbers could represent the situation?<\/strong> (See Exploration 1, p. 145.)<\/p>\n<p>Question 8.<br \/>\nVisibility in an airplane is greater than 6.5 miles.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34921 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-3.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-3\" width=\"1092\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-3.jpg 1092w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-3-300x57.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-3-1024x193.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-3-768x145.jpg 768w\" sizes=\"(max-width: 1092px) 100vw, 1092px\" \/><br \/>\nx &gt; 6.5 miles<\/p>\n<p>Explanation:<br \/>\nx &gt; 6.5 miles<\/p>\n<p>Question 9.<br \/>\nYou must sell no fewer than 20 raffle tickets for a fundraiser.<\/p>\n<p>Answer:<br \/>\nx &gt; 20<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34924 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-4.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-4\" width=\"1027\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-4.jpg 1027w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-4-300x52.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-4-1024x177.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-4-768x133.jpg 768w\" sizes=\"(max-width: 1027px) 100vw, 1027px\" \/><\/p>\n<p>Explanation:<br \/>\nx &gt; 20<\/p>\n<p>Question 10.<br \/>\nYou consume at most 1800 calories per day.<\/p>\n<p>Answer:<br \/>\nx \u2264 1800<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34933 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-5.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-5\" width=\"1082\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-5.jpg 1082w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-5-300x50.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-5-1024x169.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-5-768x127.jpg 768w\" sizes=\"(max-width: 1082px) 100vw, 1082px\" \/><\/p>\n<p>Explanation:<br \/>\nx \u2264 1800<\/p>\n<p>Question 11.<br \/>\nThe elevation of the Dead Sea is less than -400 meters.<\/p>\n<p>Answer:<br \/>\nx &lt; -400<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34940 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-6.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-6\" width=\"1051\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-6.jpg 1051w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-6-300x56.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-6-1024x191.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-6-768x143.jpg 768w\" sizes=\"(max-width: 1051px) 100vw, 1051px\" \/><\/p>\n<p>Explanation:<br \/>\nx &lt; -400<\/p>\n<p><strong>WRITING AN INEQUALITY<\/strong><br \/>\n<strong>Write the word sentence as an inequality.<\/strong><\/p>\n<p>Question 12.<br \/>\nA number y is no more than -8.<\/p>\n<p>Answer:<br \/>\ny &lt; -8<\/p>\n<p>Explanation:<br \/>\nNo more than means &lt;<br \/>\ny &lt; -8<\/p>\n<p>Question 13.<br \/>\nA number w added to 2.3 is more than 18.<\/p>\n<p>Answer:<br \/>\nw + 2.3 &gt; 18<\/p>\n<p>Explanation:<br \/>\nMore than means &gt;<br \/>\nw + 2.3 &gt; 18<br \/>\nw &gt; 18 &#8211; 2.3<br \/>\nw &gt; 15.7<\/p>\n<p>Question 14.<br \/>\nA number t multiplied by -4 is atleast &#8211;\\(\\frac{2}{5}\\).<\/p>\n<p>Answer:<br \/>\n-4t \u2265 -2\/5<\/p>\n<p>Explanation:<br \/>\nAtleast means \u2265<br \/>\n-4t \u2265 -2\/5<\/p>\n<p>Question 15.<br \/>\nA number b minus 4.2 is less than -7.5.<\/p>\n<p>Answer:<br \/>\nb &#8211; 4.2 &lt; -7.5<\/p>\n<p>Explanation:<br \/>\nLess than means &lt;<br \/>\nb &#8211; 4.2 &lt; -7.5<br \/>\nb &lt; -7.5 + 4.2<br \/>\nb &lt; -3.3<br \/>\nb &gt; 3.3<\/p>\n<p>Question 16.<br \/>\n&#8211;\\(\\frac{5}{9}\\) is no less than 5 times a number k.<\/p>\n<p>Answer:<br \/>\n-5\/9 &gt; 5k<\/p>\n<p>Explanation:<br \/>\nNo less than means &gt;<br \/>\n-5\/9 &gt; 5k<\/p>\n<p>Question 17.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend writes the word sentence as an inequality. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-67.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 67\" width=\"252\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is correct.<\/p>\n<p>Explanation:<br \/>\nTwice a number x means 2x<br \/>\nAtmost means \u2264<br \/>\nSo, 2x \u2264 -24<\/p>\n<p><strong>CHECKING SOLUTIONS<\/strong><br \/>\n<strong>Tell whether the given value is a solution of the inequality.<\/strong><\/p>\n<p>Question 18.<br \/>\nn + 8 \u2264 13; n = 4<\/p>\n<p>Answer:<br \/>\nn = 4 is the solution<\/p>\n<p>Explanation:<br \/>\n4 + 8 \u2264 13<br \/>\n12 \u2264 13<\/p>\n<p>Question 19.<br \/>\n-15 &lt; 5h; h = -5<\/p>\n<p>Answer:<br \/>\nh = -5 is the solution<\/p>\n<p>Explanation:<br \/>\n-15 &lt; 5(-5)<br \/>\n-15 &lt; -25<\/p>\n<p>Question 20.<br \/>\np + 104 \u2264 0.5; p = 0.1<\/p>\n<p>Answer:<br \/>\np = 0.1 is the solution<\/p>\n<p>Explanation:<br \/>\n0.1 + 104 \u2264 0.5<br \/>\n104.1 \u2264 0.5<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{a}{6}\\) &gt; -4; a = -18<\/p>\n<p>Answer:<br \/>\na = -18 is the solution<\/p>\n<p>Explanation:<br \/>\na\/6 &gt; -4<br \/>\n-18\/6 &gt; -4<br \/>\n-3 &gt; -4<\/p>\n<p>Question 22.<br \/>\n6 \u2265 &#8211;\\(\\frac{2}{3}\\)s ; s = -9<\/p>\n<p>Answer:<br \/>\ns = -9 is the solution<\/p>\n<p>Explanation:<br \/>\n6 \u2265 (-2\/3)s<br \/>\n6 \u2265 (-2\/3) x -9<br \/>\n6 \u2265 2 x 3<br \/>\n6 \u2265 6<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-68.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 68\" width=\"145\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\nk = 1\/4 is not the solution<\/p>\n<p>Explanation:<br \/>\n7\/8 &#8211; 3k &lt; -1\/2<br \/>\n7\/8 &#8211; 3(1\/4) &lt; -1\/2<br \/>\n7\/8 &#8211; 3\/4 &lt; -1\/2<br \/>\n(7 &#8211; 6)\/8 &lt; -1\/2<br \/>\n1\/8 &lt; -1\/2<\/p>\n<p><strong>GRAPHING AN INEQUALITY<\/strong><br \/>\n<strong>Graph the inequality on a number line.<\/strong><\/p>\n<p>Question 24.<br \/>\nr \u2264 -9<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34959 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-7.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-7\" width=\"1082\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-7.jpg 1082w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-7-300x43.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-7-1024x146.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-7-768x109.jpg 768w\" sizes=\"(max-width: 1082px) 100vw, 1082px\" \/><\/p>\n<p>Question 25.<br \/>\ng \u2265 2.75<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34964 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-8.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-8\" width=\"1059\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-8.jpg 1059w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-8-300x38.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-8-1024x131.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-8-768x98.jpg 768w\" sizes=\"(max-width: 1059px) 100vw, 1059px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-69.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 69\" width=\"79\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34970 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-9.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-9\" width=\"1046\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-9.jpg 1046w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-9-300x47.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-9-1024x161.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-9-768x120.jpg 768w\" sizes=\"(max-width: 1046px) 100vw, 1046px\" \/><\/p>\n<p>Explanation:<br \/>\nx \u2265 -7\/2<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-70.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 70\" width=\"62\" height=\"42\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-34975 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-10.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.4-10\" width=\"1039\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-10.jpg 1039w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-10-300x56.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-10-1024x190.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-10-768x143.jpg 768w\" sizes=\"(max-width: 1039px) 100vw, 1039px\" \/><\/p>\n<p>Explanation:<br \/>\n5\/4 &gt; z<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nEach day at lunchtime, atleast 53 people buy food from a food truck. Write and graph an inequality that represents this situation.<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<\/p>\n<p><strong>CHECKING SOLUTIONS<\/strong><br \/>\n<strong>Tell whether the given value is a solution of the inequality.<\/strong><\/p>\n<p>Question 29.<br \/>\n4k &lt; k + 8; k = 3<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-191.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 191\" width=\"149\" height=\"46\" \/><\/p>\n<p>Answer:<\/p>\n<p>Explanation:<\/p>\n<p>Question 31.<br \/>\n7 &#8211; 2y &gt; 3y + 13; y = -1<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-71.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 71\" width=\"186\" height=\"45\" \/><\/p>\n<p>Answer:<\/p>\n<p>Explanation:<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA single subway ride for a student costs $1.25. A monthly pass costs $35.<br \/>\na. Write an inequality that represents the numbers of times you can ride the subway each month for the monthly pass to be a better deal.<br \/>\nb. You ride the subway about 45 times per month. Should you buy the monthly pass? Explain.<\/p>\n<p>Answer:<br \/>\na. 1.25x \u2265 35<br \/>\nb. Yes, it is better to buy a monthly pass.<\/p>\n<p>Explanation:<br \/>\nA.<br \/>\n1.25x \u2265 35<br \/>\nB. 1.25x \u2265 35<br \/>\nx \u2265 35\/1.25<br \/>\nx \u2265 28<br \/>\nYes, it is better to buy a monthly pass.<\/p>\n<p>Question 34.<br \/>\n<strong>LOGIC<\/strong><br \/>\nConsider the in equality b &gt; -2.<br \/>\na. Describe the values of b that are solutions of the inequality.<br \/>\nb. Describe the values of b that are not solutions of the inequality. Write an inequality that represents these values.<br \/>\nc. What do all the values in parts (a) and (b) represent? Is this true for any similar pair of inequalities? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. b is greater than -2, The possible solutions of b are -1, 0, 1, 2, and so on<br \/>\nb. The values of b that are nor solutions are -2, -3, -4, -5, -6, &#8230;. and an inequality that represents it is b &lt; &#8211; 2<br \/>\nc. All the values in parts (A), (b) represents all whole numbers.<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA planet orbiting a star at a distance such that its temperatures are right for liquid water is said to be in the star\u2019s habitable zone. The habitable zone of a particular star is atleast 0.023 AU and at most 0.054 AU from the star (1 AU is equal to the distance between Earth and the Sun). Draw a graph that represents the habitable zone.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-72.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 72\" width=\"243\" height=\"199\" \/><\/p>\n<p>Answer:<br \/>\nx \u2265 0.023 and x \u2264 0.054<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-35012 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-11-1.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4-11\" width=\"1089\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-11-1.jpg 1089w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-11-1-300x62.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-11-1-1024x211.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.4-11-1-768x158.jpg 768w\" sizes=\"(max-width: 1089px) 100vw, 1089px\" \/><\/p>\n<p>Explanation:<br \/>\nAs the start is at least 0.023 AU means x \u2265 0.023<br \/>\nAnd it is almost 0.054 AU means x \u2264 0.054<br \/>\nx \u2265 0.023 \u2264 0.054<\/p>\n<p>Question 36.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe girth of a package is the distance around the perimeter of a face that does not include the length as a side. A postal service says that a rectangular package can have a maximum combined length and girth of 108 inches.<br \/>\na. Write an inequality that represents the allowable dimensions for the package.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-73.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 73\" width=\"247\" height=\"203\" \/><br \/>\nb. Find three different sets of allowable dimensions that are reasonable for the package. Find the volume of each package.<\/p>\n<p>Answer:<br \/>\na. x \u2265 27 inches<br \/>\nb. The three different sets of allowable dimensions are 27, 28, 29 and their volumes are 19683 cubic inches, 21952 cubic inches, 24389 cubic inches.<\/p>\n<p>Explanation:<br \/>\nGirth = 108 inches<br \/>\n4x \u2265 108<br \/>\nx \u2265 108\/4<br \/>\nx \u2265 27<br \/>\nb. The three different sets of allowable dimensions are 27, 28, 29<br \/>\nVolume = 27\u00b3 = 19683<br \/>\n= 28\u00b3 = 21952<br \/>\n= 29\u00b3 = 24389<\/p>\n<h3><a id=\"Lesson_4.5_Solving_Inequalities_Using_Addition_or_Subtraction\"><\/a>Lesson 4.5 Solving Inequalities Using Addition or Subtraction<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Writing Inequalities<\/strong><br \/>\n<strong>Work with a partner. Use two number cubes on which the odd numbers are negative on one of the number cubes and the even numbers are negative on the other number cube.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 74\" width=\"498\" height=\"458\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74-300x276.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<ul>\n<li>Roll the number cubes. Write an inequality that compares the numbers.<\/li>\n<li>Roll one of the number cubes. Add the number to each side of the inequality and record your result.<\/li>\n<li>Repeat the previous two steps \ufb01ve more times.<\/li>\n<\/ul>\n<p>a. When you add the same number to each side of an inequality, does the inequality remain true? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-75.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 75\" width=\"156\" height=\"165\" \/><br \/>\nb. When you subtract the same number from each side of an inequality, does the inequality remain true? Use inequalities generated by number cubes to justify your answer.<br \/>\nc. Use your results in parts (a) and (b) to make a conjecture about how to solve inequality of form x + a &lt; b for x. 4.5 Lesson Try It Solve the inequality.<\/p>\n<p>Answer:<br \/>\na. When you add the same number to each side of an inequality, does the inequality remains true. Because when the same quantity is added on both sides does not show any impact on the actual inequality.<br \/>\nb. When you subtract the same number from each side of an inequality, the inequality remain true. Because when the same quantity is subtracted from both sides does not show any impact on the actual inequality.<\/p>\n<p>Graph the solution.<\/p>\n<p>Question 1.<\/p>\n<p>y &#8211; 6 &gt; -7<\/p>\n<p>Answer:<br \/>\ny &gt; -1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-1.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-1\" width=\"1078\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-1.jpg 1078w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-1-300x51.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-1-1024x175.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-1-768x131.jpg 768w\" sizes=\"(max-width: 1078px) 100vw, 1078px\" \/><\/p>\n<p>Explanation:<br \/>\ny &gt; -7 + 6<br \/>\ny &gt; -1<\/p>\n<p>Question 2.<br \/>\nb &#8211; 3.8 \u2264 1.7<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-2.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-2\" width=\"1045\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-2.jpg 1045w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-2-300x41.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-2-1024x139.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-2-768x104.jpg 768w\" sizes=\"(max-width: 1045px) 100vw, 1045px\" \/><\/p>\n<p>Explanation:<br \/>\nb \u2264 1.7 + 3.8<br \/>\nb \u2264 5.5<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-76.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 76\" width=\"97\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-3.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-3\" width=\"1036\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-3.jpg 1036w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-3-300x36.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-3-1024x124.jpg 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-3-768x93.jpg 768w\" sizes=\"(max-width: 1036px) 100vw, 1036px\" \/><\/p>\n<p>Explanation:<br \/>\n-1\/2 + 1\/4 &gt; z<br \/>\n(-2 + 1)\/4 &gt; z<br \/>\n-1\/4 &gt; z<br \/>\n1\/4 &lt; z<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 4.<br \/>\nw + 3 \u2264 -1<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-4.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-4\" width=\"689\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-4.jpg 689w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-4-300x47.jpg 300w\" sizes=\"(max-width: 689px) 100vw, 689px\" \/><br \/>\nw \u2264 -4<\/p>\n<p>Explanation:<br \/>\nw \u2264 -1 &#8211; 3<br \/>\nw \u2264 -4<\/p>\n<p>Question 5.<br \/>\n8.5 \u2265 d + 10<\/p>\n<p>Answer:<br \/>\n1.5 \u2264 d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-5.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-5\" width=\"702\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-5.jpg 702w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-5-300x42.jpg 300w\" sizes=\"(max-width: 702px) 100vw, 702px\" \/><\/p>\n<p>Explanation:<br \/>\n8.5 &#8211; 10 \u2265 d<br \/>\n-1.5 \u2265 d<br \/>\n1.5 \u2264 d<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-77.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 77\" width=\"89\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\nx &gt; 3\/4<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-35214 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-6.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-6\" width=\"673\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-6.jpg 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-6-300x45.jpg 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><\/p>\n<p>Explanation:<br \/>\nx &gt; 3\/2 &#8211; 3\/4<br \/>\nx &gt; (6 &#8211; 3)\/4<br \/>\nx &gt; 3\/4<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the inequalities c + 3 &gt; 5 and c &#8211; 1 &gt; 1 equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nInequalities are equivalent.<\/p>\n<p>Explanation:<br \/>\nc + 3 &gt; 5 and c &#8211; 1 &gt; 1<br \/>\nc &gt; 5 &#8211; 3 and c &gt; 1 + 1<br \/>\nc &gt; 2 and c &gt; 2<\/p>\n<p>Question 8.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich inequality does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-78.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 78\" width=\"230\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\n-7\/4 &lt; w &#8211; 3\/4<\/p>\n<p>Explanation:<br \/>\nw + 7\/4 &lt; 3\/4<br \/>\nw &lt; 3\/4 &#8211; 7\/4<br \/>\nw &lt; -4\/4<br \/>\nw &lt; -1<br \/>\nw &#8211; 3\/4 &gt; -7\/4<br \/>\nw &gt; -7\/4 + 3\/4<br \/>\nw &gt; -4\/4<br \/>\nw &gt; -1<br \/>\nw+ 7\/4 &gt; 3\/4<br \/>\nw &gt; 3\/4 &#8211; 7\/4<br \/>\nw &gt; -4\/4<br \/>\nw &gt; -1<br \/>\n-7\/4 &lt; w &#8211; 3\/4<br \/>\n-7\/4 + 3\/4 &lt; w<br \/>\n-4\/4 &lt; w<br \/>\n-1 &lt; w<br \/>\nBy solving all inequalities we obtain w &gt; -1, but by solving -7\/4 &lt; w &#8211; 3\/4, we get -1 &lt; w.<\/p>\n<p><strong>SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 9.<br \/>\nx &#8211; 4 &gt; -6<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-7.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-7\" width=\"704\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-7.jpg 704w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-7-300x41.jpg 300w\" sizes=\"(max-width: 704px) 100vw, 704px\" \/><br \/>\nx &gt; -2<\/p>\n<p>Explanation:<br \/>\nx &gt; -6 + 4<br \/>\nx &gt; -2<\/p>\n<p>Question 10.<br \/>\nz + 4.5 \u2264 3.25<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-8.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-8\" width=\"702\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-8.jpg 702w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-8-300x38.jpg 300w\" sizes=\"(max-width: 702px) 100vw, 702px\" \/><br \/>\nz \u2264 -1.25<\/p>\n<p>Explanation:<br \/>\nz \u2264 3.25 &#8211; 4.5<br \/>\nz \u2264 -1.25<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-79.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 79\" width=\"89\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-9.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-9\" width=\"704\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-9.jpg 704w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-9-300x54.jpg 300w\" sizes=\"(max-width: 704px) 100vw, 704px\" \/><br \/>\n-1\/10 &gt; g<\/p>\n<p>Explanation:<br \/>\n7\/10 &#8211; 4\/5 &gt; g<br \/>\n(7 &#8211; 8)\/10 &gt; g<br \/>\n-1\/10 &gt; g<\/p>\n<p>Question 12.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite two different inequalities that can be represented using the graph. Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-80.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 80\" width=\"419\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-80.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-80-300x39.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Answer:<br \/>\nx &gt; -5<br \/>\nx \u2265 5<\/p>\n<p>Explanation:<br \/>\nx &gt; -5<br \/>\nBecause in the graph the point is from 5 to left side.<br \/>\nx \u2265 5<br \/>\nIn the graph, the point is also located on 5.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA volcanologist rappels 1200 feet into a volcano. He wants to climb out of the volcano in less than 4 hours. He climbs the \ufb01rst 535 feet in 100 minutes. Graph an inequality that represents the average rates at which he can climb the remaining distance and meet his goal. Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe average rate at which he climb the remaining distance and meet his goal is less than 0.21 inches per 1 minute.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-10.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-10\" width=\"681\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-10.jpg 681w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-10-300x51.jpg 300w\" sizes=\"(max-width: 681px) 100vw, 681px\" \/><\/p>\n<p>Explanation:<br \/>\nA volcanologist rappel climbs first 535 feet in 100 minutes<br \/>\nHe needs to climb the remaining 1200 &#8211; 535 = 665 feet in the remaining time.<br \/>\n(1200 &#8211; 535)x &lt; (4 x 60 &#8211; 100)<br \/>\n665x &lt; (240 &#8211; 100)<br \/>\n665x &lt; 140<br \/>\nx &lt; 140\/665<br \/>\nx &lt; 0.21<br \/>\nThe average rate at which he climb the remaining distance and meet his goal is less than 0.21 inches per 1 minute.<\/p>\n<p>Question 14.<br \/>\nYou install a mailbox by burying a post as shown. According to postal service guidelines, the bottom of the box must be at least 41 inches, but no more than 45 inches, above the road. Write and interpret two inequalities that describe the possible lengths of the post.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-81.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 81\" width=\"151\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\nThe possible length of post is in between 45 to 41 inches<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe bottom box must be at least 41 inches<br \/>\nx \u2265 41 inches<br \/>\nThe bottom box must be no more than 45 inches<br \/>\nx &lt; 45<br \/>\nBy combining both inequalities, we get<br \/>\n45 &lt; x \u2265 41<br \/>\nSo, the possible length of post is in between 45 to 41 inches.<\/p>\n<h3><a id=\"Solving_Inequalities_Using_Addition_or_Subtraction_Homework_&amp;_Practice_4.5\"><\/a>Solving Inequalities Using Addition or Subtraction Homework &amp; Practice 4.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write the word sentence as an inequality.<\/strong><\/p>\n<p>Question 1.<br \/>\nA number p is greater than 5.<\/p>\n<p>Answer:<br \/>\np &gt; 5.<\/p>\n<p>Explanation:<br \/>\ngreater than means &gt;<br \/>\np &gt; 5.<\/p>\n<p>Question 2.<br \/>\nA number z times 3 is atmost -4.8.<\/p>\n<p>Answer:<br \/>\n3z \u2264 -4.8<\/p>\n<p>Explanation:<br \/>\nAtmost means \u2264<br \/>\n3z \u2264 -4.8<\/p>\n<p>Question 3.<br \/>\nThe sum of a number n and \\(\\frac{2}{3}\\) is no less than 5\\(\\frac{1}{3}\\).<\/p>\n<p>Answer:<br \/>\nn + 2\/3 &gt; 5(1\/3)<\/p>\n<p>Explanation:<br \/>\nThe sum of n and 2\/3 is n + 2\/3<br \/>\nno less than means &gt;<br \/>\nn + 2\/3 &gt; 5(1\/3)<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n4x = 36<\/p>\n<p>Answer:<br \/>\nx = 9<\/p>\n<p>Explanation:<br \/>\n4x = 36<br \/>\nx = 36\/4<br \/>\nx = 9<br \/>\nPutting x = 9 in 4x = 36<br \/>\n4(9) = 36<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{w}{3}\\) = -9<\/p>\n<p>Answer:<br \/>\nw = -27<\/p>\n<p>Explanation:<br \/>\nw\/3 = -9<br \/>\nw = -9 x 3<br \/>\nw = -27<br \/>\nPutting w = -27 in w\/3 = -9<br \/>\n-27\/3 = -9<\/p>\n<p>Question 6.<br \/>\n-2b = 44<\/p>\n<p>Answer:<br \/>\nb = -22<\/p>\n<p>Explanation:<br \/>\n-2b = 44<br \/>\nb = -44\/2<br \/>\nb = -22<br \/>\nPutting b = -22 in -2b = 44<br \/>\n-2(-22) = 44<\/p>\n<p>Question 7.<br \/>\n60 = \\(\\frac{3}{4}\\)h<\/p>\n<p>Answer:<br \/>\nh = 80<\/p>\n<p>Explanation:<br \/>\n60 = (3\/4)h<br \/>\n60 x 4 = 3h<br \/>\n240 = 3h<br \/>\nh = 240\/3<br \/>\nh = 80<br \/>\nPutting h = 80 in 60 = (3\/4)h<br \/>\n60 = (3\/4) x 80 = 3 x 20<\/p>\n<p>Question 8.<br \/>\nWhich fraction is equivalent to -2.4?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-82.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 82\" width=\"506\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-82.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-82-300x33.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Answer:<br \/>\n-12\/5 is the equivalent to -2.4<\/p>\n<p>Explanation:<br \/>\n-12\/5 = -2.4<br \/>\n-51\/25 = -2.04<br \/>\n-8\/5 = -1.6<br \/>\n-6\/25 = -0.24<br \/>\nSo, by observing all those, we can say that -12\/5 is the equivalent to -2.4<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>WRITING AN INEQUALITY<\/strong><br \/>\n<strong>Write an inequality that compares the given numbers. Does the inequality remain true when you add 2 to each side? Justify your answer.<\/strong> (See Exploration 1, p. 151.)<\/p>\n<p>Question 9.<br \/>\n-1; 4<\/p>\n<p>Answer:<br \/>\n-1 &gt; 4<br \/>\nFalse.<\/p>\n<p>Explanation:<br \/>\n-1 &gt; 4<br \/>\n-1 + 2 &gt; 4 + 2<br \/>\n1 &gt; 6<\/p>\n<p>Question 10.<br \/>\n-3; -6<\/p>\n<p>Answer:<br \/>\n-3 &gt; &#8211; 6<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\n-3 &gt; &#8211; 6<br \/>\nBy adding 2 to each side<br \/>\n-3 + 2 &gt; -6 + 2<br \/>\n-1 &gt; -4<\/p>\n<p>Question 11.<br \/>\n-4; -1<\/p>\n<p>Answer:<br \/>\n-4 &lt; -1<br \/>\nFalse<\/p>\n<p>Explanation:<br \/>\n-4 &lt; -1<br \/>\n-4 + 2 &lt; -1 + 2<br \/>\n-2 &lt; 1<br \/>\nFalse<\/p>\n<p><strong>SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 12.<br \/>\nx + 7 \u2265 18<\/p>\n<p>Answer:<br \/>\nx \u2265 11<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-11.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-11\" width=\"765\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-11.jpg 765w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-11-300x50.jpg 300w\" sizes=\"(max-width: 765px) 100vw, 765px\" \/><\/p>\n<p>Explanation:<br \/>\nx \u2265 18 &#8211; 7<br \/>\nx \u2265 11<\/p>\n<p>Question 13.<br \/>\na &#8211; 2 &gt; 4<\/p>\n<p>Answer:<br \/>\na &gt; 6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-12.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-12\" width=\"723\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-12.jpg 723w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-12-300x45.jpg 300w\" sizes=\"(max-width: 723px) 100vw, 723px\" \/><\/p>\n<p>Explanation:<br \/>\na &gt; 4 + 2<br \/>\na &gt; 6<\/p>\n<p>Question 14.<br \/>\n3 \u2264 7 + g<\/p>\n<p>Answer:<br \/>\n-4 \u2264 g<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4_optimized.5-13.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4_optimized.5-13\" width=\"683\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4_optimized.5-13.jpg 683w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4_optimized.5-13-300x40.jpg 300w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/p>\n<p>Explanation:<br \/>\n3 &#8211; 7 \u2264 g<br \/>\n-4 \u2264 g<\/p>\n<p>Question 15.<br \/>\n8 + k \u2264 -3<\/p>\n<p>Answer:<br \/>\nk \u2264 -11<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-14.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-14\" width=\"680\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-14.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-14-300x44.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Explanation:<br \/>\nk \u2264 -3 &#8211; 8<br \/>\nk \u2264 -11<\/p>\n<p>Question 16.<br \/>\n-12 &lt; y &#8211; 6<\/p>\n<p>Answer:<br \/>\n-6 &lt; y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-15.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-15\" width=\"704\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-15.jpg 704w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-15-300x57.jpg 300w\" sizes=\"(max-width: 704px) 100vw, 704px\" \/><\/p>\n<p>Explanation:<br \/>\n-12 + 6 &lt; y<br \/>\n-6 &lt; y<\/p>\n<p>Question 17.<br \/>\nn &#8211; 4 &lt; 5<\/p>\n<p>Answer:<br \/>\nn &lt; 9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-16.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-16\" width=\"780\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-16.jpg 780w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-16-300x45.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-16-768x115.jpg 768w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/p>\n<p>Explanation:<br \/>\nn &lt; 4 + 5<br \/>\nn &lt; 9<\/p>\n<p>Question 18.<br \/>\nt &#8211; 5 \u2264 -7<\/p>\n<p>Answer:<br \/>\nt \u2264 -2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-17.jpg\" alt=\"\" width=\"691\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-17.jpg 691w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-17-300x43.jpg 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><\/p>\n<p>Explanation:<br \/>\nt \u2264 -7 + 5<br \/>\nt \u2264 -2<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 83\" width=\"88\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\np \u2265 7\/4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-18.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-18\" width=\"673\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-18.jpg 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-18-300x54.jpg 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><\/p>\n<p>Explanation:<br \/>\np \u2265 2 &#8211; (1\/4)<br \/>\np \u2265 (8 &#8211; 1)\/4<br \/>\np \u2265 7\/4<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-84.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 84\" width=\"90\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n-3\/7 &gt; b<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-19.jpg\" alt=\"\" width=\"685\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-19.jpg 685w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-19-300x49.jpg 300w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/><\/p>\n<p>Explanation:<br \/>\n2\/7 &#8211; 5\/7 &gt; b<br \/>\n(2 &#8211; 5)\/7 &gt; b<br \/>\n-3\/7 &gt; b<\/p>\n<p>Question 21.<br \/>\nz &#8211; 4.7 \u2265 -1.6<\/p>\n<p>Answer:<br \/>\nz \u2265 3.1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-20.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-20\" width=\"723\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-20.jpg 723w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-20-300x47.jpg 300w\" sizes=\"(max-width: 723px) 100vw, 723px\" \/><\/p>\n<p>Explanation:<br \/>\nz \u2265 -1.6 + 4.7<br \/>\nz \u2265 3.1<\/p>\n<p>Question 22.<br \/>\n-9.1 &lt; d &#8211; 6.3<\/p>\n<p>Answer:<br \/>\n-2.8 &lt; d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-21.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-21\" width=\"675\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-21.jpg 675w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-21-300x45.jpg 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/p>\n<p>Explanation:<br \/>\n-9.1 + 6.3 &lt; d<br \/>\n-2.8 &lt; d<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-85.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 85\" width=\"90\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n-4\/5 &gt; s<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-22.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-22\" width=\"668\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-22.jpg 668w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-22-300x43.jpg 300w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/p>\n<p>Explanation:<br \/>\n8\/5 &#8211; 12\/5 &gt; s<br \/>\n(8 &#8211; 12)\/5 &gt; s<br \/>\n-4\/5 &gt; s<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-86.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 86\" width=\"104\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n6\/8 \u2265 m<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-23.jpg\" alt=\"\" width=\"677\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-23.jpg 677w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-23-300x48.jpg 300w\" sizes=\"(max-width: 677px) 100vw, 677px\" \/><\/p>\n<p>Explanation:<br \/>\n-7\/8 + 13\/8 \u2265 m<br \/>\n6\/8 \u2265 m<\/p>\n<p>Question 25.<br \/>\nr + 0.2 &lt; -0.7<\/p>\n<p>Answer:<br \/>\nr &lt; 0.5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-24.jpg\" alt=\"\" width=\"663\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-24.jpg 663w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-24-300x48.jpg 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><\/p>\n<p>Explanation:<br \/>\nr &lt; 0.7 &#8211; 0.2<br \/>\nr &lt; 0.5<\/p>\n<p>Question 26.<br \/>\nh &#8211; 6 \u2264 -8.4<\/p>\n<p>Answer:<br \/>\nh \u2264 -2.4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-25.jpg\" alt=\"big-ideas-math-answers-grade-7-chapter-4.5-25\" width=\"699\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-25.jpg 699w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-4.5-25-300x42.jpg 300w\" sizes=\"(max-width: 699px) 100vw, 699px\" \/><\/p>\n<p>Explanation:<br \/>\nh \u2264 -8.4 + 6<br \/>\nh \u2264 -2.4<\/p>\n<p><strong>YOU BE THE TEACHER<br \/>\nYour friend solves the inequality and graphs the solution. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-87.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 87\" width=\"258\" height=\"163\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is correct.<\/p>\n<p>Explanation:<br \/>\nx &#8211; 7 &gt; &#8211; 2<br \/>\nx &gt; &#8211; 2 + 7<br \/>\nx &gt; 5<br \/>\nAs the graph says the values of x are more than 5.<br \/>\nSo, my friend is correct.<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-88.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 88\" width=\"262\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nMy friend is correct.<\/p>\n<p>Explanation:<br \/>\n8 \u2264 x + 3<br \/>\n8 &#8211; 3 \u2264 x<br \/>\n5 \u2264 x<br \/>\nAs the graph represents the values of x are less than or equal to 5.<br \/>\nSo, my friend is correct.<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA small airplane can hold 44 passengers. Fifteen passengers board the plane.<br \/>\na. Write and solve an inequality that represents the additional numbers of passengers that can board the plane.<br \/>\nb. Can 30 more passengers board the plane? Explain.<\/p>\n<p>Answer:<br \/>\na. 15 + x \u2264 44<br \/>\nb. No.<\/p>\n<p>Explanation:<br \/>\nAs the airplane can hold 44 passengers and already 15 passengers board the plane. The inequality can be expressed as<br \/>\n15 + x \u2264 44<br \/>\nHere, x is the additional number of passengers who board the plane<br \/>\nb. Can 30 more passengers board the plane<br \/>\nSo, take x as 30<br \/>\n15 + 30 \u2264 44<br \/>\n45 \u2264 44<br \/>\nAs this inequality is false. So, 30 more passengers board the plane<\/p>\n<p><strong>GEOMETRY <\/strong><br \/>\n<strong>Find the possible values of x.<\/strong><\/p>\n<p>Question 30.<br \/>\nThe perimeter is less than 28 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-89.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 89\" width=\"133\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nx &lt; 14<\/p>\n<p>Explanation:<br \/>\nPerimeter = 7 + 7 + x = 14 + x<br \/>\nThe perimeter is less than 28 feet.<br \/>\nSo, p &lt; 28<br \/>\n14 + x &lt; 28<br \/>\nx &lt; 28 &#8211; 14<br \/>\nx &lt; 14<\/p>\n<p>Question 31.<br \/>\nThe base is greater than the height.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-90.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 90\" width=\"163\" height=\"132\" \/><\/p>\n<p>Answer:<br \/>\nx &gt; 5<\/p>\n<p>Explanation:<br \/>\nHere base = (x + 3), h = 8<br \/>\nThe base is greater than the height.<br \/>\nb &gt; h<br \/>\n(x + 3) &gt; 8<br \/>\nx &gt; 8 &#8211; 3<br \/>\nx &gt; 5<\/p>\n<p>Question 32.<br \/>\nThe perimeter is less than or equal to 51 meters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-91.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 91\" width=\"183\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nx \u2264 15 m<\/p>\n<p>Explanation:<br \/>\nPerimeter = 10 + 8 + 8 + 10 + x<br \/>\n= 36 + x<br \/>\nThe perimeter is less than or equal to 51 meters.<br \/>\nperimeter \u2264 51<br \/>\n36 + x \u2264 51<br \/>\nx \u2264 51 &#8211; 36<br \/>\nx \u2264 15<\/p>\n<p>Question 33.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe inequality d + s &gt; -3 is equivalent to d &gt; -7. What is the value of s?<\/p>\n<p>Answer:<br \/>\ns = -4<\/p>\n<p>Explanation:<br \/>\nd + s &gt; -3<br \/>\nd &gt; -3 &#8211; s<br \/>\nWhen s = -4, then d + s &gt; -3 is equivalent to d &gt; -7<br \/>\nSo, s = -4<\/p>\n<p>Question 34.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou can spend up to $35 on a shopping trip.<br \/>\na. You want to buy a shirt that costs $14. Write and solve an inequality that represents the remaining amounts of money you can spend if you buy the shirt.<br \/>\nb. You notice that the shirt is on sale for 30% off. How does this change your inequality in part(a)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-92.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 92\" width=\"187\" height=\"226\" \/><\/p>\n<p>Answer:<br \/>\na. x + $14 &lt; 35<br \/>\nb. x + $9.8 &lt; 35<\/p>\n<p>Explanation:<br \/>\nYou can spend up to $35 on a shopping trip.<br \/>\na. Shirt cost = $14<br \/>\nThe inequality represents the remaining amounts of money you can spend if you buy the shirt.<br \/>\nx + $14 &lt; 35<br \/>\nb. When the shirt is on 30% sale<br \/>\nIf the shirt is on sale, then the cost of the shirt is $9.8<br \/>\nThen 35 &#8211; 9.8 = 25.2<br \/>\nThen the inequality is x + $9.8 &lt; 35<\/p>\n<p>Question 35.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIf items plugged into a circuit use more than 2400 watts of electricity, the circuit overloads. A portable heater that uses 1050 watts of electricity is plugged into the circuit.<br \/>\na. Find the additional numbers of watts you can plug in without overloading the circuit.<br \/>\nb. In addition to the portable heater, what two other items in the table can you plug in at the same time without overloading the circuit? Is there more than one possibility? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-93.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 93\" width=\"226\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\na. You can add 1350 additional watts without overloading the circuit.<br \/>\nb. You can add vacuum cleaner, television, and vacuum cleaner, aquarium.<\/p>\n<p>Explanation:<br \/>\na. Given that,<br \/>\nCircuit overloads at 2400 watts<br \/>\nElectricity used by heater = 1050 watts<br \/>\nLet,<br \/>\nx be the number of additional watts.<br \/>\nElectricity used by heater + Additional watts \u2264 Circuit&#8217;s capacity<br \/>\n1050 + x \u2264 2400<br \/>\nx \u2264 2400 &#8211; 1050<br \/>\nx \u2264 1350<br \/>\nYou can add 1350 additional watts without overloading the circuit.<br \/>\nb. Check the sum of which two numbers is less than 1350<br \/>\nYou can add vacuum cleaner, television, and vacuum cleaner, aquarium.<\/p>\n<p>Question 36.<br \/>\nThe possible values of x are given by x + 8 \u2264 6. What is the greatest possible value of 7x? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe greatest possible value of x is -14.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nx + 8 \u2264 6<br \/>\nx \u2264 6 &#8211; 8<br \/>\nx \u2264 -2<br \/>\nMultiply both sides by 7<br \/>\n7x \u2264 -14<br \/>\nSo the greatest possible value of x is -14.<\/p>\n<h3><a id=\"Lesson_4.6_Solving_Inequalities_Using_Multiplication_or_Division\"><\/a>Lesson 4.6 Solving Inequalities Using Multiplication or Division<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Writing Inequalities<\/strong><br \/>\n<strong>Work with a partner. Use two number cubes on which the odd numbers are negative on one of the number cubes and the even numbers are negative on the other number cube.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-94.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 94\" width=\"419\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-94.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-94-300x177.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<ul>\n<li>Roll the number cubes. Write an inequality that compares the numbers.<\/li>\n<li>Roll one of the number cubes. Multiply each side of the inequality by the number and record your result.<\/li>\n<li>Repeat the previous two steps nine more times.<\/li>\n<\/ul>\n<p>a. When you multiply each side of an inequality by the same number, does the inequality remain true? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-95.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 95\" width=\"151\" height=\"182\" \/><br \/>\nb. When you divide each side of an inequality by the same number, does the inequality remain true? Use inequalities generated by number cubes to justify your answer.<br \/>\nc. Use your results in parts (a) and (b) to make a conjecture about how to solve an inequality of the form ax &lt; b for x when a &gt; 0 and when a &lt; 0.<\/p>\n<p><strong>4.6 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 1.<br \/>\nn \u00f7 3 &lt; 1<\/p>\n<p>Answer:<br \/>\nn &lt; 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-77.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 77\" width=\"685\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-77.jpg 685w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-77-300x36.jpg 300w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/><\/p>\n<p>Explanation:<br \/>\nn &lt; 1 x 3<br \/>\nn &lt; 3<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-96.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 96\" width=\"77\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\n-5 \u2264 m<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-78.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 78\" width=\"685\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-78.jpg 685w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-78-300x38.jpg 300w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/><\/p>\n<p>Explanation:<br \/>\n-0.5 x 10 \u2264 m<br \/>\n-5 \u2264 m<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-97.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 97\" width=\"72\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\n-4.5 &gt; p<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-79.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 79\" width=\"673\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-79.jpg 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-79-300x60.jpg 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><\/p>\n<p>Explanation:<br \/>\n-3 &gt; (2\/3) p<br \/>\n-3 x 3 &gt; 2p<br \/>\n-9 &gt; 2p<br \/>\n-9\/2 &gt; p<br \/>\n-4.5 &gt; p<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 1.<br \/>\n4b \u2265 2<\/p>\n<p>Answer:<br \/>\nb \u2265 1\/2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-80.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 80\" width=\"670\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-80.jpg 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-80-300x46.jpg 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Explanation:<br \/>\n4b \u2265 2<br \/>\nb \u2265 2\/4<br \/>\nb \u2265 1\/2<\/p>\n<p>Question 5.<br \/>\n12k \u2264 -24.<\/p>\n<p>Answer:<br \/>\nk \u2264 -2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-81.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 81\" width=\"680\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-81.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-81-300x55.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Explanation:<br \/>\n12k \u2264 -24<br \/>\nk \u2264 -24\/12<br \/>\nk \u2264 -2<\/p>\n<p>Question 6.<br \/>\n-15 &lt; 2.5q<\/p>\n<p>Answer:<br \/>\n-6 &lt; q<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-82.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 82\" width=\"705\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-82.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-82-300x40.jpg 300w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><\/p>\n<p>Explanation:<br \/>\n-15 &lt; 2.5q<br \/>\n-15\/2.5 &lt; q<br \/>\n-6 &lt; q<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-98.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 98\" width=\"79\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\nx &gt; 12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83.jpg\" alt=\"\" width=\"694\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83.jpg 694w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83-300x47.jpg 300w\" sizes=\"(max-width: 694px) 100vw, 694px\" \/><\/p>\n<p>Explanation:<br \/>\nx &gt; -4 x -3<br \/>\nx &gt; 12<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-99.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 99\" width=\"85\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\n1 \u2265 y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-84.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 84\" width=\"675\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-84.jpg 675w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-84-300x47.jpg 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/p>\n<p>Explanation:<br \/>\n0.5 \u2264 -y\/2<br \/>\n0.5 x 2 \u2264 -y<br \/>\n1 \u2264 &#8211; y<br \/>\n1 \u2265 y<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-100.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 100\" width=\"79\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n-10 \u2265 m<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-85.jpg\" alt=\"\" width=\"688\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-85.jpg 688w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-85-300x34.jpg 300w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/><\/p>\n<p>Explanation:<br \/>\n-12 \u2265 (6\/5)m<br \/>\n-12 x 5 \u2265 6m<br \/>\n-60 \u2265 6m<br \/>\n-60\/6 \u2265 m<br \/>\n-10 \u2265 m<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-101.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 101\" width=\"90\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\nh \u2264 20<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-86.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 86\" width=\"668\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-86.jpg 668w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-86-300x48.jpg 300w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/p>\n<p>Explanation:<br \/>\n(-2\/5)h \u2264 -8<br \/>\n(2\/5)h \u2264 8<br \/>\n2h \u2264 8 x 5<br \/>\n2h \u2264 40<br \/>\nh \u2264 40\/2<br \/>\nh \u2264 20<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\n<strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p>Question 11.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an inequality that you can solve using the Division Property of Inequality where the direction of the inequality symbol must be reversed.<\/p>\n<p>Answer:<br \/>\nLet us take an inequality -3x &lt; 6<br \/>\nDivide both sides by -3<br \/>\n-3x\/-3 &lt; 6\/-3<br \/>\nx &gt; -2<br \/>\nThe solution is x &gt; -2<\/p>\n<p>Question 12.<br \/>\n<strong>PRECISION<\/strong><br \/>\nExplain how solving 4x &lt; -16 is different from \u22124x &lt; 16.<\/p>\n<p>Answer:<br \/>\n4x &lt; -16<br \/>\nx &lt; -16\/4<br \/>\nx &lt; -4<br \/>\n\u22124x &lt; 16<br \/>\n-4x\/-4 &gt; 16\/-4<br \/>\nx &gt; -4<br \/>\nFor 4x &lt; -16, we get x &lt; -4. For \u22124x &lt; 16 we get x &gt; -4 as solution.<\/p>\n<p>SOLVING AN INEQUALITY<br \/>\nSolve the inequality. Graph the solution.<\/p>\n<p>Question 13.<br \/>\n6n &lt; -42<\/p>\n<p>Answer:<br \/>\nn &lt; -7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-87.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 87\" width=\"664\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-87.jpg 664w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-87-300x44.jpg 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p>\n<p>Explanation:<br \/>\n6n &lt; -42<br \/>\nDivide both sides by 6<br \/>\n6n\/6 &lt; -42\/6<br \/>\nn &lt; -7<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-102.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 102\" width=\"64\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n32 \u2264 g<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-88.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 88\" width=\"666\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-88.jpg 666w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-88-300x38.jpg 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/p>\n<p>Explanation:<br \/>\n4 \u2265 -g\/8<br \/>\n4 x 8 \u2265 -g<br \/>\n32 \u2265 -g<br \/>\n32 \u2264 g<\/p>\n<p>Question 15.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the inequalities 12c &gt; -15 and 4c &lt; -5 equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nBoth inequalities are not equivalent.<\/p>\n<p>Explanation:<br \/>\n12c &gt; -15<br \/>\nc &gt; -15\/12<br \/>\nc &gt; -5\/4<br \/>\n4c &lt; -5<br \/>\nc &lt; -5\/4<br \/>\nSo, both inequalities are not equivalent<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\n<strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou want to put up a fence that encloses a triangular region with an area greater than or equal to 60 square feet. Describe the possible values of c.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-103.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 103\" width=\"219\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\n12 + c + \u221a(c\u00b2 + 144) \u2265 60<\/p>\n<p>Explanation:<br \/>\nFind all sides to get its perimeter<br \/>\nLet us take hypotenuse as x.<br \/>\nAsit is a right-angled triangle, hypotenuse\u00b2 = sum of squares of other sides<br \/>\nx\u00b2 = c\u00b2 + 12\u00b2<br \/>\nx\u00b2 = c\u00b2 + 144<br \/>\nx = \u221a(c\u00b2 + 144)<br \/>\nThe perimeter of the triangular region is greater than or equal to 60 square feet.<br \/>\nSo, perimeter \u2265 60<br \/>\nPerimeter = 12 + c + x = 12 + c + \u221a(c\u00b2 + 144)<br \/>\n12 + c + \u221a(c\u00b2 + 144) \u2265 60<\/p>\n<p>Question 17.<br \/>\nA motorcycle rider travels at an average speed greater than 50 miles per hour. Write and solve an inequality to determine how long it will take the motorcycle rider to travel 375 miles. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-104.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 104\" width=\"280\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\nIt may take more than 7.5 hours for a motorcycle rider to travel 375 miles<\/p>\n<p>Explanation:<br \/>\nA motorcycle rider travels at an average speed greater than 50 miles per hour.<br \/>\nspeed &gt; 50 miles per hour<br \/>\n50 miles per one hour<br \/>\nSo, 375 miles per how many hours<br \/>\n50x &gt; 375<br \/>\nx &gt;375\/50<br \/>\nx &gt; 7.5<br \/>\nSo, it may take more than 7.5 hours for a motorcycle rider to travel 375 miles<\/p>\n<h3><a id=\"Solving_Inequalities_Using_Multiplication_or_Division_Homework_&amp;_Practice_4.6\"><\/a>Solving Inequalities Using Multiplication or Division Homework &amp; Practice 4.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 1.<br \/>\nh + 4 &lt; 6<\/p>\n<p>Answer:<br \/>\nh &lt; 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-89.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 89\" width=\"703\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-89.jpg 703w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-89-300x35.jpg 300w\" sizes=\"(max-width: 703px) 100vw, 703px\" \/><\/p>\n<p>Explanation:<br \/>\nh &lt; 6 &#8211; 4<br \/>\nh &lt; 2<\/p>\n<p>Question 2.<br \/>\nc &#8211; 5 \u2265 4<\/p>\n<p>Answer:<br \/>\nc \u2265 9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-90.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities \" width=\"667\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-90.jpg 667w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-90-300x35.jpg 300w\" sizes=\"(max-width: 667px) 100vw, 667px\" \/><\/p>\n<p>Explanation:<br \/>\nc \u2265 4 + 5<br \/>\nc \u2265 9<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-105.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 105\" width=\"89\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n-1\/10 \u2264 n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-91.jpg\" alt=\" Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 91\" width=\"687\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-91.jpg 687w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-91-300x42.jpg 300w\" sizes=\"(max-width: 687px) 100vw, 687px\" \/><\/p>\n<p>Explanation:<br \/>\n7\/10 \u2264 n + 4\/5<br \/>\n7\/10 &#8211; 4\/5 \u2264 n<br \/>\n(7 &#8211; 8)\/10 \u2264 n<br \/>\n-1\/10 \u2264 n<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n-2w + 4 = -12<\/p>\n<p>Answer:<br \/>\nw = 4<\/p>\n<p>Explanation:<br \/>\n-2w = -12 + 4<br \/>\n-2w = -8<br \/>\n2w = 8<br \/>\nw = 8\/2<br \/>\nw = 4<br \/>\nPutting w = 4 in -2w = -12 + 4<br \/>\n-2(-4) = -12 + 4<br \/>\n-8 = -8<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-106.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 106\" width=\"80\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\nv = 45<\/p>\n<p>Explanation:<br \/>\nv\/5 = 3 + 6 = 9<br \/>\nv = 9 x 5<br \/>\nv = 45<br \/>\nPutting v = 45 in v\/5 &#8211; 6 = 3<br \/>\n45\/5 &#8211; 6 = 9 &#8211; 6 = 3<\/p>\n<p>Question 6.<br \/>\n3(x &#8211; 1) = 18<\/p>\n<p>Answer:<br \/>\nx = 7<\/p>\n<p>Explanation:<br \/>\n3(x &#8211; 1) = 18<br \/>\n(x &#8211; 1) = 18\/3<br \/>\nx &#8211; 1 = 6<br \/>\nx = 6 + 1<br \/>\nx = 7<br \/>\nPutting x = 7 in 3(x &#8211; 1) = 18<br \/>\n3(7 &#8211; 1) = 3 x 6 = 18<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-107.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 107\" width=\"93\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\nm = 4<\/p>\n<p>Explanation:<br \/>\nm\/4 + 50 = 51<br \/>\nm\/4 = 51 &#8211; 50<br \/>\nm\/4 = 1<br \/>\nm = 1 x 4<br \/>\nm = 4<br \/>\nPutting m = 4 in m\/4 + 50 = 51<br \/>\n4\/4 + 50 = 1 + 50 = 51<\/p>\n<p>Question 8.<br \/>\nWhat is the value of <img loading=\"lazy\" class=\"alignnone size-full wp-image-31085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-108.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 108\" width=\"67\" height=\"50\" \/>?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-109.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 109\" width=\"493\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-109.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-109-300x37.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p>Answer:<br \/>\nB.<\/p>\n<p>Explanation:<br \/>\n2\/3 + (-5\/7) = 2\/3 &#8211; 5\/7<br \/>\n= (14 &#8211; 15)\/21<br \/>\n= -1\/21<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>WRITING AN INEQUALITY<\/strong><br \/>\n<strong>Write an inequality that compares the given numbers. Does the inequality remain true when you multiply each number in the inequality by 2? by -2? Justify your answers.<\/strong> (See Exploration 1, p. 157.)<\/p>\n<p>Question 9.<br \/>\n-2; 5<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\n-2 &lt; 5<br \/>\n-2 x 2 &lt; 5 x 2<br \/>\n-4 &lt; 10<\/p>\n<p>Question 10.<br \/>\n4; -1<\/p>\n<p>Answer:<br \/>\ntrue<\/p>\n<p>Explanation:<br \/>\n4 &gt; -1<br \/>\n4 x 2 &gt; -1 x 2<br \/>\n8 &gt; -2<\/p>\n<p>Question 11.<br \/>\n6; -3<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\n6 &gt; -3<br \/>\n6 x 2 &gt; -3 x 2<br \/>\n12 &gt; -6<\/p>\n<p><strong>SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 12.<br \/>\n2n &gt; 20<\/p>\n<p>Answer:<br \/>\nn &gt; 10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-92.jpg\" alt=\"\" width=\"676\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-92.jpg 676w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-92-300x41.jpg 300w\" sizes=\"(max-width: 676px) 100vw, 676px\" \/><\/p>\n<p>Explanation:<br \/>\n2n &gt; 20<br \/>\nn &gt; 20\/2<br \/>\nn &gt; 10<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-110.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 110\" width=\"70\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\nc \u2264 -36<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-93.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 93\" width=\"670\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-93.jpg 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-93-300x49.jpg 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Explanation:<br \/>\nc\/9 \u2264 -4<br \/>\nc \u2264 -4 x 9<br \/>\nc \u2264 -36<\/p>\n<p>Question 14.<br \/>\n2.2m &lt; 11<\/p>\n<p>Answer:<br \/>\nm &lt; 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-94.jpg\" alt=\"\" width=\"691\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-94.jpg 691w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-94-300x53.jpg 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><\/p>\n<p>Explanation:<br \/>\nm &lt; 11\/2.2<br \/>\nm &lt; 5<\/p>\n<p>Question 15.<br \/>\n-16 &gt; x \u00f7 2<\/p>\n<p>Answer:<br \/>\n-32 &gt; x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-95.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 95\" width=\"681\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-95.jpg 681w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-95-300x46.jpg 300w\" sizes=\"(max-width: 681px) 100vw, 681px\" \/><\/p>\n<p>Explanation:<br \/>\n-16 &gt; x \u00f7 2<br \/>\n-16 x 2 &gt; x<br \/>\n-32 &gt; x<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-111.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 111\" width=\"81\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\nw \u2265 15<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-96.jpg\" alt=\"\" width=\"670\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-96.jpg 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-96-300x57.jpg 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Explanation:<br \/>\n(1\/6)w \u2265 2.5<br \/>\nw \u2265 2.5 x 6<br \/>\nw \u2265 15<\/p>\n<p>Question 17.<br \/>\n7 &lt; 3.5k<\/p>\n<p>Answer:<br \/>\n2 &lt; k<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-97.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 97\" width=\"681\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-97.jpg 681w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-97-300x43.jpg 300w\" sizes=\"(max-width: 681px) 100vw, 681px\" \/><\/p>\n<p>Explanation:<br \/>\n7\/3.5 &lt; k<br \/>\n2 &lt; k<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-112.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 112\" width=\"75\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nx &lt; -5\/12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-98.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 98\" width=\"737\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-98.jpg 737w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-98-300x46.jpg 300w\" sizes=\"(max-width: 737px) 100vw, 737px\" \/><\/p>\n<p>Explanation:<br \/>\n3x \u2264 -5\/4<br \/>\nx &lt; (-5\/4) x (1\/3)<br \/>\nx &lt; -5\/12<\/p>\n<p>Question 19.<br \/>\n4.2y \u2264 -12.6<\/p>\n<p>Answer:<br \/>\ny \u2264 -3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-99.jpg\" alt=\"\" width=\"665\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-99.jpg 665w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-99-300x42.jpg 300w\" sizes=\"(max-width: 665px) 100vw, 665px\" \/><\/p>\n<p>Explanation:<br \/>\n4.2y \u2264 -12.6<br \/>\ny \u2264 -12.6\/4.2<br \/>\ny \u2264 -3<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-113.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 113\" width=\"91\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\n48.59 &gt; b<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-100.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 100\" width=\"672\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-100.jpg 672w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-100-300x38.jpg 300w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><\/p>\n<p>Explanation:<br \/>\n11.3 &gt; (b\/4.3)<br \/>\n11.3 x 4.3 &gt; b<br \/>\n48.59 &gt; b<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou earn $9.20 per hour at your summer job. Write and solve an inequality that represents the numbers of hours you can work to earn enough money to buy a smart phone that costs $299.<\/p>\n<p>Answer:<br \/>\n9.2h \u2265 299<br \/>\nh \u2265 32.5<\/p>\n<p>Explanation:<br \/>\nLet us take h as the number of hours you work.<br \/>\nMultiply the number of hours by the amount you make per hour. If the total is greater than or equal to the cost of the phone, you can buy it.<br \/>\n9.2h \u2265 299<br \/>\nh \u2265 299\/9.2<br \/>\nh \u2265 32.5<\/p>\n<p>Question 22.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have $5.60 to buy avocados for a guacamole recipe. Avocados cost $1.40 each.<br \/>\na. Write and solve an inequality that represents the numbers of avocados you can buy.<br \/>\nb. Are there in\ufb01nitely many solutions in this context? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-114.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 114\" width=\"274\" height=\"175\" \/><\/p>\n<p>Answer:<br \/>\na. You can buy at most 4 avocados.<br \/>\nb. Yes<\/p>\n<p>Explanation:<br \/>\nLet x represents the number of avocados that you buy<br \/>\nThen 1.40x is the total cost of avocados.<br \/>\nSince you have $5.60 to spend, 1.40x \u2264 5.60<br \/>\nx \u2264 5.60\/1.40<br \/>\nx \u2264 4<br \/>\nYou can buy at most 4 avocados.<\/p>\n<p><strong>SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 23.<br \/>\n5n \u2265 15<\/p>\n<p>Answer:<br \/>\nn \u2265 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-101.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 101\" width=\"680\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-101.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-101-300x46.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Explanation:<br \/>\n5n \u2265 15<br \/>\nn \u2265 15\/5<br \/>\nn \u2265 3<\/p>\n<p>Question 24.<br \/>\n7w &gt; -49<\/p>\n<p>Answer:<br \/>\nw &gt; -7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-103.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 103\" width=\"690\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-103.jpg 690w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-103-300x56.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>Explanation:<br \/>\n7w &gt; -49<br \/>\nw &gt; -49\/7<br \/>\nw &gt; -7<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-115.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 115\" width=\"69\" height=\"44\" \/><\/p>\n<p>Answer:<br \/>\nh \u2264 -24<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-104.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 104\" width=\"667\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-104.jpg 667w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-104-300x46.jpg 300w\" sizes=\"(max-width: 667px) 100vw, 667px\" \/><\/p>\n<p>Explanation:<br \/>\n-1\/3 h \u2265 8<br \/>\nh \u2264 -8 x 3<br \/>\nh \u2264 -24<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-116.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 116\" width=\"84\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n45 &gt; x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-105.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 105\" width=\"670\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-105.jpg 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-105-300x47.jpg 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Explanation:<br \/>\n-9 &lt; -1\/5 x<br \/>\n-9 x -5 &gt; x<br \/>\n45 &gt; x<\/p>\n<p>Question 27.<br \/>\n-3y &lt; -14<\/p>\n<p>Answer:<br \/>\ny &gt; 42<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-106.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 106\" width=\"669\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-106.jpg 669w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-106-300x46.jpg 300w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><\/p>\n<p>Explanation:<br \/>\n-3y &lt; -14<br \/>\ny &gt; -14 x -3<br \/>\ny &gt; 42<\/p>\n<p>Question 28.<br \/>\n-2d \u2265 26<\/p>\n<p>Answer:<br \/>\nd \u2264 -13<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-107.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 107\" width=\"675\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-107.jpg 675w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-107-300x46.jpg 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/p>\n<p>Explanation:<br \/>\n-2d \u2265 26<br \/>\nd \u2264 -26\/2<br \/>\nd \u2264 -13<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-117.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 117\" width=\"90\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n-27 &gt; m<\/p>\n<figure id=\"attachment_36168\" aria-describedby=\"caption-attachment-36168\" style=\"width: 656px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" class=\"size-full wp-image-36168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-108.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 108\" width=\"666\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-108.jpg 666w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-108-300x38.jpg 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><figcaption id=\"caption-attachment-36168\" class=\"wp-caption-text\">Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 108<\/figcaption><\/figure>\n<p>Explanation:<br \/>\n-4.5 &gt; m\/6<br \/>\n-4.5 x 6 &gt; m<br \/>\n-27 &gt; m<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-118.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 118\" width=\"96\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\nk \u2265 -144<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-109.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 109\" width=\"680\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-109.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-109-300x41.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p>Explanation:<br \/>\nk\/(-0.25) \u2264 36<br \/>\nk \u2265 -36\/0.25<br \/>\nk \u2265 -144<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-119.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 119\" width=\"93\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-102.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 102\" width=\"673\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-102.jpg 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-102-300x40.jpg 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><br \/>\n6 &lt; b<\/p>\n<p>Explanation:<br \/>\n-2.4 &gt; b\/(-2.5)<br \/>\n-2.4 x -2.5 &lt; b<br \/>\n6 &lt; b<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend solves the inequality. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-120.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 120\" width=\"149\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nWrong.<\/p>\n<p>Explanation:<br \/>\nx\/3 &lt; -9<br \/>\nx &lt; -9 x 3<br \/>\nx &lt; -27<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-121.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 121\" width=\"197\" height=\"215\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\n-3m \u2265 9<br \/>\nm \u2264 -9\/3<br \/>\nm \u2264 -3<\/p>\n<p><strong>WRITING AND SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Write the word sentence as an inequality. Then solve the inequality.<\/strong><\/p>\n<p>Question 34.<br \/>\nThe quotient of a number and -4 is atmost 5.<\/p>\n<p>Answer:<br \/>\nx \u2265 -20<\/p>\n<p>Explanation:<br \/>\nx\/-4 \u2264 5<br \/>\nx \u2265 5 x -4<br \/>\nx \u2265 -20<\/p>\n<p>Question 35.<br \/>\nA number p divided by 7 is less than -3.<\/p>\n<p>Answer:<br \/>\np &lt; -21<\/p>\n<p>Explanation:<br \/>\np\/7 &lt; -3<br \/>\np &lt; -3 x 7<br \/>\np &lt; -21<\/p>\n<p>Question 36.<br \/>\nSix times a number w is atleast -24.<\/p>\n<p>Answer:<br \/>\nw \u2265 -4<\/p>\n<p>Explanation:<br \/>\n6w \u2265 -24<br \/>\nw \u2265 -24\/6<br \/>\nw \u2265 -4<\/p>\n<p>Question 37.<br \/>\nThe product of -2 and a number is greater than 30.<\/p>\n<p>Answer:<br \/>\nx &lt; -15<\/p>\n<p>Explanation:<br \/>\n-2x &gt; 30<br \/>\nx &lt; -30\/2<br \/>\nx &lt; -15<\/p>\n<p>Question 38.<br \/>\n\\(\\frac{3}{4}\\) is greater than or equal to a number k divided by -8.<\/p>\n<p>Answer:<br \/>\n-6 \u2264 k<\/p>\n<p>Explanation:<br \/>\n3\/4 \u2265 k \/ -8<br \/>\n(3\/4) x -8 \u2264 k<br \/>\n3 x -2 \u2264 k<br \/>\n-6 \u2264 k<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cryotherapy chamber uses extreme cold to reduce muscle soreness. A chamber is currently 0\u00b0F. The temperature in the chamber is dropping 2.5\u00b0F every second. Write and solve an inequality that represents the numbers of seconds that can pass for the temperature to drop below -20\u00b0F.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-122.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 122\" width=\"269\" height=\"250\" \/><\/p>\n<p>Answer:<br \/>\n8x \u2264 -20\u00b0F<\/p>\n<p>Explanation:<br \/>\nThe temperature in the chamber is dropping 2.5\u00b0F every second.<br \/>\nThe chamber is currently 0\u00b0F.<br \/>\nSo, for the 1st second the temperature is -2.5\u00b0F<br \/>\nFor the second the temperature is -5\u00b0F<br \/>\nBy calculating these seconds, we get for the 8th second the temperature dropped is below -20\u00b0F.<br \/>\nSo, the inequality can be 8x \u2264 -20\u00b0F.<\/p>\n<p>Question 40.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou are moving some of your belongings into a storage facility.<br \/>\na. Write and solve an inequality that represents the numbers of boxes that you can stack vertically in the storage unit.12.5<br \/>\nb. Can you stack 6 boxes vertically in the storage unit? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-123.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 123\" width=\"265\" height=\"195\" \/><\/p>\n<p>Answer:<br \/>\na. 27x \u2264 150<br \/>\nb. No<\/p>\n<p>Explanation:<br \/>\nGiven that the height of the storage unit is 12.5 feet = 150 inches<br \/>\nThe height of each box is 27 inches<br \/>\nLet us take x as the number of boxes that you can stack vertically in the storage unit.<br \/>\nSo, 27x \u2264 150<br \/>\nx \u2264 150\/27<br \/>\nx \u2264 5.55<br \/>\nb. By solving the inequality, we obtain value as 5.55<br \/>\nSo, we can stack only 5 boxes in the stack.<\/p>\n<p><strong>GEOMETRY<\/strong><br \/>\n<strong>Write and solve an inequality that represents x.<\/strong><\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-124.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 124\" width=\"184\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\nx \u2265 12<\/p>\n<p>Explanation:<br \/>\n10x \u2265 120<br \/>\nx \u2265 120\/10<br \/>\nx \u2265 12<\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-125.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 125\" width=\"166\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nx &lt; 5<\/p>\n<p>Explanation:<br \/>\n1\/2 * 8 * x &lt; 20<br \/>\n4x &lt; 20<br \/>\nx &lt; 20\/4<br \/>\nx &lt; 5<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA device extracts no more than 37 liters of water per day from the air. How long does it take to collect atleast 185 liters of water? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nIt takes 5 days to collect atleast 185 liters of water<\/p>\n<p>Explanation:<br \/>\nA device extracts no more than 37 liters of water per day from the air.<br \/>\nLet us take x as the number of days required to collect 185 liters of water.<br \/>\nSo, 37x \u2265 185<br \/>\nx \u2265 185\/37<br \/>\nx \u2265 5<br \/>\nSo, it takes 5 days to collect atleast 185 liters of water<\/p>\n<p>Question 44.<br \/>\n<strong>REASONING<\/strong><br \/>\nStudents in a science class are divided into 6 equal groups with atleast 4 students in each group for a project. Describe the possible numbers of students in the class.<\/p>\n<p>Answer:<br \/>\nThe possible number of students in the class are 24 or more.<\/p>\n<p>Explanation:<br \/>\nStudents in a science class are divided into 6 equal groups with at least 4 students in each group for a project.<br \/>\nSo, each group must have 4 or more students.<br \/>\nIf we take each group has 4 students, then the number of students is 6 x 4 = 24<br \/>\nSo, The possible number of students in the class are 24 or more.<\/p>\n<p>Question 45.<br \/>\n<strong>PROJECT<\/strong><br \/>\nChoose two novels to research.<br \/>\na. Use the Internet to complete the table below.<br \/>\nb. Use the table to \ufb01nd and compare the average number of copies sold per month for each novel. Which novel do you consider to be the most successful? Explain.<br \/>\nc. Assume each novel continues to sell at the average rate. For what numbers of months will the total number of copies sold exceed twice the current number sold for each novel?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-126.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 126\" width=\"167\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-126.png 167w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-126-152x300.png 152w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-127.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 127\" width=\"615\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-127.png 615w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-127-300x62.png 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-112.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 112\" width=\"602\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-112.jpg 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-112-300x60.jpg 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><br \/>\nb. As the number of copies sold is highest for Jude the Obscure so i consider it as the most successful<br \/>\nc. It purely depends on the number of copies sold.<\/p>\n<p>Question 46.<br \/>\n<strong>LOGIC<\/strong><br \/>\nWhen you multiply or divide each side of an inequality by the same negative number, you must reverse the direction of the inequality symbol. Explain why.<\/p>\n<p>Answer:<br \/>\nWhen divide or multiply the same negative number on each side of the inequality, then you need to reverse the direction of the inequality symbol. The reason behind this is, when you take an example and show it on the number line then you can understand easily.<\/p>\n<p><strong>NUMBER SENSE<\/strong><br \/>\n<strong>Describe all numbers that satisfy both inequalities. Include a graph with your description.<\/strong><\/p>\n<p>Question 47.<br \/>\n4m &gt; -4 and 3m &lt; 15<\/p>\n<p>Answer:<br \/>\nm &gt; -1 and m &lt; 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-113.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 113\" width=\"385\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-113.jpg 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-113-300x61.jpg 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Explanation:<br \/>\n4m &gt; -4 and 3m &lt; 15<br \/>\nm &gt; -4\/4 and m &lt; 15\/3<br \/>\nm &gt; -1 and m &lt; 5<br \/>\nThe possible values 4, 3, 2, 1, 0<\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-128.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 128\" width=\"154\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-128.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-128-150x51.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><\/p>\n<p>Answer:<br \/>\nn \u2265 -12 and n \u2264 -5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36541\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-114.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 114\" width=\"657\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-114.jpg 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-114-300x36.jpg 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><\/p>\n<p>Explanation:<br \/>\nn\/3 \u2265 -4 and n\/-5 \u2265 1<br \/>\nn \u2265 &#8211; 4 x 3 and n \u2264 1 x -5<br \/>\nn \u2265 -12 and n \u2264 -5<br \/>\nThe possible values of n are -11, -10, -9, -8, -7, -6.<\/p>\n<p>Question 49.<br \/>\n2x \u2265 -6 and 2x \u2265 6<\/p>\n<p>Answer:<br \/>\nx \u2265 -3 and x \u2265 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-115.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 115\" width=\"633\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-115.jpg 633w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-115-300x36.jpg 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><\/p>\n<p>Explanation:<br \/>\n2x \u2265 -6 and 2x \u2265 6<br \/>\nx \u2265 -6\/2 and x \u2265 6\/2<br \/>\nx \u2265 -3 and x \u2265 3<br \/>\nThe possible values of x are -3, -2, -1, 0, 1, &#8230;.<\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-129.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 129\" width=\"175\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\ns &lt; 14 &amp; s &lt; 36<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-116.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 116\" width=\"539\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-116.jpg 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-116-300x47.jpg 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Explanation:<br \/>\n-1\/2 s &gt; -7 and 1\/3 s &lt; 12<br \/>\n-s &gt; -7 x 2 and s &lt; 12 x 3<br \/>\n-s &gt; -14 &amp; s &lt; 36<br \/>\ns &lt; 14 &amp; s &lt; 36<\/p>\n<h3><a id=\"Lesson_4.7_Solving_Two_Step_Inequalities\"><\/a>Lesson 4.7 Solving Two-Step Inequalities<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using Algebra Tiles to Solve Inequalities<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. What is being modeled by the algebra tiles below? What is the solution?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-130.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 130\" width=\"335\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-130.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-130-300x219.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nb. Use properties of inequality to solve the original inequality in part(a). How do your steps compare to the steps performed with algebra tiles?<br \/>\nc. Write the three inequalities modeled by the algebra tiles below. Then solve each inequality using algebra tiles. Check your answer using properties of inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-131.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 131\" width=\"532\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-131.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-131-300x153.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nd. Explain how solving a two-step inequality is similar to solving a two-step equation.<\/p>\n<p><strong>4.7 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 1.<br \/>\n6y &#8211; 7 &gt; 5<\/p>\n<p>Answer:<br \/>\ny &gt; 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-117.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 117\" width=\"551\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-117.jpg 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-117-300x51.jpg 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Explanation:<br \/>\n6y &#8211; 7 &gt; 5<br \/>\n6y &gt; 7 + 5<br \/>\n6y &gt; 12<br \/>\ny &gt; 12\/6<br \/>\ny &gt; 2<\/p>\n<p>Question 2.<br \/>\n4 &#8211; 3d \u2265 19<\/p>\n<p>Answer:<br \/>\nd \u2264 -5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-118.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 118\" width=\"642\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-118.jpg 642w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-118-300x37.jpg 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p>Explanation:<br \/>\n4 &#8211; 3d \u2265 19<br \/>\n-3d \u2265 19 &#8211; 4<br \/>\n-3d \u2265 15<br \/>\nd \u2264 -15\/3<br \/>\nd \u2264 -5<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-132.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 132\" width=\"96\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\nw &lt; -4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-119.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 119\" width=\"639\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-119.jpg 639w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-119-300x39.jpg 300w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><\/p>\n<p>Explanation:<br \/>\nw\/-4 + 8 &gt; 9<br \/>\nw\/-4 &gt; 9 &#8211; 8<br \/>\nw\/-4 &gt; 1<br \/>\nw &lt; 1 x -4<br \/>\nw &lt; -4<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n2(k &#8211; 5) &lt; 6<\/p>\n<p>Answer:<br \/>\nk &lt; 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-120.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 120\" width=\"532\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-120.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-120-300x50.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Explanation:<br \/>\n2(k &#8211; 5) &lt; 6<br \/>\n(k &#8211; 5) &lt; 6\/2<br \/>\n(k &#8211; 5) &lt; 3<br \/>\nk &lt; 3 + 5<br \/>\nk &lt; 8<\/p>\n<p>Question 5.<br \/>\n-4(n &#8211; 10) &lt; 32<\/p>\n<p>Answer:<br \/>\nn &gt; 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-117.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 117\" width=\"551\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-117.jpg 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-117-300x51.jpg 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Explanation:<br \/>\n-4(n &#8211; 10) &lt; 32<br \/>\n(n &#8211; 10) &gt; -32\/4<br \/>\n(n &#8211; 10) &gt; -8<br \/>\nn &gt; -8 + 10<br \/>\nn &gt; 2<\/p>\n<p>Question 6.<br \/>\n-3 \u2264 0.5(8 + y)<\/p>\n<p>Answer:<br \/>\n-14 \u2264\u00a0 y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-121.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 121\" width=\"537\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-121.jpg 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-121-300x52.jpg 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Explanation:<br \/>\n-3 \u2264 0.5(8 + y)<br \/>\n-3\/0.5 \u2264 (8 + y)<br \/>\n-6 \u2264 (8 + y)<br \/>\n-6 &#8211; 8 \u2264\u00a0 y<br \/>\n-14 \u2264\u00a0 y<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 7.<br \/>\n3d &#8211; 7 \u2265 8<\/p>\n<p>Answer:<br \/>\nd \u2265 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-122.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-122\" width=\"553\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-122.jpg 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-122-300x46.jpg 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Explanation:<br \/>\n3d &#8211; 7 \u2265 8<br \/>\n3d \u2265 8 + 7<br \/>\n3d \u2265 15<br \/>\nd \u2265 15\/3<br \/>\nd \u2265 5<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-133.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 133\" width=\"105\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\n-14 &lt; z<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-121.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 121\" width=\"537\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-121.jpg 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-121-300x52.jpg 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Explanation:<br \/>\n-6 &#8211; 1 &gt; z\/-2<br \/>\n-7 &gt; z\/-2<br \/>\n-7 x -2 &lt; z<br \/>\n-14 &lt; z<\/p>\n<p>Question 9.<br \/>\n-6(g + 4) \u2264 12<\/p>\n<p>Answer:<br \/>\ng \u2265 -6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-123.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 123\" width=\"559\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-123.jpg 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-123-300x43.jpg 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Explanation:<br \/>\n-6(g + 4) \u2264 12<br \/>\n(g + 4) \u2265 -12\/6<br \/>\ng + 4 \u2265 -2<br \/>\ng \u2265 -2 &#8211; 4<br \/>\ng \u2265 -6<\/p>\n<p>Question 10.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe two different ways to solve the inequality 3(a + 5) &lt; 9.<\/p>\n<p>Answer:<br \/>\na &lt; -3<\/p>\n<p>Explanation:<br \/>\n3(a + 5) &lt; 9<br \/>\ndivide both sides by 3<br \/>\na + 5 &lt; 9\/3<br \/>\na + 5 &lt; 3<br \/>\nSubtract 5 from both sides<br \/>\na + 5 &#8211; 5 &lt; 3 &#8211; 5<br \/>\na &lt; -2<br \/>\n3(a + 5) &lt; 9<br \/>\nexpand 3<br \/>\n3a + 15 &lt; 9<br \/>\n3a &lt; 9 &#8211; 15<br \/>\n3a &lt; -6<br \/>\na &lt; -6\/2<br \/>\na &lt; -3<\/p>\n<p>Question 11.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the inequalities -6x + 18 \u2264 12 and 2x &#8211; 4 \u2264 -2 equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nYes, both inequalities are equivalent<\/p>\n<p>Explanation:<br \/>\n-6x + 18 \u2264 12 and 2x &#8211; 4 \u2264 -2<br \/>\n-6x \u2264 12 &#8211; 18 and 2x \u2264 -2 + 4<br \/>\n-6x \u2264 -6 and 2x \u2264 2<br \/>\nx \u2265 -6\/6 and x \u2264 2\/2<br \/>\nx \u2265 -1 and x \u2264 1<br \/>\nYes, both inequalities are equivalent<\/p>\n<p>Question 12.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a two-step inequality that can be represented by the graph. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-134.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 134\" width=\"419\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-134.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-134-300x39.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Answer:<br \/>\nx + a &gt; -5 + a<\/p>\n<p>Explanation:<br \/>\nThe solution should be x &gt; -5<br \/>\nAdd any number to both sides<br \/>\nx + a &gt; -5 + a<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\nA fair rents a thrill ride for $3000. It costs $4 to purchase a token for the ride. Write and solve an inequality to determine the numbers of ride tokens that can be sold for the fair to make a pro\ufb01t of at least $750.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-135.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 135\" width=\"207\" height=\"236\" \/><\/p>\n<p>Answer:<br \/>\nThe number of ride tokens that can be sold for the fair to make a pro\ufb01t of at least $750 is 937<\/p>\n<p>Explanation:<br \/>\nA fair rents a thrill ride for $3000. It costs $4 to purchase a token for the ride.<br \/>\nSo, 3000\/4 = 750 ride tokens can be sold without loss or profit.<br \/>\nThe number of ride tokens that can be sold for the fair to make a pro\ufb01t of at least $750.<br \/>\nSo, the total amount collected at the fair is 3000 + 750 = 3750<br \/>\nEach ticket cost 4.<br \/>\n4x \u2265 3750<br \/>\nx \u2265 3750\/4<br \/>\nx \u2265 937.5<br \/>\nSo, The number of ride tokens that can be sold for the fair to make a pro\ufb01t of at least $750 is 937<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA theater manager predicts that 1000 tickets to a play will be sold if each ticket costs $60. The manager predicts that 20 less tickets will be sold for every $1 increase in price. For what prices can the manager predict that at least 800 tickets will be sold?<\/p>\n<p>Answer:<br \/>\nThe manager predict that at least 800 tickets will be sold for $ 70.<\/p>\n<p>Explanation:<br \/>\nThe 1000 tickets will be sold when each ticket costs $60.<br \/>\nThe manager wants to sell at least 800 tickets which is maximum<br \/>\n1000 &#8211; 800 = 200 tickets less than 1000.<br \/>\nGiven that for 20 less tickets will be sold for every $1 increase in price.<br \/>\nSo, 20 x 2 = 40 less tickets will be sold for $1 x 2 = $2 increase in price.<br \/>\nProceeding in a similar way, for any natural number n:<br \/>\n20 x n less tickets will be sold for $1 x n=$n increase in price.<br \/>\nHere, 200 = 20 x 10, so n = 10<br \/>\nSo, 20 x 10 less tickets will be sold for $1 x 10 = $10 increase in price.<br \/>\nHence, the manager can increase the price of each ticket up to $10.<br \/>\nSo, to sell at least 800 tickets, the maximum price of each ticket can be $60 + $10 = $70.<br \/>\nHence, the value of p is p \u2264 $70.<\/p>\n<h3><a id=\"Solving_Two_Step_Inequalities_Homework_&amp;_Practice_4.7\"><\/a>Solving Two-Step Inequalities Homework &amp; Practice 4.7<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Solve the inequality. Graph the solution.<\/p>\n<p>Question 1.<br \/>\n-3x \u2265 18<\/p>\n<p>Answer:<br \/>\nx \u2264 -6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-124.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 124\" width=\"541\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-124.jpg 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-124-300x45.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Explanation:<br \/>\n-3x \u2265 18<br \/>\nx \u2264 -18\/3<br \/>\nx \u2264 -6<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-136.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 136\" width=\"63\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nd &gt; 12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83.jpg\" alt=\"\" width=\"694\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83.jpg 694w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-83-300x47.jpg 300w\" sizes=\"(max-width: 694px) 100vw, 694px\" \/><\/p>\n<p>Explanation:<br \/>\n2\/3 d &gt; 8<br \/>\n2d &gt; 8 x 3<br \/>\n2d &gt; 24<br \/>\nd &gt; 24\/2<br \/>\nd &gt; 12<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-137.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 137\" width=\"76\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n-8 \u2264 g<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-138.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-138\" width=\"534\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-138.jpg 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-138-300x40.jpg 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Explanation:<br \/>\n2 \u2265 g\/-4<br \/>\n2 x -4 \u2264 g<br \/>\n-8 \u2264 g<\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-138.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 138\" width=\"242\" height=\"74\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-139-1.png\" alt=\"Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-139\" width=\"234\" height=\"70\" \/><\/p>\n<p>Explanation:<br \/>\n12 = 4 x 3. So, 7x 3 = 21<br \/>\n7x 4 = 28. So, 4 x 4 = 16<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-139.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 139\" width=\"220\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-139-1-1.png\" alt=\"\" width=\"220\" height=\"76\" \/><\/p>\n<p>Explanation:<br \/>\n3 = 6 x 0.5. So, 10 x 0.5 = 5<br \/>\n50 = 10 x 5. So, 6 x 5 = 30<\/p>\n<p>Question 6.<br \/>\nWhat is the volume of the cube?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-140.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 140\" width=\"435\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-140.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-140-300x104.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Answer:<br \/>\nA. 8 ft\u00b3<\/p>\n<p>Explanation:<br \/>\nCube volume formula = side\u00b3<br \/>\nGiven side = 2 feet<br \/>\nVolume = 2\u00b3<br \/>\n= 2 x 2 x 2 = 8 ft\u00b3<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>USING ALGEBRA TILES<\/strong><br \/>\n<strong>Write the inequality modeled by the algebra tiles. Then solve the inequality using algebra tiles. Check your answer using properties of inequality.<\/strong> (See Exploration 1, p. 165.)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-141.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 141\" width=\"208\" height=\"65\" \/><\/p>\n<p>Answer:<br \/>\nx \u2265 -5<\/p>\n<p>Explanation:<br \/>\nx + 1 + 1 + x + 1 + 1 \u2265 -1 &#8211; 1-1-1-1-1<br \/>\n2x + 4 \u2265 -6<br \/>\n2x \u2265 -6 &#8211; 4<br \/>\n2x \u2265 -10<br \/>\nx \u2265 -10\/2<br \/>\nx \u2265 -5<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-142.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 142\" width=\"183\" height=\"69\" \/><\/p>\n<p>Answer:<br \/>\nx &lt; -2<\/p>\n<p>Explanation:<br \/>\n-x + 1 -x + 1 &gt; +1 + 1+ 1+ 1+ 1+ 1<br \/>\n-2x + 2 &gt; 6<br \/>\n-2x &gt; 6 &#8211; 2<br \/>\n-2x &gt; 4<br \/>\nx &lt; -4\/2<br \/>\nx &lt; -2<\/p>\n<p><strong>SOLVING A TWO-STEP INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 9.<br \/>\n8y &#8211; 5 &lt; 3<\/p>\n<p>Answer:<br \/>\ny &lt; 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-137.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-137\" width=\"537\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-137.jpg 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-137-300x41.jpg 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Explanation:<br \/>\n8y &#8211; 5 &lt; 3<br \/>\n8y &lt; 3 + 5<br \/>\n8y &lt; 8<br \/>\ny &lt; 1<\/p>\n<p>Question 10.<br \/>\n3p + 2 \u2265 -10<\/p>\n<p>Answer:<br \/>\np \u2265 -4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-135.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-135\" width=\"540\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-135.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-135-300x33.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Explanation:<br \/>\n3p + 2 \u2265 -10<br \/>\n3p \u2265 -10 &#8211; 2<br \/>\n3p \u2265 -12<br \/>\np \u2265 -12\/3<br \/>\np \u2265 -4<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-143.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 143\" width=\"88\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n-4.5 &lt; h<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-136.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-136\" width=\"543\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-136.jpg 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-136-300x36.jpg 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Explanation:<br \/>\n2 &#8211; 8 &gt; -4\/3 h<br \/>\n-6 &gt; -4\/3 h<br \/>\n-6 x 3 &gt; -4h<br \/>\n-18 &gt; -4h<br \/>\n-18\/-4 &lt; h<br \/>\n-9\/2 &lt; h<br \/>\n-4.5 &lt; h<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-144.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 144\" width=\"94\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n30 &gt; m<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-134.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-134\" width=\"535\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-134.jpg 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-134-300x38.jpg 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Explanation:<br \/>\n-2 + 7 &gt; m\/6<br \/>\n5 &gt; m\/6<br \/>\n5 x 6 &gt; m<br \/>\n30 &gt; m<\/p>\n<p>Question 13.<br \/>\n-1.2b &#8211; 5.3 \u2265 1.9<\/p>\n<p>Answer:<br \/>\nb \u2264 -6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-124.jpg\" alt=\"Big Ideas Math Answers 7th Grade Chapter 4 Equations and Inequalities 124\" width=\"541\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-124.jpg 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-124-300x45.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Explanation:<br \/>\n-1.2b \u2265 1.9 + 5.3<br \/>\n-1.2b \u2265 7.2<br \/>\nb \u2264 -7.2\/1.2<br \/>\nb \u2264 -6<\/p>\n<p>Question 14.<br \/>\n-1.3 \u2265 2.9 &#8211; 0.6r<\/p>\n<p>Answer:<br \/>\n7 \u2265 r<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-133.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-133\" width=\"533\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-133.jpg 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-133-300x37.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Explanation:<br \/>\n-1.3 \u2265 2.9 &#8211; 0.6r<br \/>\n-1.3 &#8211; 2.9 \u2264 &#8211; 0.6r<br \/>\n-4.2 \u2264 -0.6r<br \/>\n-4.2\/-0.6 \u2265 r<br \/>\n7 \u2265 r<\/p>\n<p>Question 15.<br \/>\n5(g + 4) &gt; 15<\/p>\n<p>Answer:<br \/>\ng &gt; -1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-132.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-132\" width=\"534\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-132.jpg 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-132-300x32.jpg 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Explanation:<br \/>\n5(g + 4) &gt; 15<br \/>\n(g + 4) &gt; 15\/5<br \/>\n(g + 4) &gt; 3<br \/>\ng &gt; 3 &#8211; 4<br \/>\ng &gt; -1<\/p>\n<p>Question 16.<br \/>\n4(w &#8211; 6) \u2264 -12<\/p>\n<p>Answer:<br \/>\nw \u2264 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-131.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-131\" width=\"530\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-131.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-131-300x35.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Explanation:<br \/>\n(w &#8211; 6) \u2264 -12\/4<br \/>\n(w &#8211; 6) \u2264 -3<br \/>\nw \u2264 -3 + 6<br \/>\nw \u2264 3<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-145.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 145\" width=\"110\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n-18 \u2264 k<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-130.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-130\" width=\"529\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-130.jpg 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-130-300x41.jpg 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Explanation:<br \/>\n-8 x 5 \u2264 2(k &#8211; 2)<br \/>\n-40 \/ 2 \u2264 k &#8211; 2<br \/>\n-20 \u2264 k &#8211; 2<br \/>\n-20 + 2 \u2264 k<br \/>\n-18 \u2264 k<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-146.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 146\" width=\"120\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\nd &gt; -9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-129.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-129\" width=\"531\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-129.jpg 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-129-300x37.jpg 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Explanation:<br \/>\n-1(d + 1) &lt; 2 x 4<br \/>\n-1(d + 1) &lt; 8<br \/>\nd + 1 &gt; -8<br \/>\nd &gt; -8 &#8211; 1<br \/>\nd &gt; -9<\/p>\n<p>Question 19.<br \/>\n7.2 &gt; 0.9(n + 8.6)<\/p>\n<p>Answer:<br \/>\n-0.6 &gt; n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-128.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-128\" width=\"532\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-128.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-128-300x39.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Explanation:<br \/>\n7.2\/0.9 &gt; (n + 8.6)<br \/>\n8 &gt; (n + 8.6)<br \/>\n8 &#8211; 8.6 &gt; n<br \/>\n-0.6 &gt; n<\/p>\n<p>Question 20.<br \/>\n20 \u2265 -3.2(c &#8211; 4.3)<\/p>\n<p>Answer:<br \/>\n-1.95 \u2264 c<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-127.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-127\" width=\"531\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-127.jpg 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-127-300x34.jpg 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Explanation:<br \/>\n20 \u2265 -3.2(c &#8211; 4.3)<br \/>\n20\/-3.2 \u2264 (c &#8211; 4.3)<br \/>\n-6.25 \u2264 c &#8211; 4.3<br \/>\n-6.25 + 4.3 \u2264 c<br \/>\n-1.95 \u2264 c<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend solves the inequality. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-147.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 147\" width=\"136\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nx\/3+ 4 &lt; 6<br \/>\nx\/3 &lt; 6 &#8211; 4<br \/>\nx\/3 &lt; 2<br \/>\nx &lt; 2 x 6<br \/>\nx &lt; 12<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-148.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 148\" width=\"166\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\n3(w &#8211; 2) \u2265 10<br \/>\nw &#8211; 2 \u2265 10\/3<br \/>\nw \u2265 10\/3 + 2<br \/>\nw \u2265(10+6)\/3<br \/>\nw \u2265 16\/3<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe \ufb01rst jump in a unicycle high-jump contest is shown. The bar is raised 2 centimeters after each jump. Solve the inequality 2n + 10 \u2265 26 to \ufb01nd the numbers of additional jumps needed to meet or exceed the goal of clearing a height of 26 centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-148.1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 148.1\" width=\"312\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-148.1.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-148.1-300x206.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Answer:<br \/>\nThe numbers of additional jumps needed to meet or exceed the goal of clearing a height of 26 centimeters is 8.<\/p>\n<p>Explanation:<br \/>\n2n + 10 \u2265 26<br \/>\n2n \u2265 26 &#8211; 10<br \/>\n2n \u2265 16<br \/>\nn \u2265 16\/2<br \/>\nn \u2265 8<br \/>\nThe numbers of additional jumps needed to meet or exceed the goal of clearing a height of 26 centimeters is 8.<\/p>\n<p><strong>SOLVING AN INEQUALITY<\/strong><br \/>\n<strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 24.<br \/>\n9x &#8211; 4x + 4 \u2265 36 &#8211; 12<\/p>\n<p>Answer:<br \/>\nx \u2265 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-126.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 126\" width=\"542\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-126.jpg 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-126-300x37.jpg 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Explanation:<br \/>\n9x &#8211; 4x + 4 \u2265 36 &#8211; 12<br \/>\n5x + 4 \u2265 24<br \/>\n5x \u2265 24 &#8211; 4<br \/>\n5x \u2265 20<br \/>\nx \u2265 20\/5<br \/>\nx \u2265 4<\/p>\n<p>Question 25.<br \/>\n3d &#8211; 7d + 2.8 &lt; 5.8 &#8211; 27<\/p>\n<p>Answer:<br \/>\nd &gt; -0.075<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-125.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 125\" width=\"527\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-125.jpg 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-125-300x37.jpg 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Explanation:<br \/>\n-4d + 2.8 &lt; 3.1<br \/>\n-4d &lt; 3.1 &#8211; 2.8<br \/>\n-4d &lt; 0.3<br \/>\nd &gt; -0.3\/4<br \/>\nd &gt; -0.075<\/p>\n<p>Question 26.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cave explorer is at an elevation of 38 feet. The explorer starts moving at a rate of 12 feet per minute. Write and solve an inequality that represents how long it will take the explorer to reach an elevation deeper than -200 feet.<\/p>\n<p>Answer:<br \/>\nIt takes 13 minutes 30 seconds for a cave explorer to reach an elevation deeper than -200 feet.<\/p>\n<p>Explanation:<br \/>\nA cave explorer is at an elevation of 38 feet.<br \/>\nThe explorer starts moving at a rate of 12 feet per minute.<br \/>\nHe should reach an elevation deeper than -200 feet.<br \/>\nSo, 38 + 12n \u2264\u00a0200<br \/>\n12n \u2264 200 &#8211; 38<br \/>\n12n \u2264 162<br \/>\nn \u2264 162\/12<br \/>\nn \u2264 13.5<br \/>\nSo, it takes 13 minutes 30 seconds for a cave explorer to reach an elevation deeper than -200 feet.<\/p>\n<p>Question 27.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA contestant in a weight-loss competition wants to lose an average of atleast 8 pounds per month during a \ufb01ve-month period. Based on the progress report, how many pounds must the contestant lose in the \ufb01fth month to meet the goal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-148.2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 148.2\" width=\"194\" height=\"165\" \/><\/p>\n<p>Answer:<br \/>\n6 pounds must the contestant lose in the \ufb01fth month to meet the goal<\/p>\n<p>Explanation:<br \/>\nThe total weight loss in five months = 12 + 9 + 5 + 8<br \/>\n= 34<br \/>\nA contestant in a weight-loss competition wants to lose an average of atleast 8 pounds per month during a \ufb01ve-month period.<br \/>\nSo, he must loss at least 8 x 5 = 40 pounds on overall<br \/>\nHence, he should lost 40 &#8211; 34 = 6 more pounds to meet the goal.<\/p>\n<p>Question 28.<br \/>\n<strong>REASONING<\/strong><br \/>\nA student theater charges $8.50 per ticket.<br \/>\na. The theater has already sold 70 tickets. How many more tickets does the theater need to sell to earn atleast $750?<br \/>\nb. The theater increases the ticket price by $1. Without solving an inequality, describe how this aspects the total number of tickets needed to earn atleast $750. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. 18 more tickets needed.<br \/>\nb. If the theater charges more per ticket, then they can sell fewer tickets to rach their goal $750.<\/p>\n<p>Explanation:<br \/>\na. Let t represent the number of additional tickets.<br \/>\nt + 70 is the total number of tickets sold.<br \/>\nEach ticket cost is $8.50, the theatre will earn a tota of $8.50(t + 70)<br \/>\nThe theater wants to earn at least $750. So, 8.50(t + 70) \u2265 750<br \/>\n(t + 70) \u2265 750\/8.50<br \/>\nt + 70 \u2265 88.23<br \/>\n(t) \u2265 88.23 &#8211; 70<br \/>\nt \u2265 18.235<br \/>\nSo, 18 more tickets needed.<br \/>\nb. If the theater charges more per ticket, then they can sell fewer tickets to rach their goal $750.<\/p>\n<p>Question 29.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA zoo does not have room to add any more tigers to an enclosure. According to regulations, the area of the enclosure must increase by 150 square feet for each tiger that is added. The zoo is able to enlarge the 450 square foot enclosure for a total area no greater than 1000 square feet. a. Write and solve an inequality that represents this situation. b. Describe the possible numbers of tigers that can be added to the enclosure. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-149.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 149\" width=\"276\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-149.png 276w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-149-150x150.png 150w\" sizes=\"(max-width: 276px) 100vw, 276px\" \/><\/p>\n<p>Answer:<br \/>\n(a + 150)t &lt; 1000<\/p>\n<p>Explanation:<br \/>\nLet us take the area of enclosure for a tiget as a.<br \/>\nThe number of tigers as t<br \/>\nthe area of the enclosure must increase by 150 square feet for each tiger that is added.<br \/>\nThe zoo is able to enlarge the 450 square foot enclosure<br \/>\n(a + 150)t = 450<br \/>\n(a + 150)t &lt; 1000<\/p>\n<p>Question 30.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nFor what values of r will the area of the shaded region be greater than or equal to 12 square units?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-150.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 150\" width=\"164\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nFor r greater than equal to 8 the area of the shaded region be greater than or equal to 12 square units<\/p>\n<p>Explanation:<br \/>\nTotal area of rectangle = 3 x r = 3r<br \/>\nArea of unshaded triangle = 1\/2 x r x 3 = 1.5r<br \/>\nThe area of the shaded region = Total area of rectangle &#8211; Area of unshaded triangle<br \/>\n= 3r &#8211; 1.5r = 1.5r<br \/>\nThe area of the shaded region be greater than or equal to 12 square units<br \/>\n1.5r \u2265 12<br \/>\nr \u2265 12\/1.5<br \/>\nr \u2265 8<br \/>\nFor r greater than equal to 8 the area of the shaded region be greater than or equal to 12 square units<\/p>\n<h3><a id=\"Equations_and_Inequalities_Connecting_Concepts\"><\/a>Equations and Inequalities Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nFencing costs $7 per foot. You install feet of the fencing along one side of a property, as shown. The property has an area of 15,750 square feet. What is the total cost of the fence?<br \/>\n<strong>Understand the problem.<\/strong><br \/>\nYou know the area, height, and one base length of the trapezoid-shaped property. You are asked to \ufb01nd the cost of x feet of fencing, given that the fencing costs $7 per foot.<br \/>\n<strong>Make a plan. <\/strong><br \/>\nUse the formula for the area of a trapezoid to \ufb01nd the length of fencing that you buy. Then multiply the length of fencing by $7 to \ufb01nd the total cost.<br \/>\n<strong>Solve and check <\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nThe total cost of the fence is $840.<\/p>\n<p>Explanation:<br \/>\nThe given image is in the shape of a trapezoid.<br \/>\nTraperzoid area formula = (a + b) xh\/2<br \/>\nHere a = 90, b = x, h = 150<br \/>\nArea of property = (90 + x) x 150\/2<br \/>\n= (90 + x) x 75<br \/>\nGiven that, property area is 15,750 sq ft.<br \/>\n15750 = (90 + x)75<br \/>\n15750\/75 = 90 + x<br \/>\n210 = 90 + x<br \/>\n210 &#8211; 90 = x<br \/>\nx = 120<br \/>\nMultiply x by fencing cost$7 to get total cost<br \/>\nTotal cost = 120 x 7 = $840<\/p>\n<p>Question 2.<br \/>\nA pool is in the shape of a rectangular prism with a length of 15 feet, a width of 10 feet, and a depth of 4 feet. The pool is \ufb01lled with water at a rate no faster than 3 cubic feet per minute. How long does it take to \ufb01ll the pool?<\/p>\n<p>Answer:<br \/>\nThe time is taken to fill the pool is more than 200 minutes.<\/p>\n<p>Explanation:<br \/>\nPool length = 15 ft, width = 10 ft, depth = 4 ft<br \/>\nPool volume = length x width x depth<br \/>\n= 15 x 10 x 4 = 600 cubic feet<br \/>\nThe water filled per minute is 3 cubic feet.<br \/>\nThe time is taken to fill the pool = 600\/3 = 200 minutes<\/p>\n<p>Question 3.<br \/>\nThe table shows your scores on 9 out of 10 quizzes that are each worth 20 points. What score do you need on the \ufb01nal quiz to have a mean score of atleast 17 points?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-151.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 151\" width=\"431\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-151.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-151-300x66.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Answer:<br \/>\nYou need to score 18 points<\/p>\n<p>Explanation:<br \/>\nThe total score on quiz = (15 + 14 + 16 + 19 + 18 + 19 + 20 + 15 + 16 + x)<br \/>\n= 152 + x<br \/>\nMean of total score = (152 + x)\/ 10<br \/>\nSo, (152 + x)\/ 10 \u2265 17<br \/>\n152 + x \u2265 17 x 10<br \/>\n152 + x \u2265 170<br \/>\nx \u2265 170 &#8211; 152<br \/>\nx \u2265 18<br \/>\nSo, you need to score 18 points<\/p>\n<p><strong>Performance Task<\/strong><br \/>\n<strong>Distance and Brightness of the Stars <\/strong><br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cSpace Cadets.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-152.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 152\" width=\"282\" height=\"201\" \/><\/p>\n<h3><a id=\"Equations_and_Inequalities_Chapter_Review\"><\/a>Equations and Inequalities Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-153.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 153\" width=\"641\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-153.png 641w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-153-300x29.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><br \/>\n<strong>Graphic Organizers<\/strong><br \/>\nYou can use a Summary Triangle to explain a concept. Here is an example of Summary Triangle for Addition Property of Equality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-154.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 154\" width=\"528\" height=\"364\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-154.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-154-300x207.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><br \/>\nChoose and complete a graphic organizer to help you study the concept.<\/p>\n<ol>\n<li>equivalent equations<\/li>\n<li>Subtraction Property of Equality<\/li>\n<li>Multiplication Property of Equality<\/li>\n<li>Division Property of Equality<\/li>\n<li>graphing inequalities<\/li>\n<li>Addition and Subtraction Properties of Inequality<\/li>\n<li>Multiplication and Division Properties of Inequality<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-155.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 155\" width=\"259\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-155.png 259w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-155-232x300.png 232w\" sizes=\"(max-width: 259px) 100vw, 259px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><br \/>\n<strong>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-156.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities 156\" width=\"652\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-156.png 652w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-4-Equations-and-Inequalities-156-300x41.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><\/p>\n<p><strong>4.1 Solving Equations Using Addition or Subtraction<\/strong> (pp. 127\u2013132)<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\np &#8211; 3 = -4<\/p>\n<p>Answer:<br \/>\np = -1<\/p>\n<p>Explanation:<br \/>\np &#8211; 3 = -4<br \/>\np = -4 + 3<br \/>\np = -1<br \/>\nPutting p = -1 in p &#8211; 3 = -4<br \/>\n-1 &#8211; 3 = -4<\/p>\n<p>Question 2.<br \/>\n6 + q = 1<\/p>\n<p>Answer:<br \/>\nq = -5<\/p>\n<p>Explanation:<br \/>\n6 + q = 1<br \/>\nq = 1 &#8211; 6<br \/>\nq = -5<br \/>\nPutting q = -5 in 6 + q = 1<br \/>\n6 + (-5) = 6 &#8211; 5 = 1<\/p>\n<p>Question 3.<br \/>\n-2 + j = -22<\/p>\n<p>Answer:<br \/>\nj = -20<\/p>\n<p>Explanation:<br \/>\n-2 + j = -22<br \/>\nj = -22 + 2<br \/>\nj = -20<br \/>\nPutting j = -20 in -2 + j = -22<br \/>\n-2 + (-20) = -2 &#8211; 20 = -22<\/p>\n<p>Question 4.<br \/>\nb &#8211; 19 = -11<\/p>\n<p>Answer:<br \/>\nb = 8<\/p>\n<p>Explanation:<br \/>\nb &#8211; 19 = -11<br \/>\nb = -11 + 19<br \/>\nb = 8<br \/>\nPutting b = 8 in b &#8211; 19 = -11<br \/>\n8 &#8211; 19 = -11<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-157.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 157\" width=\"82\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\nn = -1\/2<\/p>\n<p>Explanation:<br \/>\nn + 3\/4 = 1\/4<br \/>\nn = 1\/4 &#8211; 3\/4<br \/>\nn = -2\/4<br \/>\nn = -1\/2<br \/>\nputting n = -1\/2 in n + 3\/4 = 1\/4<br \/>\n-1\/2 + 3\/4 = (-2 + 3)\/4 = 1\/4<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-158.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 158\" width=\"95\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\nv = -1\/24<\/p>\n<p>Explanation:<br \/>\nv &#8211; 5\/6 = -7\/8<br \/>\nv = -7\/8 + 5\/6<br \/>\nv = (-21 + 20)\/24<br \/>\nv = -1\/24<br \/>\nPutting v = -1\/24 in v &#8211; 5\/6 = -7\/8<br \/>\n-1\/24 &#8211; 5\/6 = (-1 &#8211; 20)\/24 = -21\/24 = -7\/8<\/p>\n<p>Question 7.<br \/>\nt &#8211; 3.7 = 1.2<\/p>\n<p>Answer:<br \/>\nt = 4.9<\/p>\n<p>Explanation:<br \/>\nt = 1.2 + 3.7<br \/>\nt = 4.9<br \/>\nPutting t = 4.9 in t &#8211; 3.7 = 1.2<br \/>\n4.9 &#8211; 3.7 = 1.2<\/p>\n<p>Question 8.<br \/>\nl + 15.2 = -4.5<\/p>\n<p>Answer:<br \/>\nI = -19.7<\/p>\n<p>Explanation:<br \/>\nl + 15.2 = -4.5<br \/>\nI = -4.5 &#8211; 15.2<br \/>\nI = -19.7<br \/>\nPutting I = -19.7 in l + 15.2 = -4.5<br \/>\n-19.7 + 15.2 = -4.5<\/p>\n<p>Question 9.<br \/>\nWrite the word sentence as an equation. Then solve the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-159.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 159\" width=\"224\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n5 + x = -4<br \/>\nx = -9<\/p>\n<p>Explanation:<br \/>\n5 more than a number x is -4<br \/>\n5 + x = -4<br \/>\nx = -4 &#8211; 5<br \/>\nx = -9<\/p>\n<p>Question 10.<br \/>\nThe perimeter of the trapezoid-shaped window frame is 23.59 feet. Write and solve an equation to \ufb01nd the unknown side length (in feet).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-160.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 160\" width=\"260\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown side length is 8.7 feet<\/p>\n<p>Explanation:<br \/>\nPerimeter = 23.59<br \/>\n3.65 + 5.62 + 5.62 + x = 23.59<br \/>\n14.89 + x = 23.59<br \/>\nx = 23.59 &#8211; 14.89<br \/>\nx = 8.7<br \/>\nThe unknown side length is 8.7 feet<\/p>\n<p>Question 11.<br \/>\nYou are 5 years older than your cousin. How old is your cousin when you are 12 years old? Justify your answer.<\/p>\n<p>Answer:<br \/>\nCousin age is 7 years when you are 12 years old.<\/p>\n<p>Explanation:<br \/>\nMy age = cousin + 5<br \/>\nWhen my age is 12 years<br \/>\n12 = cousin + 5<br \/>\ncousin = 12 &#8211; 5<br \/>\ncousin = 7 years<br \/>\nCousin age is 7 years when you are 12 years old.<\/p>\n<p><strong>4.2 Solving Equations Using Multiplication or Division<\/strong> (pp. 133\u2013138)<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-161.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 161\" width=\"66\" height=\"41\" \/><\/p>\n<p>Answer:<br \/>\nx = -24<\/p>\n<p>Explanation:<br \/>\nx = -8 x 3<br \/>\nx = -24<br \/>\nPutting x = -24 in x\/3 = -8<br \/>\n-24\/3 = -8<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-162.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 162\" width=\"65\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\ny = -49<\/p>\n<p>Explanation:<br \/>\n-7 = y\/7<br \/>\n-7 x 7 = y<br \/>\ny = -49<br \/>\nPutting y = -49 in -7 = y\/7<br \/>\n-7 = -49\/7<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-163.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 163\" width=\"81\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\nz = 3<\/p>\n<p>Explanation:<br \/>\n-z\/4 = -3\/4<br \/>\nz\/4 = 3\/4<br \/>\nz = (3\/4) x 4<br \/>\nz = 3<br \/>\nPutting z = 3 in -z\/4 = -3\/4<br \/>\n-3\/4 = -3\/4<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-164.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 164\" width=\"98\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\nw = 50<\/p>\n<p>Explanation:<br \/>\n-w\/20 = -2.5<br \/>\nw = 2.5 x 20<br \/>\nw = 50<br \/>\nPutting w = 50 in -w\/20 = -2.5<br \/>\n-50\/20 = -2.5<\/p>\n<p>Question 16.<br \/>\n4x = -8<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\n4x = -8<br \/>\nx = -8\/4<br \/>\nx = -2<br \/>\nPutting x = -2 in 4x = -8<br \/>\n4(-2) = -8<\/p>\n<p>Question 17.<br \/>\n-10 = 2y<\/p>\n<p>Answer:<br \/>\ny = -5<\/p>\n<p>Explanation:<br \/>\n-10 = 2y<br \/>\ny = -10\/2<br \/>\ny = -5<br \/>\nPutting y = -5 in -10 = 2y<br \/>\n-10 = 2(-5)<\/p>\n<p>Question 18.<br \/>\n-5.4z = -32.4<\/p>\n<p>Answer:<br \/>\nz = 6<\/p>\n<p>Explanation:<br \/>\n-5.4z = -32.4<br \/>\nz = 32.4\/5.4<br \/>\nz = 6<br \/>\nPutting z = 6 in -5.4z = -32.4<br \/>\n-5.4(6) = -32.4<\/p>\n<p>Question 19.<br \/>\n-6.8w = 3.4<\/p>\n<p>Answer:<br \/>\nw = -0.5<\/p>\n<p>Explanation:<br \/>\n-6.8w = 3.4<br \/>\nw = -3.4\/6.8<br \/>\nw = -0.5<br \/>\nPutting w = -0.5 in -6.8w = 3.4<br \/>\n-6.8(-0.5) = 3.4<\/p>\n<p>Question 20.<br \/>\nWrite \u201c3 times a number is 42\u201d as an equation. Then solve the equation.<\/p>\n<p>Answer:<br \/>\nx = 14<\/p>\n<p>Explanation:<br \/>\n3 times a number is 42<br \/>\n3x = 42<br \/>\nx = 42\/3<br \/>\nx = 14<\/p>\n<p>Question 21.<br \/>\nThe mean temperature change is -3.2\u00b0F per day for 5 days. Write and solve an equation to \ufb01nd the total change over the 5-day period.<\/p>\n<p>Answer:<br \/>\nThe total change in temperature for 5 days is -16\u00b0F.<\/p>\n<p>Explanation:<br \/>\nThe mean temperature change is -3.2\u00b0F per day<br \/>\nThe total change in temperature for 5 days = 5 x -3.2 = -16\u00b0F<br \/>\nx= 5 x -3.2<br \/>\nx = -16\u00b0F<\/p>\n<p>Question 22.<br \/>\nDescribe a real-life situation that can be modeled by 7x = 1.75.<\/p>\n<p>Answer:<br \/>\nx = 0.25<\/p>\n<p>Explanation:<br \/>\n7x = 1.75.<br \/>\nx = 1.75\/7<br \/>\nx = 0.25<\/p>\n<p><strong>4.3 Solving Two-Step Equations<\/strong> (pp. 139\u2013144)<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 23.<br \/>\n-2c + 6 = -8<\/p>\n<p>Answer:<br \/>\nc = 2<\/p>\n<p>Explanation:<br \/>\n-2c = -8 &#8211; 6<br \/>\n-2c = -14<br \/>\nc = 14\/2<br \/>\nc = 7<br \/>\nPutting c = 7 in -2c + 6 = -8<br \/>\n-2(7) + 6 = -14 + 6 = -8<\/p>\n<p>Question 24.<br \/>\n5 &#8211; 4t = 6<\/p>\n<p>Answer:<br \/>\nt = -1\/4<\/p>\n<p>Explanation:<br \/>\n-4t = 6 &#8211; 5<br \/>\n-4t = 1<br \/>\nt = -1\/4<br \/>\nPutting t = -1\/4 in 5 &#8211; 4t = 6<br \/>\n5 &#8211; 4(-1\/4) = 5 + 1 = 6<\/p>\n<p>Question 25.<br \/>\n-3x &#8211; 4.6 = 5.9<\/p>\n<p>Answer:<br \/>\nx = -3.5<\/p>\n<p>Explanation:<br \/>\n-3x = 5.9 + 4.6<br \/>\n-3x = 10.5<br \/>\nx = -10.5\/3<br \/>\nx = -3.5<br \/>\nPutting x = -3.5 in -3x &#8211; 4.6 = 5.9<br \/>\n-3(-3.5) &#8211; 4.6 = 10.5 &#8211; 4.6 = 5.9<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-165.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 165\" width=\"111\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\nw = -12<\/p>\n<p>Explanation:<br \/>\nw\/6 + 5\/8 = -11\/8<br \/>\nw\/6 = -11\/8 &#8211; 5\/8<br \/>\nw\/6 = -16\/8<br \/>\nw\/6 = -2<br \/>\nw = -2 x 6<br \/>\nw = -12<br \/>\nPutting w = -12 in w\/6 + 5\/8 = -11\/8<br \/>\n-12\/6 + 5\/8 = -2 + 5\/8<br \/>\n= (-16 + 5)\/8 = -11\/8<\/p>\n<p>Question 27.<br \/>\n3(3w &#8211; 4) = -20<\/p>\n<p>Answer:<br \/>\nw = -8\/9<\/p>\n<p>Explanation:<br \/>\n3(3w &#8211; 4) = -20<br \/>\n(3w &#8211; 4) = -20\/3<br \/>\n3w = -20\/3 + 4<br \/>\n3w = (-20 + 12)\/3<br \/>\n3w = -8\/3<br \/>\nw = -8\/3 x 1\/3<br \/>\nw = -8\/9<br \/>\nPutting w = -8\/9 in 3(3w &#8211; 4) = -20<br \/>\n3(3(-8\/9) &#8211; 4) = 3(-8\/3 &#8211; 4)<br \/>\n= 3(-8 &#8211; 12)\/3 = -20<\/p>\n<p>Question 28.<br \/>\n-6y + 8y = -24<\/p>\n<p>Answer:<br \/>\ny = -12<\/p>\n<p>Explanation:<br \/>\n2y = -24<br \/>\ny = -24\/2<br \/>\ny = -12<br \/>\nputting y = -12 in -6y + 8y = -24<br \/>\n-6(-12) + 8(-12) = 72 &#8211; 96 = -24<\/p>\n<p>Question 29.<br \/>\nThe \ufb02oor of a canyon has an elevation of -14.5 feet. Erosion causes the elevation to change by -1.5 feet per year. How many years will it take for the canyon \ufb02oor to reach an elevation of 31 feet? Justify your solution.<\/p>\n<p>Answer:<br \/>\nIt takes 11 years for the canyon \ufb02oor to reach an elevation of 31 feet<\/p>\n<p>Explanation:<br \/>\nThe \ufb02oor of a canyon has an elevation of -14.5 feet<br \/>\nErosion causes the elevation to change by -1.5 feet per year<br \/>\nLet us take x as the no of years take for the canyon \ufb02oor to reach an elevation of 31 feet<br \/>\n-14.5 &#8211; 1.5x &gt; 31<br \/>\n-1.5x &gt; -31 + 14.5<br \/>\n-1.5x &gt; -16.5<br \/>\nx &lt; 16.5\/1.5<br \/>\nx &lt; 11<br \/>\nSo, it take 11 years.<\/p>\n<p><strong>4.4 Writing and Graphing Inequalities<\/strong> (pp. 145\u2013150)<\/p>\n<p>Write the word sentence as an inequality.<\/p>\n<p>Question 30.<br \/>\nA number w is greater than -3.<\/p>\n<p>Answer:<br \/>\nw &gt; -3<\/p>\n<p>Explanation:<br \/>\nGreater than means &gt;<br \/>\nw &gt; -3<\/p>\n<p>Question 31.<br \/>\nA number y minus \\([\\frac{1}{2}\/latex] is no more than &#8211;[latex][\\frac{3}{2}\/latex].<\/p>\n<p>Answer:<br \/>\ny &#8211; 1\/2 &lt; -3\/2<\/p>\n<p>Explanation:<br \/>\nNo more than means &lt;<br \/>\ny &#8211; 1\/2 &lt; -3\/2<\/p>\n<p><strong>Tell whether the given value is a solution of the inequality.<\/strong><\/p>\n<p>Question 32.<br \/>\n5 + j &gt; 8; j = 7<\/p>\n<p>Answer:<br \/>\nj = 7 is the solution of the inequality.<\/p>\n<p>Explanation:<br \/>\n5 + j &gt; 8; j = 7<br \/>\n5 + 7 &gt; 8<br \/>\n12 &gt; 8<\/p>\n<p>Question 33.<br \/>\n6 \u00f7 n \u2264 -5; n = -3<\/p>\n<p>Answer:<br \/>\nn = -3 is not the solution of the inequality.<\/p>\n<p>Explanation:<br \/>\n6 \u00f7 n \u2264 -5; n = -3<br \/>\n6 \u00f7 -3 \u2264 -5<br \/>\n-2 \u2264 -5<br \/>\n2 \u2265 5<\/p>\n<p>Question 34.<br \/>\n7p \u2265 p &#8211; 12; p = -2<\/p>\n<p>Answer:<br \/>\np = -2 is the solution of the inequality.<\/p>\n<p>Explanation:<br \/>\n7p \u2265 p &#8211; 12; p = -2<br \/>\n7(-2) \u2265 -2 &#8211; 12<br \/>\n-14 \u2265 -14<\/p>\n<p><strong>Graph the inequality on a number line.<\/strong><\/p>\n<p>Question 35.<br \/>\nq &gt; -1.3<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-139.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-139\" width=\"661\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-139.jpg 661w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-139-300x34.jpg 300w\" sizes=\"(max-width: 661px) 100vw, 661px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-165.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 165.1\" width=\"64\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\ns &lt; 7\/4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-140.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-140\" width=\"532\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-140.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-140-300x33.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 37.<br \/>\nThe Enhanced Fujita scale rates the intensity of tornadoes based on wind speed and damage caused. An EF5 tornado is estimated to have wind speeds greater than 200 miles per hour. Write and graph an inequality that represents this situation.<\/p>\n<p>Answer:<br \/>\nw &gt; 200<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-141.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-141\" width=\"547\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-141.jpg 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-141-300x47.jpg 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Explanation:<br \/>\nThe wind speed is greater than 200 miles per hour<br \/>\nw &gt; 200<\/p>\n<p><strong>4.5 Solving Inequalities Using Addition or Subtraction<\/strong> (pp. 151\u2013156)<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 38.<br \/>\nd + 12 &lt; 19<\/p>\n<p>Answer:<br \/>\nd &lt; 7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-142.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-142\" width=\"530\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-142.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-142-300x38.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Explanation:<br \/>\nd + 12 &lt; 19<br \/>\nd &lt; 19 &#8211; 12<br \/>\nd &lt; 7<\/p>\n<p>Question 39.<br \/>\nt &#8211; 4 \u2264 -14<\/p>\n<p>Answer:<br \/>\nt \u2264 -10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-143.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-143\" width=\"638\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-143.jpg 638w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-143-300x37.jpg 300w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p>Explanation:<br \/>\nt &#8211; 4 \u2264 -14<br \/>\nt &#8211; 4 + 4 \u2264 -14 + 4<br \/>\nt \u2264 -10<\/p>\n<p>Question 40.<br \/>\n-8 \u2264 z + 6.4<\/p>\n<p>Answer:<br \/>\n-14.4 \u2264 z<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-144.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-144\" width=\"541\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-144.jpg 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-144-300x46.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Explanation:<br \/>\n-8 \u2264 z + 6.4<br \/>\n-8 -6.4 \u2264 z + 6.4 -6.4<br \/>\n-14.4 \u2264 z<\/p>\n<p>Question 41.<br \/>\nA small cruise ship can hold up to 500 people. There are 115 crew members on board the ship.<br \/>\na. Write and solve an inequality that represents the additional numbers of people that can board the ship.<br \/>\nb. Can 385 more people board the ship? Explain.<\/p>\n<p>Answer:<br \/>\na. 115 + x &lt; 500<br \/>\nb. Yes<\/p>\n<p>Explanation:<br \/>\nA small cruise ship can hold up to 500 people. There are 115 crew members on board the ship.<br \/>\na. 115 + x &lt; 500<br \/>\nb. a. 115 + x &lt; 500<br \/>\na. 115 + x &#8211; 115 &lt; 500 -115<br \/>\na &lt; 385<\/p>\n<p>Question 42.<br \/>\nWrite an inequality that can be solved using the Subtraction Property of Inequality and has a solution of all numbers less than -3.<\/p>\n<p>Answer:<br \/>\nx + 15 &lt; 12<\/p>\n<p>Explanation:<br \/>\nx + 15 &lt; 12<br \/>\nx + 15 &#8211; 15 &lt; 12 &#8211; 15<br \/>\nx &lt; -3<\/p>\n<p><strong>4.6 Solving Inequalities Using Multiplication or Division<\/strong> (pp. 157\u2013164)<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 43.<br \/>\n6q &lt; -18<\/p>\n<p>Answer:<br \/>\nq &lt; -3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-145.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-145\" width=\"543\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-145.jpg 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-145-300x38.jpg 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Explanation:<br \/>\n6q &lt; -18<br \/>\n6q\/6 &lt; -18\/6<br \/>\nq &lt; -3<\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-166.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 166\" width=\"63\" height=\"44\" \/><\/p>\n<p>Answer:<br \/>\nr \u2265-18<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-146.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-146\" width=\"532\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-146.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-146-300x37.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Explanation:<br \/>\n-r\/3 \u2264 6<br \/>\n-r \u2264 6 * 3<br \/>\n-r \u2264 18<br \/>\nr \u2265-18<\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-166.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 166.1\" width=\"83\" height=\"42\" \/><\/p>\n<p>Answer:<br \/>\n3 &lt; s<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-147.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-147\" width=\"543\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-147.jpg 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-147-300x38.jpg 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Explanation:<br \/>\n-4 x 3 &gt; -4s<br \/>\n-12 &gt; -4s<br \/>\n12 &lt; 4s<br \/>\n12\/4 &lt; s<br \/>\n3 &lt; s<\/p>\n<p>Question 46.<br \/>\nWrite the word sentence as an inequality. Then solve the inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-167.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 167\" width=\"366\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-167.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-167-300x33.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Answer:<br \/>\np &lt; -7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-148.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-148\" width=\"533\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-148.jpg 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-148-300x41.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Explanation:<br \/>\n-3p &gt; 21<br \/>\n-p &gt; 21\/3<br \/>\n-p &gt; 7<br \/>\np &lt; -7<\/p>\n<p>Question 47.<br \/>\nYou are organizing books on a shelf. Each book has a width of [latex]\\frac{3}{4}\\) inch. Write and solve an inequality for the numbers of books b that can \ufb01t on the shelf.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-168.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 168\" width=\"281\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\n32 books will \ufb01t on the shelf.<\/p>\n<p>Explanation:<br \/>\nWidth of book = 3\/4 inch<br \/>\nThe total width of shelf = 24 in<br \/>\n3\/4 b &lt; 24<br \/>\n3b &lt; 24 x 4<br \/>\n3b &lt; 96<br \/>\nb &lt; 96\/3<br \/>\nb &lt; 32<br \/>\nSo, 32 books will \ufb01t on the shelf.<\/p>\n<p><strong>4.7 Solving Two-Step Inequalities<\/strong> (pp. 165\u2013170)<\/p>\n<p>Solve the inequality. Graph the solution.<\/p>\n<p>Question 48.<br \/>\n3x + 4 &gt; 16<\/p>\n<p>Answer:<br \/>\nx &gt; 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-149.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 149\" width=\"527\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-149.jpg 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-149-300x35.jpg 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Explanation:<br \/>\n3x + 4 &gt; 16<br \/>\n3x + 4 &#8211; 4 &gt; 16 &#8211; 4<br \/>\n3x &gt; 12<br \/>\nx &gt; 12\/3<br \/>\nx &gt; 4<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-169.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 169\" width=\"101\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\nz \u2265 -8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-150.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities 150\" width=\"540\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-150.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-150-300x43.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Explanation:<br \/>\nz \/ -2 \u2264 -2 + 6<br \/>\nz\/-2 \u2264 4<br \/>\nz \u2265 4 x -2<br \/>\nz \u2265 -8<\/p>\n<p>Question 50.<br \/>\n-2t &#8211; 5 &lt; 9<\/p>\n<p>Answer:<br \/>\nt &gt; -7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-151.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-151\" width=\"546\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-151.jpg 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-151-300x41.jpg 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Explanation:<br \/>\n-2t &#8211; 5 + 5 &lt; 9 + 5<br \/>\n-2t &lt; 14<br \/>\nt &gt; -14\/2<br \/>\nt &gt; -7<\/p>\n<p>Question 51.<br \/>\n7(q + 2) &lt; -77<\/p>\n<p>Answer:<br \/>\nq &lt; -13<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-152.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-152\" width=\"538\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-152.jpg 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-152-300x48.jpg 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Explanation:<br \/>\n7(q + 2) &lt; -77<br \/>\nq + 2 &lt; -77\/7<br \/>\nq + 2 &lt; -11<br \/>\nq &lt; -11 &#8211; 2<br \/>\nq &lt; -13<\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-170.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 170\" width=\"111\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\np \u2265 -21<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-153.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-153\" width=\"534\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-153.jpg 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-153-300x42.jpg 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Explanation:<br \/>\n-1\/3 (p + 9) \u2264 4<br \/>\n(p + 9) \u2265 -4 x 3<br \/>\np + 9 \u2265 -12<br \/>\np \u2265 -12 &#8211; 9<br \/>\np \u2265 -21<\/p>\n<p>Question 53.<br \/>\n1.2(j + 3.5) \u2265 4.8<\/p>\n<p>Answer:<br \/>\nj \u2265 0.5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-154.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-154\" width=\"540\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-154.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-154-300x31.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Explanation:<br \/>\n1.2(j + 3.5) \u2265 4.8<br \/>\n(j + 3.5) \u2265 4.8\/1.2<br \/>\n(j + 3.5) \u2265 4<br \/>\nj \u2265 4 &#8211; 3.5<br \/>\nj \u2265 0.5<\/p>\n<p>Question 54.<br \/>\nYour goal is to raise at least $50 in a charity fundraiser. You earn $3.50 for each candle sold. You also receive a $15 donation. Write and solve an inequality that represents the numbers of candles you must sell to reach your goal.<\/p>\n<p>Answer:<br \/>\nYou must sell 10 candles to reach your goal.<\/p>\n<p>Explanation:<br \/>\nYour goal is to raise at least $50 in a charity fundraiser.<br \/>\ngoal \u2265 50<br \/>\nYou earn $3.50 for each candle sold. You also receive a $15 donation.<br \/>\n3.5x + 15 \u2265 50<br \/>\n3.5x \u2265 50 &#8211; 15<br \/>\n3.5x \u2265 35<br \/>\nx \u2265 35\/3.5<br \/>\nx \u2265 10<\/p>\n<h3><a id=\"Equations_and_Inequalities_Practice_Test\"><\/a>Equations and Inequalities Practice Test<\/h3>\n<p><strong>Solve the equation. Check your solution. <\/strong><\/p>\n<p>Question 1.<br \/>\n7x = -3<\/p>\n<p>Answer:<br \/>\nx = -3\/7<\/p>\n<p>Explanation:<br \/>\n7x = -3<br \/>\nx = -3\/7<br \/>\nPutting x = -3\/7 in 7x = -3<br \/>\n7(-3\/7) = -3<\/p>\n<p>Question 2.<br \/>\n2(x + 1) = -2<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\n2(x + 1) = -2<br \/>\nx + 1 = -2\/2<br \/>\nx + 1 = -1<br \/>\nx = -1 &#8211; 1<br \/>\nx = -2<br \/>\nPutting x = -2 in 2(x + 1) = -2<br \/>\n2(-2 + 1) = 2(-1) = -2<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-171.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 171\" width=\"71\" height=\"44\" \/><\/p>\n<p>Answer:<br \/>\ng = -36<\/p>\n<p>Explanation:<br \/>\n(2\/9)g = -8<br \/>\n2g = -8 x 9<br \/>\n2g = -72<br \/>\ng = -72\/2<br \/>\ng = -36<br \/>\nPutting g = -36 in (2\/9)g = -8<br \/>\n(2\/9) x (-36) = 2 x -4 = -8<\/p>\n<p>Question 4.<br \/>\nz + 14.5 = 5.4<\/p>\n<p>Answer:<br \/>\nz = -9.2<\/p>\n<p>Explanation:<br \/>\nz + 14.5 = 5.4<br \/>\nz = 5.4 &#8211; 14.5<br \/>\nz = -9.2<br \/>\nPutting z = -9.2 in z + 14.5 = 5.4<br \/>\n-9.2 + 14.5 = 5.4<\/p>\n<p>Question 5.<br \/>\n-14 = c &#8211; 10<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n-14 + 10 = c<br \/>\nc = -4<br \/>\nPutting c = -4 in -14 = c &#8211; 10<br \/>\n-14 = -4 &#8211; 10<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-172.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 172\" width=\"112\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\nk = -7<\/p>\n<p>Explanation:<br \/>\n(2\/7)k &#8211; 3\/8 = -19\/8<br \/>\n(2\/7)k = -19\/8 + 3\/8<br \/>\n(2\/7)k = -16\/8<br \/>\n(2\/7)k = -2<br \/>\n2k = -2 x 7<br \/>\n2k = -14<br \/>\nk = -14\/2<br \/>\nk = -7<br \/>\nPutting k = -7 in (2\/7)k &#8211; 3\/8 = -19\/8<br \/>\n(2\/7)(-7) &#8211; 3\/8 = -2 &#8211; 3\/8<br \/>\n= (-16 &#8211; 3)\/8 = -19\/8<\/p>\n<p><strong>Write the word sentence as an inequality.<\/strong><\/p>\n<p>Question 7.<br \/>\nA number k plus 19.5 is less than or equal to 40.<\/p>\n<p>Answer:<br \/>\nk + 19.5 \u2264 40<\/p>\n<p>Explanation:<br \/>\nA number k plus 19.5 is less than or equal to 40.<br \/>\nless than or equal to means \u2264<br \/>\nk + 19.5 \u2264 40<\/p>\n<p>Question 8.<br \/>\nA number q multiplied by \\(\\frac{1}{4}\\) is greater than -16.<\/p>\n<p>Answer:<br \/>\nq\/4 &gt; -16<\/p>\n<p>Explanation:<br \/>\nA number q multiplied by 1\/4 is greater than -16.<br \/>\ngreater than means &gt;<br \/>\nq (1\/4) &gt; -16<br \/>\nq\/4 &gt; -16<\/p>\n<p><strong>Tell whether the given value is a solution of the inequality.<\/strong><\/p>\n<p>Question 9.<br \/>\nn &#8211; 3 \u2264 4; n = 7<\/p>\n<p>Answer:<br \/>\nThe given value is the solution for the inequality.<\/p>\n<p>Explanation:<br \/>\nPutting n = 7 in n &#8211; 3 \u2264 4<br \/>\n7 &#8211; 3 \u2264 4<br \/>\n4 \u2264 4<br \/>\nSo, the given value is the solution for the inequality.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-173.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 173\" width=\"180\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\nThe given value is not the solution for the inequality.<\/p>\n<p>Explanation:<br \/>\nPutting m = -7 in (-3\/7)m &lt; 1 + m<br \/>\n(-3\/7)(-7) &lt; 1 + (-7)<br \/>\n3 &lt; -6<br \/>\nSo, the given value is not the solution for the inequality.<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><\/p>\n<p>Question 11.<br \/>\nx &#8211; 4 &gt; -6<\/p>\n<p>Answer:<br \/>\nx &gt; -2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-70.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-70\" width=\"530\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-70.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-70-300x33.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Explanation:<br \/>\nx &#8211; 4 &gt; -6<br \/>\nx &gt; -6 + 4<br \/>\nx &gt; -2<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-174.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 174\" width=\"97\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\ny \u2264 7\/9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-71.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-71\" width=\"526\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-71.jpg 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-71-300x46.jpg 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Explanation:<br \/>\n-2\/9 + y \u2264 5\/9<br \/>\ny \u2264 5\/9 + 2\/9<br \/>\ny \u2264 7\/9<\/p>\n<p>Question 13.<br \/>\n-6z \u2265 36<\/p>\n<p>Answer:<br \/>\nz \u2265 -6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-72.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-72\" width=\"536\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-72.jpg 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-72-300x39.jpg 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Explanation:<br \/>\n-6z \u2265 36<br \/>\nz \u2265 -36\/6<br \/>\nz \u2265 -6<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-174.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 174.1\" width=\"76\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\n-20.8 \u2265 p<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-73.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-73\" width=\"534\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-73.jpg 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-73-300x48.jpg 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Explanation:<br \/>\n-5.2 \u2265 p\/4<br \/>\n-5.2 x 4 \u2265 p<br \/>\n-20.8 \u2265 p<\/p>\n<p>Question 15.<br \/>\n4k &#8211; 8 \u2265 20<\/p>\n<p>Answer:<br \/>\nk \u2265 7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-75.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-75\" width=\"533\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-75.jpg 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-75-300x35.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Explanation:<br \/>\n4k &#8211; 8 \u2265 20<br \/>\n4k \u2265 20 + 8<br \/>\n4k \u2265 28<br \/>\nk \u2265 28\/4<br \/>\nk \u2265 7<\/p>\n<p>Question 16.<br \/>\n-0.6 &gt; -0.3(d + 6)<\/p>\n<p>Answer:<br \/>\n-4 &gt; d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74.jpg\" alt=\"Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74\" width=\"533\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74.jpg 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-4-Equations-and-Inequalities-74-300x37.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Explanation:<br \/>\n-0.6\/(-0.3) &gt; (d + 6)<br \/>\n2 &gt; d + 6<br \/>\n2 &#8211; 6 &gt; d<br \/>\n-4 &gt; d<\/p>\n<p>Question 17.<br \/>\nYou lose 0.3 point for stepping out of bounds during a gymnastics \ufb02oor routine. Your \ufb01nal score is 9.124. Write and solve an equation to \ufb01nd your score without the penalty.<\/p>\n<p>Answer:<br \/>\nMy score without penalty is 9.424<\/p>\n<p>Explanation:<br \/>\nYou lose 0.3 point for stepping out of bounds during a gymnastics \ufb02oor routine.<br \/>\nAssume my score without penalty as x.<br \/>\nYour \ufb01nal score is 9.124.<br \/>\nx &#8211; 0.3 = 9.124<br \/>\nx = 9.124 + 0.3<br \/>\nx = 9.424<br \/>\nSo, my score without penalty is 9.424<\/p>\n<p>Question 18.<br \/>\nHalf the area of the rectangle shown is 24 square inches. Write and solve an equation to \ufb01nd the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-175.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 175\" width=\"146\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nx = 2<\/p>\n<p>Explanation:<br \/>\nRectangle area = length x breadth<br \/>\n6(x+ 2) = 24<br \/>\n(x + 2) = 24\/6<br \/>\nx + 2 = 4<br \/>\nx = 4 &#8211; 2<br \/>\nx = 2<\/p>\n<p>Question 19.<br \/>\nYou can spend no more than $100 on a party you are hosting. The cost per guest is $8.<br \/>\na. Write and solve an inequality that represents the numbers of guests you can invite to the party.<br \/>\nb. What is the greatest number of guests that you can invite to the party? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-176.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 176\" width=\"357\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-176.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-176-300x148.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Answer:<br \/>\na. You can invite 12 guests to the party.<br \/>\nb. The greatest number of guests that you can invite to the party is 13.<\/p>\n<p>Explanation:<br \/>\nYou can spend no more than $100 on a party you are hosting. The cost per guest is $8.<br \/>\na. 8x &lt; 100<br \/>\nx &lt; 100\/8<br \/>\nx &lt; 12.5<br \/>\nSo, you can invite 12 guests to the party.<br \/>\nb. x &lt; 12.5<br \/>\nSo, the greatest number of guests that you can invite to the party is 13.<\/p>\n<p>Question 20.<br \/>\nYou have $30 to buy baseball cards. Each pack of cards costs $5. Write and solve an inequality that represents the numbers of packs of baseball cards you can buy and still have atleast $10 left.<\/p>\n<p>Answer:<br \/>\nI can buy at least 4 packs of baseball cards<\/p>\n<p>Explanation:<br \/>\nYou have $30 to buy baseball cards. Each pack of cards costs $5.<br \/>\nI must have at least 10 left after shopping<br \/>\nSo, 5x + 10 \u2265 30<br \/>\n5x \u2265 30 &#8211; 10<br \/>\n5x \u2265 20<br \/>\nx \u2265 20\/5<br \/>\nx \u2265 4<br \/>\nSo, I can buy at least 4 packs of baseball cards<\/p>\n<p>Question 21.<br \/>\nThe sum of the lengths of any two sides of a triangle is greater than the length of the third side.<br \/>\na. Write and solve three inequalities for the previous statement using the triangle shown.<br \/>\nb. What values for x make sense?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-177.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 177\" width=\"152\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\na. 6.4 &gt; x<br \/>\nb. The values of x can be less than 64.<\/p>\n<p>Explanation:<br \/>\nThe sum of the lengths of any two sides of a triangle is greater than the length of the third side.<br \/>\n17 + 15 &gt; 5x<br \/>\n32 &gt; 5x<br \/>\n32\/5 &gt; x<br \/>\n6.4 &gt; x<br \/>\nb. x can be less than 64.<\/p>\n<h3><a id=\"Equations_and_Inequalities_Cumulative_Practice\"><\/a>Equations and Inequalities Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhich equation represents the word sentence?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-178.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 178\" width=\"309\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-178.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-178-300x189.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-179.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 179\" width=\"351\" height=\"402\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-179.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-179-262x300.png 262w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<p>Answer:<br \/>\nB. b\/0.3 = -10<\/p>\n<p>Explanation:<br \/>\nThe quotient of b and 0.3 means b\/0.3<br \/>\nThe quotient of b and 0.3 equal to negative 10.<br \/>\nSo, b\/0.3 = -10<\/p>\n<p>Question 2.<br \/>\nWhat is the value of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-180.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 180\" width=\"272\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\n-3\/8 x 2\/5 = -3\/20<\/p>\n<p>Explanation:<br \/>\n-3\/8 x 2\/5 = (-3\/4) x (1\/5)<br \/>\n= (-3\/20)<\/p>\n<p>Question 3.<br \/>\nWhich graph represents the inequality?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-181.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 181\" width=\"630\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-181.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-181-300x73.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p>\n<p>Answer:<br \/>\nA.<\/p>\n<p>Explanation:<br \/>\nx\/-4 &#8211; 8 \u2265 -9<br \/>\nx\/-4 \u2265 -9 + 8<br \/>\nx\/-4 \u2265 -1<br \/>\nx \u2264 -1 x -4<br \/>\nx \u2264 4<\/p>\n<p>Question 4.<br \/>\nWhich equation is equivalent to <img loading=\"lazy\" class=\"alignnone size-full wp-image-31165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-182.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 182\" width=\"107\" height=\"49\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-182.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 182.1\" width=\"496\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-182.1.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-182.1-300x70.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Answer:<br \/>\nF.<\/p>\n<p>Explanation:<br \/>\n-3\/4 x + 1\/8 = -3\/8<br \/>\n-3\/4 x =-3\/8 &#8211; 1\/8<\/p>\n<p>Question 5.<br \/>\nWhat is the decimal form of 2\\(\\frac{5}{8}\\) ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-183.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 183\" width=\"90\" height=\"70\" \/><\/p>\n<p>Answer:<br \/>\nThe decimal form of 2(5\/8) is 2.25<\/p>\n<p>Explanation:<br \/>\nThe decimal form of 2(5\/8)<br \/>\n= 18\/8 = 2.25<\/p>\n<p>Question 6.<br \/>\nWhat is the value of the expression when x = -5, y = 3, and z = -1?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-184.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 184\" width=\"81\" height=\"55\" \/><br \/>\nA. -34<br \/>\nB. -16<br \/>\nC. 16<br \/>\nD. 34<\/p>\n<p>Answer:<br \/>\nB. -16<\/p>\n<p>Explanation:<br \/>\nPutting x = -5, y = 3, and z = -1 in (x\u00b2 &#8211; 3y)\/z<br \/>\n= ((-5)\u00b2 &#8211; 3(3))\/(-1)<br \/>\n= (25 &#8211; 9)\/(-1)<br \/>\n= -16<\/p>\n<p>Question 7.<br \/>\nWhich expression is equivalent to 9h &#8211; 6 + 7h &#8211; 5?<br \/>\nF. 3h + 2<br \/>\nG. 16h + 1<br \/>\nH. 2h &#8211; 1<br \/>\nI. 16h &#8211; 11<\/p>\n<p>Answer:<br \/>\nI. 16h &#8211; 11<\/p>\n<p>Explanation:<br \/>\n9h &#8211; 6 + 7h &#8211; 5 = 16h &#8211; 11<\/p>\n<p>Question 8.<br \/>\nYour friend solved the equation -96 = -6(x &#8211; 15).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-185.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 185\" width=\"239\" height=\"204\" \/><br \/>\nWhat should your friend do to correct her error?<br \/>\nA. First add 6 to both sides of the equation.<br \/>\nB. First subtract from both sides of the equation.<br \/>\nC. Distribute the -6 to get 6x &#8211; 90.<br \/>\nD. Distribute the -6 to get -6x + 90.<\/p>\n<p>Answer:<br \/>\nD. Distribute the -6 to get -6x + 90.<\/p>\n<p>Explanation:<br \/>\n-96 = -6(x &#8211; 15)<br \/>\n96 = 6(x &#8211; 15)<br \/>\nx &#8211; 15 = 96\/6<br \/>\nx &#8211; 15 = 16<br \/>\nx = 16 + 15<br \/>\nx = 31<\/p>\n<p>Question 9.<br \/>\nWhich expression does not represent the perimeter of the rectangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-186.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 186\" width=\"187\" height=\"104\" \/><br \/>\nF. 4j(60)<br \/>\nG. 8j + 120<br \/>\nH. 2(4j + 60)<br \/>\nI. 8(j + 15)<\/p>\n<p>Answer:<br \/>\nF. 4j(60)<\/p>\n<p>Explanation:<br \/>\nThe perimeter of rectangle = 2(length + breadth)<br \/>\n= 2(4j + 60) = 8j + 120 = 8(j + 15)<\/p>\n<p>Question 10.<br \/>\nWhat is the value of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-187.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 187\" width=\"235\" height=\"72\" \/><\/p>\n<p>Answer:<br \/>\n5\/12 &#8211; 7\/8 = -11\/24<\/p>\n<p>Explanation:<br \/>\n5\/12 &#8211; 7\/8 = (10 &#8211; 21)\/24<br \/>\n= -11\/24<\/p>\n<p>Question 11.<br \/>\nYou are selling T-shirts to raise money for a charity. You sell the T-shirts for $10 each.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-188.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 188\" width=\"77\" height=\"88\" \/><br \/>\n<strong>Part A<\/strong><br \/>\nYou have already sold 2 T-shirts. How many more T-shirts must you sell to raise at least $500? Explain.<br \/>\n<strong>Part B<\/strong><br \/>\nYour friend is raising money for the same charity and has not sold any T-shirts previously. He sells the T-shirts for $8 each. What are the total numbers of T-shirts he can sell to raise atleast $500? Explain.<br \/>\n<strong>Part C<\/strong><br \/>\nWho has to sell more T-shirts in total? How many more? Explain.<\/p>\n<p>Answer:<br \/>\nA. You need to sell 48 more t-shirts to raise at least $500<br \/>\nB. You need to sell more than 63 T-shirts to raise atleast $500<br \/>\nC. The person who is selling $8 per T-shirt has to sell more when compared with others.<\/p>\n<p>Explanation:<br \/>\nThe cost of each T-shirt = $10<br \/>\nA. You have already sold 2 T-shirts.<br \/>\nSo, you earned = 2 x 10 = 20<br \/>\nThe more number of T-shirts must you sell to raise at least $500<br \/>\n2 + 10x \u2265 500<br \/>\n10x \u2265 500 &#8211; 2<br \/>\n10x \u2265 488<br \/>\nx \u2265 488\/10<br \/>\nx \u2265 48.8<br \/>\nB. The cost of each T-shirt = $8<br \/>\nThe total numbers of T-shirts he can sell to raise atleast $500<br \/>\n8x \u2265 500<br \/>\nx \u2265 500\/8<br \/>\nx \u2265 62.5<br \/>\nYou need to sell more than 63 T-shirts to raise atleast $500<br \/>\nC. The person who is selling $8 per T-shirt has to sell more when compared with others.<\/p>\n<p>Question 12.<br \/>\nWhich expression has the same value as <img loading=\"lazy\" class=\"alignnone size-full wp-image-31173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-189.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 189\" width=\"92\" height=\"49\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-189.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 189.1\" width=\"448\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-189.1.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-189.1-300x73.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Answer:<br \/>\nA. -1\/3 + 1\/9<\/p>\n<p>Explanation:<br \/>\nSolve all the expressions and check which solution represents the given expression.<br \/>\n-2\/3 &#8211; (-4\/9) = -2\/3 + 4\/9<br \/>\n= (-6 + 4)\/9<br \/>\n= -2\/9<br \/>\nA. -1\/3 + 1\/9 = (-3 + 1)\/9<br \/>\n= -2\/9<br \/>\nB. -2\/3 x (-13) = 2\/9<br \/>\nAs option A and given expression has the same solution. A is the answer.<\/p>\n<p>Question 13.<br \/>\nYou recycle (6c + 10) water bottles. Your friend recycles twice as many water bottles as you recycle. Which expression represents the amount of water bottles your friend recycles?<br \/>\nF. 3c + 5<br \/>\nG. 12c + 10<br \/>\nH. 12c + 20<br \/>\nI. 6c + 12<\/p>\n<p>Answer:<br \/>\nH. 12c + 20<\/p>\n<p>Explanation:<br \/>\nFriend recycles twice as many water bottles as you recycle.<br \/>\nYou recycle (6c + 10) water bottles.<br \/>\nSo, my friend recycles 2(6c + 10) = 12c + 20<\/p>\n<p>Question 14.<br \/>\nWhat is the value of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-190.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 4 Equations and Inequalities 190\" width=\"414\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-190.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-4-Equations-and-Inequalities-190-300x125.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<p>Answer:<br \/>\n-4\/5 + (-2\/3) = -22\/15<\/p>\n<p>Explanation:<br \/>\n-4\/5 + (-2\/3) = -4\/5 &#8211; 2\/3<br \/>\n= (-12 &#8211; 10)\/15<br \/>\n= -22\/15<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>We have provided the Big Ideas Math Answers Grade 7 Chapter 4 Equations and Inequalities to master your child in maths. If you are lagging in this topic, then this article is the best guide for your preparation. You can download all Pdfs for free of cost. Check our page regularly to get the latest and trending updates on all Grade Mathematics. All your doubts will be clarified on regular basis by us if you tell us in the comment section.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hey guys!! Are you in search of the concept of Equations and Inequalities? If yes, then here is the quick material for the candidates. With the help of Big Ideas Math Grade 7 Answer Key for Chapter 4 Equations and Inequalities, you will get diverse opportunities, and also it provides problem-solving skills. 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