{"id":33786,"date":"2022-04-06T18:30:37","date_gmt":"2022-04-06T13:00:37","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=33786"},"modified":"2022-04-07T11:36:56","modified_gmt":"2022-04-07T06:06:56","slug":"big-ideas-math-algebra-1-answers-chapter-1","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-1\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations"},"content":{"rendered":"<p><strong>Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations<\/strong> available here are free of cost. Students can seek homework help and solve the questions covered in the Ch 1 lessons. Also, these solutions of BIM Algebra 1 Ch 1 Answer Book improve their math skills and become math proficient in the future. Choosing the right track during the preparation can change your education life. So, accessing the<a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\"> Big Ideas Math Book Solutions<\/a> Algebra 1 Ch 1 solving linear equations is a better &amp; fun-learning way for students of high school. Also, it clarifies all your doubts about the concepts of chapter 2 BIM Textbook Solutions.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Chapter 1 Solving Linear Equations<\/h2>\n<p>Get free access to the below available links just by tapping on them and make use of the handy Big Ideas Math Algebra 1 Chapter 1 Solving Linear Equations Solution Key to solve all the questions that appeared in homework, assignments, and yearly exams. <strong>Algebra 1 BIM Ch 1 Solving Linear Equations Answer key<\/strong> is explained by the subject experts as per the latest edition of common core standards. So, kids can easily understand the concepts of ch 1 and gain more subject knowledge with the help of the Big Ideas Math Book Solution key of Algebra 1 Chapter 1 Solving Linear Equations.<\/p>\n<ul>\n<li><a href=\"#Solving_Linear_Equations_Maintaining_Mathematical_Proficiency\">Solving Linear Equations Maintaining Mathematical Proficiency &#8211; Page 1<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_Monitoring_Progress\">Solving Linear Equations Monitoring Progress &#8211; Page 2<\/a><\/li>\n<li><a href=\"#Lesson_1.1_Solving_Simple_Equations\">Lesson 1.1 Solving Simple Equations &#8211; Page(4-10)<\/a><\/li>\n<li><a href=\"#Solving_Simple_Equations_1.1_Exercises\">Solving Simple Equations 1.1 Exercises &#8211; Page(8-10)<\/a><\/li>\n<li><a href=\"#Lesson_1.2_Solving_Multi-step_Equations\">Lesson 1.2 Solving Multi-step Equations &#8211; Page(12-18)<\/a><\/li>\n<li><a href=\"#Solving_Multi-step_Equations_1.2_Exercises\">Solving Multi-step Equations 1.2 Exercises &#8211; Page(16-18)<\/a><\/li>\n<li><a href=\"#Lesson_1.3_Solving_Equations_with_Variables_on_Both_Sides\">Lesson 1.3 Solving Equations with Variables on Both Sides &#8211; Page(20-24)<\/a><\/li>\n<li><a href=\"#Solving_Equations_with_Variables_on_Both_Sides_1.3_Exercises\">Solving Equations with Variables on Both Sides 1.3 Exercises &#8211; Page(23-24)<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_Study_Skills:_Completing\">Solving Linear Equations Study Skills: Completing &#8211; Page 25<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_1.1-1.3_Quiz\">Solving Linear Equations 1.1-1.3 Quiz &#8211; Page 26\u00a0<\/a><\/li>\n<li><a href=\"#Lesson_1.4_Solving_Absolute_Value_Equations\">Lesson 1.4 Solving Absolute Value Equations &#8211; Page(28-34)<\/a><\/li>\n<li><a href=\"#Solving_Absolute_Value_Equations_1.4_Exercises\">Solving Absolute Value Equations 1.4 Exercises &#8211; Page(32-34)<\/a><\/li>\n<li><a href=\"#Lesson_1.5_Rewriting_Equations_and_Formulas\">Lesson 1.5 Rewriting Equations and Formulas &#8211; Page(36-42)<\/a><\/li>\n<li><a href=\"#Rewriting_Equations_and_Formulas_1.5_Exercices\">Rewriting Equations and Formulas 1.5 Exercices &#8211; Page(40-42)<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_Performance_Task:_Magic_of_Mathematics\">Solving Linear Equations Performance Task: Magic of Mathematics &#8211; Page 43<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_Chapter_Review\">Solving Linear Equations Chapter Review -Page (44-46)<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_Chapter_Test\">Solving Linear Equations Chapter Test &#8211; Page 47<\/a><\/li>\n<li><a href=\"#Solving_Linear_Equations_Cumulative_Assessment\">Solving Linear Equations Cumulative Assessment Page(48-49)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Solving_Linear_Equations_Maintaining_Mathematical_Proficiency\"><\/a>Solving Linear Equations Maintaining Mathematical Proficiency<\/h3>\n<p><b>Add or subtract.<\/b><\/p>\n<p>Question 1.<br \/>\n-5 + (-2)<br \/>\nAnswer:<br \/>\n-5 + (-2 ) = -7<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-5 + ( -2 ) = -5 &#8211; 2<br \/>\n= &#8211; ( 5 + 2 )<br \/>\n= -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n-5 + ( -2 ) = -7<\/p>\n<p>Question 2.<br \/>\n0 + (-13)<br \/>\nAnswer:<br \/>\n0 + -13 = -13<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n0 + ( -13 ) = 0 &#8211; 13<br \/>\n= -13<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n0 + ( -13 ) = -13<\/p>\n<p>Question 3.<br \/>\n-6 + 14<br \/>\nAnswer:<br \/>\n-6 + 14 = 8<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-6 + 14 = +14 &#8211; 6<br \/>\n= +8<br \/>\n= 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-6 +14 = 8<\/p>\n<p>Question 4.<br \/>\n19 &#8211; (-13)<br \/>\nAnswer:<br \/>\n19 &#8211; ( -13 ) = 32<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n19 &#8211; ( -13 ) = 10 + 9 + 10 + 3<br \/>\n= 20 + 12<br \/>\n= 32<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n19 &#8211; (-13 ) = 32<\/p>\n<p>Question 5.<br \/>\n-1 &#8211; 6<br \/>\nAnswer:<br \/>\n-1 -6 = -7<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-1 &#8211; 6 = &#8211; ( 1 + 6 )<br \/>\n= -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-1 -6 = -7<\/p>\n<p>Question 6.<br \/>\n&#8211; 5 &#8211; (-7)<br \/>\nAnswer:<br \/>\n-5 &#8211; ( -7 ) = 2<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-5 &#8211; ( -7 ) = -5 + 7<br \/>\n= 7 &#8211; 5<br \/>\n= 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-5 &#8211; ( -7 ) = 2<\/p>\n<p>Question 7.<br \/>\n17 + 5<br \/>\nAnswer:<br \/>\n17 + 5 = 22<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n17 + 5 = 15 + 2 + 5<br \/>\n= 22<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n17 + 5 = 22<\/p>\n<p>Question 8.<br \/>\n8 + (-3)<br \/>\nAnswer:<br \/>\n8 + ( -3 ) = 5<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n8 + ( -3 ) = 8 &#8211; 3<br \/>\n= 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n8\u00a0 + ( -3 ) = 5<\/p>\n<p>Question 9.<br \/>\n11 &#8211; 15<br \/>\nAnswer:<br \/>\n11 &#8211; 15 = -4<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n11 &#8211; 15 = -15 + 11<br \/>\n= &#8211; ( 15 &#8211; 11 )<br \/>\n= -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n11 &#8211; 15 = -4<\/p>\n<p><b>Multiply or divide.<\/b><\/p>\n<p>Question 10.<br \/>\n-3(8)<br \/>\nAnswer:<br \/>\n-3(8) = -3 \u00d7 8<br \/>\n= -24<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-3(8) = -3 \u00d7 +8<br \/>\n= -24<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-3 ( 8 ) = -24<\/p>\n<p>Question 11.<br \/>\n-7 \u2022 (-9)<br \/>\nAnswer:<br \/>\n-7 . ( -9 ) = -7 \u00d7 +9<br \/>\n= -63<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-7 . ( 9 ) = -7 \u00d7 +9<br \/>\n= -63<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-7 . ( 9 ) = -63<\/p>\n<p>Question 12.<br \/>\n4 \u2022 (-7)<br \/>\nAnswer:<br \/>\n4 . ( -7 ) = 4 \u00d7 ( -7 )<br \/>\n= -28<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n4. (-7 ) = +4 \u00d7 -7<br \/>\n= -28<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n4 . ( -7 ) = -28<\/p>\n<p>Question 13.<br \/>\n-24 \u00f7 (-6)<br \/>\nAnswer:<br \/>\n-24 \u00f7 ( -6 ) = 4<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00f7 &#8211; = +<br \/>\nB) + \u00f7 &#8211; = &#8211;<br \/>\nC) + \u00f7 + = +<br \/>\nD) &#8211; \u00f7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-24 \u00f7 ( -6 ) = + ( 24 \u00f7 6 )<br \/>\n= 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-24 \u00f7 ( -6 ) = 4<\/p>\n<p>Question 14.<br \/>\n-16 \u00f7 2<br \/>\nAnswer:<br \/>\n-16 \u00f7 2 = -8<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00f7 &#8211; = +<br \/>\nB) + \u00f7 &#8211; = &#8211;<br \/>\nC) + \u00f7 + = +<br \/>\nD) &#8211; \u00f7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-16 \u00f7 2 = -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-16 \u00f7 2 = -8<\/p>\n<p>Question 15.<br \/>\n12 \u00f7 (-3)<br \/>\nAnswer:<br \/>\n12 \u00f7 ( -3 ) = -4<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00f7 &#8211; = +<br \/>\nB) + \u00f7 &#8211; = &#8211;<br \/>\nC) + \u00f7 + = +<br \/>\nD) &#8211; \u00f7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n12 \u00f7 ( -3 )<br \/>\n= 12 \u00f7 -3<br \/>\n= -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n12 \u00f7 ( -3 ) = -4<\/p>\n<p>Question 16.<br \/>\n6 \u2022 8<br \/>\nAnswer:<br \/>\n6 . 8 = 6 \u00d7 8<br \/>\n= 48<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n6 . 8 = 6 \u00d7 8<br \/>\n= 48<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n6 . 8 = 48<\/p>\n<p>Question 17.<br \/>\n36 \u00f7 6<br \/>\nAnswer:<br \/>\n36 \u00f7 6 = 6<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00f7 &#8211; = +<br \/>\nB) + \u00f7 &#8211; = &#8211;<br \/>\nC) + \u00f7 + = +<br \/>\nD) &#8211; \u00f7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n36 \u00f7 6 = ( 30 + 6 ) \u00f7 6<br \/>\n= ( 30 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 5 + 1<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n36 \u00f7 6 = 6<\/p>\n<p>Question 18.<br \/>\n-3(-4)<br \/>\nAnswer:<br \/>\n-3 ( -4 ) = -3 \u00d7 -4<br \/>\n= -12<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nSo,<br \/>\n-3 ( -4 ) = -3 \u00d7 -4<br \/>\n= +12<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n-3 ( &#8211; 4 ) = 12<\/p>\n<p>Question 19.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nSummarize the rules for<br \/>\n(a) adding integers,<br \/>\n(b) subtracting integers,<br \/>\n(c) multiplying integers, and<br \/>\n(d) dividing integers.<br \/>\nGive an example of each.<br \/>\nAnswer:<br \/>\na) Adding integers:<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation i.e., Addition or subtraction follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nExample:<br \/>\nLet take the two numbers -2 and 3<br \/>\nSo,<br \/>\nThe addition of -2 and 3 is:<br \/>\n-2 + 3 = +1<br \/>\n= 1 ( Since the big number has a positive sign )<\/p>\n<p>b) Subtracting integers:<br \/>\nWe know that,<br \/>\nThe result of any mathematical operation i.e., Addition or subtraction follows the sign of the big number and if the two numbers have the same sign, then the result of that also operation also follows the same sign and if there is no sign before the number, then we can take that number as positive number i.e., +a<br \/>\nExample:<br \/>\nLet take the two numbers -3 and +8<br \/>\nSo,<br \/>\nThe subtraction of -3 and +8 is:<br \/>\n-3 &#8211; ( +8 ) = -3 &#8211; 8<br \/>\n= &#8211; ( 3 + 8 )<br \/>\n= -11 ( Since both the numbers have a negative sign )<\/p>\n<p>c) Multiplying integers:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00d7 &#8211; = +<br \/>\nB) + \u00d7 &#8211; = &#8211;<br \/>\nC) + \u00d7 + = +<br \/>\nD) &#8211; \u00d7 + = &#8211;<br \/>\nExample:<br \/>\nLet take the two numbers +8 and -3<br \/>\nSo,<br \/>\nThe multiplication of +8 and -3 is:<br \/>\n+8 ( -3 ) = 8 \u00d7 -3<br \/>\n= -24 ( Since + \u00d7 &#8211; = &#8211; )<\/p>\n<p>d) Dividing integers:<br \/>\nWe know that,<br \/>\nA) &#8211; \u00f7 &#8211; = +<br \/>\nB) + \u00f7 &#8211; = &#8211;<br \/>\nC) + \u00f7 + = +<br \/>\nD) &#8211; \u00f7 + = &#8211;<br \/>\nExample:<br \/>\nLet take the two numbers -12 and -2<br \/>\nSo,<br \/>\nThe division of -12 and -2 is:<br \/>\n-12 \u00f7 ( -2 ) = -12 \u00f7 -2<br \/>\n= ( -10 + -2 ) \u00f7 -2<br \/>\n= ( -10 \u00f7 -2 ) + ( -2 \u00f7 -2 )<br \/>\n= 5 + 1<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude all the rules for the four basic mathematical operations.<\/p>\n<h3><a id=\"Solving_Linear_Equations_Monitoring_Progress\"><\/a>Solving Linear Equations Monitoring Progress<\/h3>\n<p><b>Solve the problem and specify the units of measure.<\/b><\/p>\n<p>Question 1.<br \/>\nThe population of the United States was about 280 million in 2000 and about 310 million in 2010. What was the annual rate of change in population from 2000 to 2010?<br \/>\nAnswer:<br \/>\nThe annual rate of change in population from 2000 to 2010 is: 30 million<\/p>\n<p>Explanation:<br \/>\nIt is given that the population of the United States was about 280 million in 2000 and about 310 million in 2010.<br \/>\nSo,<br \/>\nThe annual rate of change in population from 2000 to 2010 = ( The population of United States in 2010 ) &#8211; ( The population of United States in 2000 )<br \/>\n= 310 &#8211; 280<br \/>\n= 30 million<br \/>\nHence, from the above,<br \/>\nWe can conclude that the annual rate of change in population from 2000 to 2010 is: 30 million<\/p>\n<p>Question 2.<br \/>\nYou drive 240 miles and use 8 gallons of gasoline. What was your car\u2019s gas mileage (in miles per gallon)?<br \/>\nAnswer:<br \/>\nYour car&#8217;s gas mileage ( in miles per gallon ) is: 30<\/p>\n<p>Explanation:<br \/>\nIt is given that you drive 240 miles and use 8 gallons of gasoline.<br \/>\nSo,<br \/>\nThe mileage of your car = ( The total number of miles driven by your car ) \u00f7 ( The number of gallons of gasoline used by your car )<br \/>\n= 240 \u00f7 8<br \/>\n= ( 160 + 80 ) \u00f7 8<br \/>\n= ( 160 \u00f7 8 ) + ( 80 \u00f7 8 )<br \/>\n= 20 + 10<br \/>\n= 30 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the mileage of your car is: 30 miles per gallon<\/p>\n<p>Question 3.<br \/>\nA bathtub is in the shape of a rectangular prism. Its dimensions are 5 feet by 3 feet by 18 inches. The bathtub is three-fourths full of water and drains at a rate of 1 cubic foot per minute. About how long does it take for all the water to drain?<br \/>\nAnswer:<br \/>\nThe total time taken for the water to drain is: 2,430 minutes<\/p>\n<p>Explanation:<br \/>\nIt is given that a bathtub is in the shape of a rectangular prism. Its dimensions are 5 feet by 3 feet by 18 inches. The bathtub is three-fourths full of water and drains at a rate of 1 cubic foot per minute.<br \/>\nSo,<br \/>\nThe volume of the rectangular prism = The dimensions of the rectangular prism<br \/>\n= 5 \u00d7 3 \u00d7 18 \u00d7 12<br \/>\n= 3,240 cubic feet<br \/>\nNow,<br \/>\nThe volume of the bathtub which is three-fourths full of water = \\(\\) {3}{4}[\\latex] \u00d7 3240<br \/>\n= 2,430 cubic feet<br \/>\nIt is also given that that the bathtub drains at a rate of 1 cubic foot per minute.<br \/>\nSo,<br \/>\nThe time taken to drain 2,430 cubic feet of water in minutes = 2,430 \u00d7 1<br \/>\n= 2,430 minutes<br \/>\nHence, from the above,<br \/>\nWe can conclude that the time taken for the water to drain from the bathtub at a rate of 1 cubic foot per minute is: 2,430 minutes<\/p>\n<h3><a id=\"Lesson_1.1_Solving_Simple_Equations\"><\/a>Lesson 1.1 Solving Simple Equations<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you use simple equations to solve real-life problems?<\/p>\n<p><b>Exploration 1<br \/>\nMeasuring Angles<\/b><\/p>\n<p><b>Work with a partner. <\/b>Use a protractor to measure the angles of each quadrilateral. Copy and complete the table to organize your results. (The notation m\u2220A denotes the measure of angle A.) How precise are your measurements?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1.jpg\" alt=\"\" width=\"579\" height=\"342\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1.jpg 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-300x177.jpg 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 2\" width=\"222\" height=\"231\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nMaking a Conjecture<\/b><\/p>\n<p><b>Work with a partner.<\/b> Use the completed table in Exploration 1 to write a conjecture about the sum of the angle measures of a quadrilateral. Draw three quadrilaterals that are different from those in Exploration 1 and use them to justify your conjecture.<br \/>\nAnswer:<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1.jpg\" alt=\"\" width=\"579\" height=\"342\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1.jpg 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-300x177.jpg 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><br \/>\nFrom\u00a0the above table,<br \/>\nWe can say that the sum of all the angle in any quadrilateral is: 360 degrees<br \/>\nSo,<br \/>\nFrom the above table,<br \/>\nThe angles in Quadrilateral a is: 60 degrees, 125 degrees, 120 degrees, and 55 degrees<br \/>\nWe know that,<br \/>\nThe quadrilateral will have n angles based on the shape.<br \/>\nThe shape which has more than 3 sides is called a Quadrilateral.<br \/>\nEx: Rectangle, Square, Pentagon, Hexagon, etc.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-1.jpg\" alt=\"\" width=\"581\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-1.jpg 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-1-300x107.jpg 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\nFrom the above quadrilaterals,<br \/>\nWe can say that all the sides in each quadrilateral are equal.<br \/>\nSo,<br \/>\nThe angles in each quadrilateral are also equal.<br \/>\nSo,<br \/>\nIn a rectangle, there are 4 sides<br \/>\nSo,<br \/>\nBy measuring, we can observe that each angle of a rectangle is: 90 degrees<br \/>\nHence,<br \/>\nThe sum of all angles in a rectangle = 90 + 90 + 90 + 90 = 360 degrees<br \/>\nIn a pentagon, there are 5 sides<br \/>\nBy measuring, we can observe that each rectangle of a pentagon<br \/>\nHence,<br \/>\nThe sum of all the angles in a pentagon = = 72+ 72 + 72 + 72 + 72 = 360 degrees<br \/>\nIn a Hexagon, there are 6 sides<br \/>\nSo,<br \/>\nBy measuring, we can observe that each angle of a hexagon is: 60 degrees<br \/>\nHence,<br \/>\nThe sum of all angle is a Hexagon = 60 + 60 + 60 + 60 + 60 + 60 = 360 degrees<br \/>\nHence, from the above-drawn quadrilaterals,<br \/>\nWe can conclude that our conjecture is proven.<\/p>\n<p><b>EXPLORATION 3<br \/>\nApplying Your Conjecture<\/b><\/p>\n<p><b>Work with a partner. <\/b>Use the conjecture you wrote in Exploration 2 to write an equation for each quadrilateral. Then solve the equation to find the value of x. Use a protractor to check the reasonableness of your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 3\" width=\"536\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-3.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-3-300x85.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 3\" width=\"536\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-3.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-3-300x85.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><br \/>\nFrom Exploration 2, the proven conjecture is:<br \/>\nThe sum of all angles in a quadrilateral is: 360 degrees<br \/>\nNow,<br \/>\nIn Quadrilateral a.,<br \/>\nBy using the above-proven conjecture,<br \/>\n85 + 80 + 100 + x = 360 degrees<br \/>\n265 + x = 360 degrees<br \/>\nx = 360 &#8211; 265<br \/>\n= 95 degrees<br \/>\nSo,<br \/>\nThe angle x is: 95 degrees<br \/>\nIn Quadrilateral b.,<br \/>\nBy using the above-proven conjecture,<br \/>\n72 + 78 + 60 + x = 360 degrees<br \/>\n210 + x = 360 degrees<br \/>\nx = 360 &#8211; 210<br \/>\n= 150 degrees<br \/>\nSo,<br \/>\nThe angle of x is: 150 degrees<br \/>\nIn Quadrilateral c.,<br \/>\nBy using the above-proven conjecture,<br \/>\n90 + 90\u00a0 +30 + x = 360 degrees<br \/>\n210 + x = 360 degrees<br \/>\nx = 360 &#8211; 210<br \/>\n= 150 degrees<br \/>\nSo,<br \/>\nThe angle of x is: 150 degrees<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow can you use simple equations to solve real-life problems?<\/p>\n<p>Question 5.<br \/>\nDraw your own quadrilateral and cut it out. Tear off the four corners of the quadrilateral and rearrange them to affirm the conjecture you wrote in Exploration 2. Explain how this affirms the conjecture.<br \/>\nAnswer:<br \/>\nYour Quadrilateral is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-2.jpg\" alt=\"\" width=\"390\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-2.jpg 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-2-300x155.jpg 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\nFrom the above Quadrilateral,<br \/>\nWe can observe that the tear-off corners of the quadrilateral are joined and it becomes the triangle.<br \/>\nSo,<br \/>\nIn the above Quadrilateral, there are two quadrilaterals.<br \/>\nWe know that,<br \/>\nThe sum of all angles in a triangle is: 180 degrees<br \/>\nSo,<br \/>\nThe sum of all angles in the two triangles = 180 + 180 = 360 degrees<br \/>\nThese two triangles form a quadrilateral.<br \/>\nSo,<br \/>\nThe sum of all angles in a quadrilateral is: 360 degrees<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can prove Exploration 2&#8217;s conjecture by your own example.<\/p>\n<p><b>1.1 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Justify each step. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\nn + 3 = -7<br \/>\nAnswer:<br \/>\nThe value of n is: -10<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nn + 3 = -7<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nn + 3 = -7<br \/>\nn = -7 &#8211; (+3 )<br \/>\nn = -7 &#8211; 3<br \/>\n= -10<br \/>\nHence from the above,<br \/>\nWe can conclude that the value of n is: -10<\/p>\n<p>Question 2.<br \/>\ng &#8211; \\(\\frac{1}{3}\\) = &#8211;\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nThe value of g is: &#8211;\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ng &#8211; \\(\\frac{1}{3}\\) = &#8211;\\(\\frac{2}{3}\\)<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\ng &#8211; \\(\\frac{1}{3}\\) = &#8211;\\(\\frac{2}{3}\\)<br \/>\ng = &#8211;\\(\\frac{2}{3}\\) + \\(\\frac{1}{3}\\)<br \/>\ng = \\(\\frac{-2 + 1}{3}\\)<br \/>\ng = \\(\\frac{-1}{3}\\)<br \/>\ng = &#8211;\\(\\frac{1}{3}\\)<br \/>\nHence, fromthe above,<br \/>\nWe can conclude that the value of g is: &#8211;\\(\\frac{1}{3}\\)<\/p>\n<p>Question 3.<br \/>\n-6.5 = p + 3.9<br \/>\nAnswer:<br \/>\nThe value of p is: -10.4<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-6.5 = p + 3.9<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-6.5 = p + 3.9<br \/>\np = -6.5 &#8211; 3.9<br \/>\n= &#8211; ( 6.5 + 3.9 )<br \/>\n= &#8211; 10.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of p is: -10.4<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Justify each step. Check your solution.<\/b><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{y}{3}\\) = -6<br \/>\nAnswer:<br \/>\nThe value of y is: -18<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{y}{3}\\) = -6<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n\\(\\frac{y}{3}\\) = -6<br \/>\n\\(\\frac{y}{1}\\) \u00d7 \\(\\frac{1}{3}\\) = -6<br \/>\n\\(\\frac{y}{1}\\) = -6 \u00f7 \\(\\frac{1}{3}\\)<br \/>\ny = -6 \u00d7 -3<br \/>\ny = -18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: -18<\/p>\n<p>Question 5.<br \/>\n9\u03c0 = \u03c0x<br \/>\nAnswer:<br \/>\nThe value of x is: 9<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n9\u03c0 = \u03c0x<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n9\u03c0 = \u03c0x<br \/>\n9 \u00d7 \u03c0 = \u03c0 \u00d7 x<br \/>\nx = ( 9 \u00d7 \u03c0 ) \u00f7 \u03c0<br \/>\nx = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 9<\/p>\n<p>Question 6.<br \/>\n0.05w = 1.4<br \/>\nAnswer:<br \/>\nThe value of w is: 28<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n0.05w = 1.4<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n0.05w = 1.4<br \/>\n0.05 \u00d7 w = 1.4<br \/>\n\\(\\frac{5}{100}\\) \u00d7 w = \\(\\frac{14}{10}\\)<br \/>\nw = \\(\\frac{14}{10}\\) \u00f7 \\(\\frac{5}{100}\\)<br \/>\nw = \\(\\frac{14}{10}\\) \u00d7 \\(\\frac{100}{5}\\)<br \/>\nw = \\(\\frac{14 \u00d7 100}{10 \u00d7 5}\\)<br \/>\nw = \\(\\frac{28}{1}\\)<br \/>\nw = 28<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: 28<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 7.<br \/>\nSuppose Usain Bolt ran 400 meters at the same average speed that he ran the 200 meters. How long would it take him to run 400 meters? Round your answer to the nearest hundredth of a second.<br \/>\nAnswer:<br \/>\nThe time it took for him to run 400 meters is: 0.50 seconds<\/p>\n<p>Explanation:<br \/>\nIt is given that Usain Bolt ran 400 meters at the same average speed that he ran the 200 meters.<br \/>\nWe know that,<br \/>\nSpeed = Distance \u00f7 Time<br \/>\nBut, it is given that the average speed is the same.<br \/>\nHence,<br \/>\nSpeed = Constant<br \/>\nSo,<br \/>\nSince speed is constant, distance is directly proportional to time.<br \/>\nSo,<br \/>\nThe time taken by Usain Bolt to run 400 meters = 200 \u00f7 400<br \/>\n= ( 2 \u00d7 100 ) \u00f7 ( 4 \u00d7 100 )<br \/>\n= 10 \u00f7 20<br \/>\n= 0.50 seconds ( 0.5 and 0.50 are the same values Only for the representation purpose, we will add &#8216;0&#8217; after 5 )<br \/>\nHence from the above,<br \/>\nWe can conclude that the time is taken by Usain Bolt to run 400 meters when rounded-off to the nearest hundredth is: 0.50 seconds<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 8.<br \/>\nYou thought the balance in your checking account was $68. When your bank statement arrives, you realize that you forgot to record a check. The bank statement lists your balance as $26. Write and solve an equation to find the amount of the check that you forgot to record.<br \/>\nAnswer:<br \/>\nThe amount of the check that you forgot to record is: $42<\/p>\n<p>Explanation:<br \/>\nIt is given that you thought the balance in your checking account was $68 and when your bank statement arrives, you realize that you forgot to record a check and the bank statement lists your balance as $26.<br \/>\nNow,<br \/>\nLet the amount you forgot to record be: x<br \/>\nSo,<br \/>\nThe total balance in your checking account = ( The listed balance ) + ( The amount that you forgot to record a check )<br \/>\n68 = 26 + x<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n68 = 26 + x<br \/>\nx = 68 &#8211; 26<br \/>\nx = $42<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount that forgot to record is: $42<\/p>\n<h3><a id=\"Solving_Simple_Equations_1.1_Exercises\"><\/a>Solving Simple Equations 1.1 Exercises<\/h3>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201314, solve the equation. Justify each step. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b> Which of the operations +, -, \u00d7, and \u00f7 are inverses of each other?<br \/>\nAnswer:<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n+ is inverse of &#8211;\u00a0 and vice-versa<br \/>\n\u00d7 is inverse of \u00f7 and vice-versa<\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY<\/b> Are the equations -2x = 10 and -5x = 25 equivalent? Explain.<br \/>\nAnswer:<br \/>\nThe equations -2x = 10 and -5x = 25 are equivalent<\/p>\n<p>Explanation:<br \/>\nThe given equations are:<br \/>\n-2x = 10 and -5x = 25<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nWe know that,<br \/>\nA) &#8211; \u00f7 &#8211; = +<br \/>\nB) + \u00f7 &#8211; = &#8211;<br \/>\nC) + \u00f7 + = +<br \/>\nD) &#8211; \u00f7 + = &#8211;<br \/>\nSo,<br \/>\nFrom -2x = 10,<br \/>\nx = 10 \u00f7 ( -2 )<br \/>\nx = -10 \u00f7 2<br \/>\nx = -5<br \/>\nFrom -5x = 25,<br \/>\nx = 25 \u00f7 ( -5 )<br \/>\nx = -25 \u00f7 5<br \/>\nx = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equations -2x = 10 and -5x = 25 are equivalent<\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b> Which property of equality would you use to solve the equation 14x = 56? Explain.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n14x = 56<br \/>\nSo,<br \/>\nIt can be re-written as<br \/>\n14 \u00d7 x = 56<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx = 56 \u00f7 14<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 4<\/p>\n<p>Question 4.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b> Which expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-501.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 501\" width=\"474\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-501.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-501-300x37.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\nAnswer:<br \/>\nThe equation C) does not belong to the other three<\/p>\n<p>Explanation:<br \/>\nLet the given equations be named as A), B), C), and D)<br \/>\nSo,<br \/>\nThe given equations are:<br \/>\nA) 8 = x \u00f7 2<br \/>\nB) 3 = x \u00f7 4<br \/>\nC) x &#8211; 6 = 5<br \/>\nD) x \u00f7 3 = 9<br \/>\nSo,<br \/>\nFrom the above equations,<br \/>\nThe equations A, B), and D) are dividing the numbers whereas equation C) subtracting the numbers<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\nThe equation C) does not belong to the other three.<\/p>\n<p>Question 5.<br \/>\nx + 5 = 8<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q5.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q5\" width=\"395\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q5.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q5-300x181.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 6.<br \/>\nm + 9 = 2<br \/>\nAnswer:<br \/>\nThe value of m is: -5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-3.jpg\" alt=\"\" width=\"581\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-3.jpg 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-3-300x187.jpg 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 7.<br \/>\ny &#8211; 4 = 3<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q7.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q7\" width=\"328\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q7.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q7-300x220.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 8.<br \/>\ns &#8211; 2 = 1<br \/>\nAnswer:<br \/>\nThe value of s is: 3<\/p>\n<p>Explanation;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-5.jpg\" alt=\"\" width=\"581\" height=\"288\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-5.jpg 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-5-300x149.jpg 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 9.<br \/>\nw + 3 = -4<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q9.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q9\" width=\"392\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q9.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q9-300x183.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 10.<br \/>\nn &#8211; 6 = -7<br \/>\nAnswer:<br \/>\nThe value of n is: -1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-6.jpg\" alt=\"\" width=\"581\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-6.jpg 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-6-300x199.jpg 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 11.<br \/>\n-14 = p &#8211; 11<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q11.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q11\" width=\"355\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q11.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q11-300x202.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>Question 12.<br \/>\n0 = 4 + q<br \/>\nAnswer:<br \/>\nThe value of q is: -4<\/p>\n<p>Explanation;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-8.jpg\" alt=\"\" width=\"540\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-8.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-8-300x198.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 13.<br \/>\nr + (-8) = 10<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q13.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q13\" width=\"475\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q13.png 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q13-300x171.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 14.<br \/>\nt &#8211; (-5) = 9<br \/>\nAnswer:<br \/>\nThe value of t is: 4<\/p>\n<p>Explanation;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-9.jpg\" alt=\"\" width=\"485\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-9.jpg 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-9-300x291.jpg 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 15.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA discounted amusement park ticket costs $12.95 less than the original price p. Write and solve an equation to find the original price.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 4\" width=\"199\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nThe equation for the original price is:<br \/>\np = x + $12.95<\/p>\n<p>Explanation:<br \/>\nIt is given that a discounted amusement park ticket costs $12.95 less than the original price p.<br \/>\nSo,<br \/>\nLet the discounted amusement park ticket be: x<br \/>\nThe given original price is: p<br \/>\nSo,<br \/>\nThe discounted amusement park ticket cost = p &#8211; $12.95<br \/>\nx = p &#8211; 12.95<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into &#8211; in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\np = x + $12.95<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation for the original price is:<br \/>\np = x + $12.95<\/p>\n<p>Question 16.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou and a friend are playing a board game. Your final score x is 12 points less than your friend\u2019s final score. Write and solve an equation to find your final score.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 5\" width=\"241\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nYour final score is:<br \/>\nx = ( The score of your friend ) &#8211; 12<\/p>\n<p>Explanation:<br \/>\nIt is given that you and a friend are playing a board game. Your final score x is 12 points less than your friend\u2019s final score.<br \/>\nSo,<br \/>\nThe scores table is shown below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 5\" width=\"241\" height=\"127\" \/><br \/>\nFrom the above table,<br \/>\nThe final score of your friend is: 195<br \/>\nLet the final score of yours is: x<br \/>\nSo,<br \/>\nx = ( The final score of your friend ) &#8211; 12<br \/>\n= 195 &#8211; 12<br \/>\n= 183 points<br \/>\nHence, from the above,<br \/>\nWe can conclude that the final score of yours is: 183 points<\/p>\n<p><b>USING TOOLS<br \/>\nThe sum of the angle measures of a quadrilateral is 360\u00b0. In Exercises 17\u201320, write and solve an equation to find the value of x. Use a protractor to check the reasonableness of your answer.<\/b><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 6\" width=\"159\" height=\"132\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q17.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q17\" width=\"300\" height=\"166\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 7\" width=\"148\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x is: 85 degrees<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nThe sum of angles in a quadrilateral is: 360 degrees<br \/>\nSo,<br \/>\n150 + 48 + 77 + x = 360<br \/>\n275 + x = 360<br \/>\nx = 360 &#8211; 275<br \/>\nx = 85 degrees<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 85 degrees<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 8\" width=\"143\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q19.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q19\" width=\"280\" height=\"170\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 9\" width=\"135\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x is: 100 degrees<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nThe sum of all angles in a quadrilateral is: 360 degrees<br \/>\nSo,<br \/>\n115 + 85 + 60 + x = 360<br \/>\n260 + x = 360<br \/>\nx = 360 &#8211; 260<br \/>\nx = 100 degrees<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 100 degrees<\/p>\n<p><b>In Exercises 21\u201330, solve the equation. Justify each step. Check your solution.<\/b><\/p>\n<p>Question 21.<br \/>\n5g = 20<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q21.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q21\" width=\"335\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q21.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q21-300x234.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Question 22.<br \/>\n4q = 52<br \/>\nAnswer:<br \/>\nThe value of g is: 13<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n4g = 52<br \/>\n4 \u00d7 g = 52<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\ng = 52 \u00f7 4<br \/>\n= ( 44 + 8 ) \u00f7 4<br \/>\n= ( 44 \u00f7 4 ) + ( 8 \u00f7 4 )<br \/>\n= 11 + 2<br \/>\n= 13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of g is: 13<\/p>\n<p>Question 23.<br \/>\np \u00f7 5 = 3<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q23.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q23\" width=\"446\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q23.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q23-300x174.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><\/p>\n<p>Question 24.<br \/>\ny \u00f7 7 = 1<br \/>\nAnswer:<br \/>\nThe value of y is: 7<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ny \u00f7 7 = 1<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\ny = 1 \u00d7 7<br \/>\ny = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 7<\/p>\n<p>Question 25.<br \/>\n-8r = 64<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q25.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q25\" width=\"367\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q25.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q25-300x211.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p>Question 26.<br \/>\nx \u00f7(-2) = 8<br \/>\nAnswer:<br \/>\nThe value of x is: -16<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx \u00f7 ( -2 ) = 8<br \/>\nWe know that,<br \/>\nA) \u2013 \u00f7 \u2013 = +<br \/>\nB) + \u00f7 \u2013 = \u2013<br \/>\nC) + \u00f7 + = +<br \/>\nD) \u2013 \u00f7 + = \u2013<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx \u00f7 ( -2 ) = 8<br \/>\nx = 8 \u00d7 ( -2 )<br \/>\nx = -16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -16<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{x}{6}\\) = 8<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q27.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q27\" width=\"418\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q27.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q27-300x219.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\frac{w}{-3}\\) = 6<br \/>\nAnswer:<br \/>\nThe value of w is: -18<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{w}{-3}\\) = 6<br \/>\nWe know that,<br \/>\nA) \u2013 \u00f7 \u2013 = +<br \/>\nB) + \u00f7 \u2013 = \u2013<br \/>\nC) + \u00f7 + = +<br \/>\nD) \u2013 \u00f7 + = \u2013<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n\\(\\frac{w}{-3}\\) = 6<br \/>\nw = 6 \u00d7 ( -3 )<br \/>\nw = -18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: -18<\/p>\n<p>Question 29.<br \/>\n-54 = 9s<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q29.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q29\" width=\"344\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q29.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q29-300x228.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><\/p>\n<p>Question 30.<br \/>\n-7 = \\(\\frac{t}{7}\\)<br \/>\nAnswer:<br \/>\nThe value of t is: -49<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-7 = \\(\\frac{t}{7}\\)<br \/>\nWe know that,<br \/>\nA) \u2013 \u00f7 \u2013 = +<br \/>\nB) + \u00f7 \u2013 = \u2013<br \/>\nC) + \u00f7 + = +<br \/>\nD) \u2013 \u00f7 + = \u2013<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-7 = \\(\\frac{t}{7}\\)<br \/>\nt = -7 \u00d7 7<br \/>\nt = -49<br \/>\nHence, from the above<br \/>\nWe can conclude that the value of t is: -49<\/p>\n<p><b>In Exercises 31\u2013 38, solve the equation. Check your solution.<\/b><\/p>\n<p>Question 31.<br \/>\n\\(\\frac{3}{2}\\) + t = \\(\\frac{1}{2}\\)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q31.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q31\" width=\"233\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q31.png 233w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q31-183x300.png 183w\" sizes=\"(max-width: 233px) 100vw, 233px\" \/><\/p>\n<p>Question 32.<br \/>\nb &#8211; \\(\\frac{3}{16}\\) = \\(\\frac{5}{16}\\)<br \/>\nAnswer:<br \/>\nThe value of b is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nb &#8211; \\(\\frac{3}{16}\\) = \\(\\frac{5}{16}\\)<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nb = \\(\\frac{5}{16}\\) + \\(\\frac{3}{16}\\)<br \/>\nSince the denominators of both the numerators are equal, add the numerators making the denominator common<br \/>\nSo,<br \/>\nb = \\(\\frac{5 + 3}{16}\\)<br \/>\nb = \\(\\frac{8}{16}\\)<br \/>\nb = \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of b is: \\(\\frac{1}{2}\\)<\/p>\n<p>Question 33.<br \/>\n\\(\\frac{3}{7}\\)m = 6<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q33.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q33\" width=\"231\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q33.png 231w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q33-220x300.png 220w\" sizes=\"(max-width: 231px) 100vw, 231px\" \/><\/p>\n<p>Question 34.<br \/>\n&#8211;\\(\\frac{2}{5}\\)y = 4<br \/>\nAnswer:<br \/>\nThe value of y is: 10<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n&#8211;\\(\\frac{2}{5}\\)y = 4<br \/>\nWe know that,<br \/>\nA) \u2013 \u00f7 \u2013 = +<br \/>\nB) + \u00f7 \u2013 = \u2013<br \/>\nC) + \u00f7 + = +<br \/>\nD) \u2013 \u00f7 + = \u2013<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n&#8211;\\(\\frac{2}{5}\\)y = 4<br \/>\n&#8211;\\(\\frac{2}{5}\\) \u00d7 y = 4<br \/>\ny = 4 \u00f7 &#8211;\\(\\frac{2}{5}\\)<br \/>\ny = 4 \u00d7 &#8211;\\(\\frac{5}{2}\\)<br \/>\ny = -4 \u00d7 &#8211;\\(\\frac{5}{2}\\)<br \/>\ny = &#8211;\\(\\frac{4}{1}\\) \u00d7 &#8211;\\(\\frac{5}{2}\\)<br \/>\ny = &#8211;\\(\\frac{4 \u00d7 5}{1 \u00d7 2}\\)<br \/>\ny = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 10<\/p>\n<p>Question 35.<br \/>\n5.2 = a &#8211; 0.4<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q35.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q35\" width=\"233\" height=\"249\" \/><\/p>\n<p>Question 36.<br \/>\nf + 3\u03c0 = 7\u03c0<br \/>\nAnswer:<br \/>\nThe value of f is: 4\u03c0<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nf + 3\u03c0 = 7\u03c0<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nf + 3\u03c0 = 7\u03c0<br \/>\nf = 7\u03c0 &#8211; 3\u03c0<br \/>\nf = \u03c0 ( 7 &#8211; 3 )<br \/>\nf = \u03c0 ( 4 )<br \/>\nf = 4\u03c0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of f is: 4\u03c0<\/p>\n<p>Question 37.<br \/>\n&#8211; 108\u03c0 = 6\u03c0j<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q37.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q37\" width=\"270\" height=\"283\" \/><\/p>\n<p>Question 38.<br \/>\nx \u00f7 (-2) = 1.4<br \/>\nAnswer:<br \/>\nThe value of x is: &#8211;\\(\\frac{14}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx \u00f7 ( -2 ) = 1.4<br \/>\nWe know that,<br \/>\nA) \u2013 \u00f7 \u2013 = +<br \/>\nB) + \u00f7 \u2013 = \u2013<br \/>\nC) + \u00f7 + = +<br \/>\nD) \u2013 \u00f7 + = \u2013<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx \u00f7 ( -2 ) = 1.4<br \/>\nx \u00f7 ( -2 ) = \\(\\frac{14}{10}\\)<br \/>\nx \u00f7 ( -2 ) = \\(\\frac{7}{5}\\)<br \/>\nx = \\(\\frac{7}{5}\\) \u00d7 ( -2 )<br \/>\nx = &#8211; \\(\\frac{7}{5}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\nx = &#8211;\\(\\frac{14}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: &#8211;\\(\\frac{14}{5}\\)<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 39 and 40, describe and correct the error in solving the equation.<\/b><\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 10\" width=\"286\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q39.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q39\" width=\"477\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q39.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q39-300x105.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 11\" width=\"295\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nA negative 3 should have been multiplied to each side.<br \/>\nWe know that,<br \/>\nA) \u2013 \u00d7 \u2013 = +<br \/>\nB) + \u00d7 \u2013 = \u2013<br \/>\nC) + \u00d7 + = +<br \/>\nD) \u2013 \u00d7 + = \u2013<br \/>\nSo,<br \/>\n-(\\(\\frac{m}{3}\\) ) =-4<br \/>\n-3\u00a0 ( \\(\\frac{m}{3}\\) ) = -4 ( -3 )<br \/>\n3 ( \\(\\frac{m}{3}\\) ) = -4 ( -3 )<br \/>\n3 ( \\(\\frac{m}{3}\\) ) = 12<br \/>\n\\(\\frac{m}{3}\\)\u00a0 \u00d7 \\(\\frac{3}{1}\\) = 12<br \/>\nm = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is: 12<\/p>\n<p>Question 41.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nA baker orders 162 eggs. Each carton contains 18 eggs. Which equation can you use to find the number x of cartons? Explain your reasoning and solve the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 12\" width=\"282\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q41.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q41\" width=\"534\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q41.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q41-300x152.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p><b>MODELING WITH MATHEMATICS<br \/>\nIn Exercises 42\u2013 44, write and solve an equation to answer the question.<\/b><\/p>\n<p>Question 42.<br \/>\nThe temperature at 5 P.M. is 20\u00b0F. The temperature at 10 P.M. is -5\u00b0F. How many degrees did the temperature fall?<br \/>\nAnswer:<br \/>\nThe fall in temperature is: 25 degrees Fahrenheit<\/p>\n<p>Explanation:<br \/>\nIt is given that the temperature at 5 P.M. is 20\u00b0F and the temperature at 10 P.M. is -5\u00b0F.<br \/>\nSo,<br \/>\nThe fall in temperature = ( The temperature at 5 P.M ) &#8211; ( The temperature at 10 P.M )<br \/>\nWe know that,<br \/>\nA) \u2013 \u00d7 \u2013 = +<br \/>\nB) + \u00d7 \u2013 = \u2013<br \/>\nC) + \u00d7 + = +<br \/>\nD) \u2013 \u00d7 + = \u2013<br \/>\nSo,<br \/>\nThe fall in temperature = 20 &#8211; ( -5 )<br \/>\n= 20 + 5<br \/>\n= 25 degrees Fahrenheit<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fall in temperature is: 25 degrees Fahrenheit<\/p>\n<p>Question 43.<br \/>\nThe length of an American flag is 1.9 times its width. What is the width of the flag?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 13\" width=\"161\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q43.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q43\" width=\"415\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q43.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q43-300x215.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p>Question 44.<br \/>\nThe balance of an investment account is $308 more than the balance 4 years ago. The current balance of the account is $4708. What was the balance 4 years ago?<br \/>\nAnswer:<br \/>\nThe balance 4 years ago is: $4,400<\/p>\n<p>Explanation:<br \/>\nIt is given that the balance of an investment account is $308 more than the balance 4 years ago. The current balance of the account is $4708.<br \/>\nSo,<br \/>\nThe current balance of the account = ( The balance of an investment account 4 years ago ) + $308<br \/>\nLet the balance of an investment account four years ago be x.<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n$4,708 = x + $308<br \/>\nx = 4,708 &#8211; 308<br \/>\nx = $4,400<br \/>\nHence, from the above,<br \/>\nWe can conclude that the balance of an investment account four years ago is: $4,400<\/p>\n<p>Question 45.<br \/>\n<b>REASONING<\/b><br \/>\nIdentify the property of equality that makes Equation 1 and Equation 2 equivalent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 14\" width=\"243\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q45.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q45\" width=\"440\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q45.png 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q45-300x64.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p><b>PROBLEM-SOLVING<br \/>\nQuestion 46.<\/b><br \/>\nTatami mats are used as a floor covering in Japan. One possible layout uses four identical rectangular mats and one square mat, as shown. The area of the square mat is half the area of one of the rectangular mats.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 15\" width=\"267\" height=\"145\" \/><br \/>\na. Write and solve an equation to find the area of one rectangular mat.<br \/>\nAnswer:<br \/>\nThe area of one rectangular mat is: 18 ft\u00b2<\/p>\n<p>Explanation:<br \/>\nIt is given that the tatami mats are used as a floor covering in Japan and for that, one layout of tatami mats requires the four identical rectangular mats and the one square mat<br \/>\nSo,<br \/>\nThe total area of the tatami mats = ( The area of the four rectangular mats ) + ( The area of the one square mat )<br \/>\nThe give tatami mat layout is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 15\" width=\"267\" height=\"145\" \/><br \/>\nFrom the layout,<br \/>\nWe can observe that<br \/>\nThe total area of the layout is: 81 ft\u00b2<br \/>\nSo,<br \/>\nThe total area of tatami mats = 81 ft\u00b2<br \/>\n( The area of the four rectangular mats ) + ( The area of the one square mat ) = 81 ft\u00b2<br \/>\nIt is also given that<br \/>\nThe area of a square mat is half of one of the rectangular mats<br \/>\nSo,<br \/>\nArea of the square mat = ( Area of the rectangular mat ) \u00f7 2<br \/>\nSo,<br \/>\n( The area of the four rectangular mats ) + \\(\\frac{Area of the rectangular mat}{2}\\)\u00a0 = 81 ft\u00b2<br \/>\n4 ( The area of the rectangular mat ) + \\(\\frac{Area of the rectangular mat}{2}\\)\u00a0 = 81 ft\u00b2<br \/>\n\\(\\frac{8}{2}\\) ( The area of the rectangular mat ) + \\(\\frac{1}{2}\\) ( The area of the rectangular mat ) = 81 ft\u00b2<br \/>\n( The area of the rectangular mat ) [ \\(\\frac{8}{2}\\) + \\(\\frac{1}{2}\\) ] = 81 ft\u00b2<br \/>\n\\(\\frac{9}{2}\\) ( The area of the rectangular mat ) = 81 ft\u00b2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nThe area of the rectangular mat = 81 \u00f7 \\(\\frac{9}{2}\\)<br \/>\n= 81 \u00d7 \\(\\frac{2}{9}\\)<br \/>\n= \\(\\frac{81}{1}\\) \u00d7 \\(\\frac{2}{9}\\)<br \/>\n= \\(\\frac{81 \u00d7 2}{9 \u00d7 1}\\)<br \/>\n= 18 ft\u00b2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of one rectangular mat is: 18 ft\u00b2<\/p>\n<p>b. The length of a rectangular mat is twice the width. Use Guess, Check, and Revise to find the dimensions of one rectangular mat.<br \/>\nAnswer:<br \/>\nThe dimensions of the rectangular mat are:<br \/>\nLength: 6 ft<br \/>\nWidth: 3 ft<\/p>\n<p>Explanation:<br \/>\nFrom the above problem,<br \/>\nThe area of the rectangular mat = 18 ft\u00b2<br \/>\nIt is given that the length of a rectangular mat is twice the width.<br \/>\nWe know that the area of the rectangle = ( Length ) \u00d7 ( Width )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nIt is also given that the length of a rectangular mat is twice the width<br \/>\nSo,<br \/>\nLength of a rectangular mat = 2 \u00d7 Width<br \/>\nNow,<br \/>\nThe area of the rectangular mat = Length \u00d7 Width<br \/>\n18 = 2 \u00d7 Width \u00d7 Width<br \/>\nWidth \u00d7 Width = 18 \u00f7 2<br \/>\nWidth \u00d7 Width = 9<br \/>\nFrom guessing,<br \/>\nWe can say that<br \/>\nWidth of the rectangular mat = 3 ft<br \/>\nNow,<br \/>\nThe length of the rectangular mat = 2 \u00d7 3<br \/>\n= 6 ft<br \/>\nHence, from the above,<br \/>\nWe can conclude that the dimensions of the rectangular mat are:<br \/>\nLength: 6 ft<br \/>\nWidth: 3 ft<\/p>\n<p>Question 47.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nYou spend $30.40 on 4 CDs. Each CD costs the same amount and is on sale for 80% of the original price.<br \/>\na. Write and solve an equation to find how much you spend on each CD.<br \/>\nb. The next day, the CDs are no longer on sale. You have $25. Will you be able to buy 3 more CDs? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-15.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 15.1\" width=\"152\" height=\"132\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q47.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q47\" width=\"557\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q47.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q47-300x184.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nAs c increases, does the value of x increase, decrease, or stay the same for each equation? Assume c is positive.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-16.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 16\" width=\"236\" height=\"164\" \/><\/p>\n<p>Answer:<br \/>\nLet assume the values of c be: 0,1,2,3<br \/>\nSo,<br \/>\nThe completed table by taking the values of c is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-10.jpg\" alt=\"\" width=\"234\" height=\"173\" \/><br \/>\nBy taking the values of c positive i.e., 0, 1, 2, 3<br \/>\nWe can observe that as the value of c increases, the values of x sometimes increasing and sometimes stays the same but not decreasing.<\/p>\n<p>Question 49.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nUse the values -2, 5, 9, and 10 to complete each statement about the equation ax = b &#8211; 5.<br \/>\na. When a = ___ and b = ___, x is a positive integer.<br \/>\nb. When a = ___ and b = ___, x is a negative integer.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51\" width=\"550\" height=\"288\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51-300x157.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe circle graph shows the percents of different animals sold at a local pet store in 1 year.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 17\" width=\"255\" height=\"208\" \/><br \/>\na. What percent is represented by the entire circle?<br \/>\nAnswer:<br \/>\nThe percent represented by the entire circle is = 69 % + x %<\/p>\n<p>Explanation:<br \/>\nIt is given that the circle represents the percent of different animals sold at a local store for 1 year<br \/>\nNow,<br \/>\nThe given circle is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 17\" width=\"255\" height=\"208\" \/><br \/>\nWe know that,<br \/>\nIn terms of percentages, any circle represents 100%<br \/>\nSo,<br \/>\nThe equation representing the circle is:<br \/>\nThe percentage of different animals in the circle = 48 + 5 + 9 + 7 +x<br \/>\nThe percentage of different animals in the circle= 69% + x%<\/p>\n<p>b. How does the equation 7 + 9 + 5 + 48 + x = 100 relate to the circle graph? How can you use this equation to find the percent of cats sold?<br \/>\nAnswer:<br \/>\nThe percent of cats sold is: 31%<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nIn terms of percentages, any circle represents 100%<br \/>\nSo,<br \/>\nThe total percent of animals = The percent of animals that are represented by the circle<br \/>\n100% = 69% + x%<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx% = 100% &#8211; 69%<br \/>\nx% = 31%<br \/>\nHence, from the above,<br \/>\nWe can conclude that the percent of cats is: 31%<\/p>\n<p>Question 51.<br \/>\n<b>REASONING<\/b><br \/>\nOne-sixth of the girls and two-sevenths of the boys in a school marching band are in the percussion section. The percussion section has 6 girls and 10 boys. How many students are in the marching band? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51-1.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51\" width=\"550\" height=\"288\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51-1.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q51-1-300x157.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nWrite a real-life problem that can be modeled by an equation equivalent to the equation 5x = 30. Then solve the equation and write the answer in the context of your real-life problem.<\/p>\n<p>Answer:<br \/>\nLet suppose there is some number of boys. The number of girls is five times of the boys and the total number of girls is 30. Find the number of boys?<br \/>\nAns:<br \/>\nLet,<br \/>\nThe number of boys is x.<br \/>\nIt is given that the number of girls is five times of boys.<br \/>\nSo,<br \/>\nThe number of girls = 5x<br \/>\nIt is also given that<br \/>\nThe number of girls = 30<br \/>\nSo,<br \/>\n5x = 30<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5 \u00d7 x = 30<br \/>\nx = 30 \u00f7 5<br \/>\nx = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of boys is: 6<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 53\u201356, find the height h or the area of the base B of the solid.<\/b><\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-18.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 18\" width=\"127\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q53.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q53\" width=\"523\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q53.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q53-300x115.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 19\" width=\"164\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the cuboid is: 9 cm<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 19\" width=\"164\" height=\"146\" \/><br \/>\nWe know that,<br \/>\nThe volume of a cuboid = L \u00d7 B \u00d7 H<br \/>\nWe know that,<br \/>\nThe cuboid is made from a rectangle<br \/>\nWe know that,<br \/>\nThe area of a rectangle = L \u00d7 H<br \/>\nSo,<br \/>\nThe volume of a cuboid = A \u00d7 B<br \/>\nFrom the above figure,<br \/>\nThe given volume is: 1323 cm\u00b3<br \/>\nThe given Area is: 147 cm\u00b2<br \/>\nSo,<br \/>\n1323 = 147 \u00d7 H<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nH = 1323 \u00f7 147<br \/>\nH = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the height of the cuboid is: 9 cm<\/p>\n<p>Question 55.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-20.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 20\" width=\"130\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q55.png\" alt=\"\" width=\"486\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q55.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q55-300x150.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 21\" width=\"178\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the prism is: \\(\\frac{5}{6}\\) ft<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 21\" width=\"178\" height=\"141\" \/><br \/>\nWe know that,<br \/>\nThe volume of the prism = \u00a0Area \u00d7 Height<br \/>\nFrom the above figure,<br \/>\nThe volume of the prism = 35 ft\u00b3<br \/>\nThe area of the prism = 30 ft\u00b2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n35 = 30 \u00d7 H<br \/>\nH = 35 \u00f7 30<br \/>\nH = \\(\\frac{5}{6}\\) ft<br \/>\nHence, from the above,<br \/>\nWe can conclude that the height of the prism is: \\(\\frac{5}{6}\\) ft<\/p>\n<p>Question 57.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nIn baseball, a player\u2019s batting average is calculated by dividing the number of hits by the number of at-bats. The table shows Player A\u2019s batting average and the number of at-bats for three regular seasons.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-22.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 22\" width=\"300\" height=\"121\" \/><br \/>\na. How many hits did Player A have in the 2011 regular season? Round your answer to the nearest whole number.<br \/>\nb. Player B had 33 fewer hits in the 2011 season than Player A but had a greater batting average. Your friend concludes that Player B had more at-bats in the 2011 season than Player A. Is your friend correct? Explain. Maintaining<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q57.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q57\" width=\"557\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q57.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q57-300x165.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Use the Distributive Property to simplify the expression.<\/b><\/p>\n<p>Question 58.<br \/>\n8(y + 3)<br \/>\nAnswer:<br \/>\n8 ( y + 3 ) = 8y + 24<\/p>\n<p>Explanation:<br \/>\nThe given expression is: 8 ( y + 3 )<br \/>\nWe know that,<br \/>\nBy using the Distributive Property,<br \/>\na ( b + c ) = ( a \u00d7 b ) + ( a \u00d7 c )<br \/>\nSo,<br \/>\nBy using the above Property,<br \/>\n8 ( y + 3 ) = ( 8 \u00d7 y ) + ( 8 \u00d7 3 )<br \/>\n= 8y + 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n8 ( y + 3 ) = 8y + 24<\/p>\n<p>Question 59.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 23\" width=\"91\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q59.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q59\" width=\"363\" height=\"288\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q59.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q59-300x238.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 60.<br \/>\n5(m + 3 + n)<br \/>\nAnswer:<br \/>\n5 ( m + 3 + n ) = 5m + 5n + 15<\/p>\n<p>Explanation:<br \/>\nThe given expression is: 5 ( m + 3 + n )<br \/>\nBy using the Distributive Property,<br \/>\na ( b + c ) = ( a \u00d7 b ) + ( a \u00d7 c )<br \/>\nSo,<br \/>\nBy using the above Property,<br \/>\n5 ( m + 3 + n ) = ( 5 \u00d7 m ) + ( 5 \u00d7 3 ) + ( 5 \u00d7 n )<br \/>\n= 5m + 15 + 5n<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\n5 ( m + 3 + n ) = 5m + 15 + 5n<\/p>\n<p>Question 61.<br \/>\n4(2p + 4q + 6)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q61.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q61\" width=\"396\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q61.png 396w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q61-300x51.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p><b>Copy and complete the statement. Round to the nearest hundredth, if necessary.<\/b><\/p>\n<p>Question 62.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-24.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 24\" width=\"102\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\nThe missing number is: \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nLet the missing number be: x<br \/>\nSo,<br \/>\nThe given equation is:<br \/>\n\\(\\frac{5L}{min}\\) = \\(\\frac{x L}{h}\\)<br \/>\nWe know that,<br \/>\n1 hour = 60 minutes<br \/>\nSo,<br \/>\n1 min = \\(\\frac{1}{60}\\) hour<br \/>\nSo,<br \/>\n\\(\\frac{5 L}{min}\\) = \\(\\frac{5 L \u00d7 1}{60h}\\)<br \/>\n\\(\\frac{5 L}{min}\\) = \\(\\frac{1 L }{12h}\\)<br \/>\nSo,<br \/>\nx = \\(\\frac{1}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\nThe missing number is: \\(\\frac{1}{12}\\)<\/p>\n<p>Question 63.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 25\" width=\"117\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q63.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q63\" width=\"442\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q63.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q63-300x39.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 64.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-26.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 26\" width=\"111\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\nThe missing number is: \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nLet the missing number be: x<br \/>\nSo,<br \/>\nThe given equation is:<br \/>\n\\(\\frac{7 gal}{min}\\) = \\(\\frac{x qin}{sec}\\)<br \/>\nWe know that,<br \/>\n1 min = 60 seconds<br \/>\n1 quintal = 100 kg<br \/>\n1 gallon = 3.78 kg = 4 kg<br \/>\nSo,<br \/>\n1 gallon = 0.04 quintal<br \/>\n1 sec = \\(\\frac{1}{60}\\) min<br \/>\nSo,<br \/>\n\\(\\frac{7 gal}{min}\\) = \\(\\frac{x qin \u00d7 1}{60min}\\)<br \/>\n\\(\\frac{7 gal}{min}\\) = \\(\\frac{1 L }{12h}\\)<br \/>\nSo,<br \/>\nx = \\(\\frac{1}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\nThe missing number is: \\(\\frac{1}{12}\\)<\/p>\n<p>Question 65.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 27\" width=\"112\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q65.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q65\" width=\"465\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q65.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.1-Q65-300x37.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<h3><a id=\"Lesson_1.2_Solving_Multi-step_Equations\"><\/a>Lesson 1.2 Solving Multi-step Equations<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p><b>How can you use multi-step equations to solve real-life problems?<\/b><\/p>\n<p><b>EXPLORATION 1<br \/>\nSolving for the Angle Measures of a Polygon<\/b><\/p>\n<p><b>Work with a partner.<\/b> The sum S of the angle measures of a polygon with n sides can be found using the formula S = 180(n &#8211; 2). Write and solve an equation to find each value of x. Justify the steps in your solution. Then find the angle measures of each polygon. How can you check the reasonableness of your answers?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 27.1\" width=\"770\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-27.1.png 770w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-27.1-300x150.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-27.1-768x384.png 768w\" sizes=\"(max-width: 770px) 100vw, 770px\" \/><br \/>\nAnswer:<br \/>\nThe given polygons are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-11.jpg\" alt=\"\" width=\"556\" height=\"382\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-11.jpg 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-11-300x206.jpg 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\nIt is given that,<br \/>\nThe sum S of the angle measures of a polygon with n sides can be found using the formula S = 180(n &#8211; 2).<br \/>\na)<br \/>\nThe number of sides (n ) = 3<br \/>\nSo,<br \/>\nThe sum of angles ( S ) = 180 ( n &#8211; 2 )<br \/>\n= 180 ( 3 &#8211; 2 )<br \/>\n= 180 ( 1 )<br \/>\n= 180<br \/>\nNow,<br \/>\nThe given sides of a polygon are: 30, 9x, (30 + x )<br \/>\nSo,<br \/>\n30 + 9x + 30 + x = 180<br \/>\n60 + 10x = 180<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n10x = 180 &#8211; 60<br \/>\n10x = 120<br \/>\nx = 120 \u00f7 10<br \/>\nx = 12<br \/>\nHence, from the above,<br \/>\nThe angle measures of the given polygon are:<br \/>\n30, 9 \u00d7 12, 30 + 12<br \/>\n= 30, 108, 45 degrees<br \/>\nb)<br \/>\nThe number of sides (n ) = 3<br \/>\nSo,<br \/>\nThe sum of angles ( S ) = 180 ( n &#8211; 2 )<br \/>\n= 180 ( 3 &#8211; 2 )<br \/>\n= 180 ( 1 )<br \/>\n= 180<br \/>\nNow,<br \/>\nThe given sides of a polygon are: 30, 9x, (30 + x )<br \/>\nSo,<br \/>\n50 + x + 10 + 20 + x = 180<br \/>\n80 + 2x = 180<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2x = 180 &#8211; 80<br \/>\n2x = 100<br \/>\nx = 100 \u00f7 2<br \/>\nx = 50<br \/>\nHence, from the above,<br \/>\nThe angle measures of the given polygon are:<br \/>\n50, 50 + 10, 50 + 20<br \/>\n= 50, 60, 70 degrees<br \/>\nc)<br \/>\nThe number of sides (n ) = 4<br \/>\nSo,<br \/>\nThe sum of angles ( S ) = 180 ( n &#8211; 2 )<br \/>\n= 180 ( 4 &#8211; 2 )<br \/>\n= 180 ( 2 )<br \/>\n= 360<br \/>\nNow,<br \/>\nThe given sides of a polygon are: 50, x, ( 2x + 20), ( 2x + 30 )<br \/>\nSo,<br \/>\n50 + x + 2x + 20 + 2x + 30 = 360<br \/>\n100 + 5x = 360<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5x = 360 &#8211; 100<br \/>\n5x = 260<br \/>\nx = 260 \u00f7 5<br \/>\nx = 52<br \/>\nHence, from the above,<br \/>\nThe angle measures of the given polygon are:<br \/>\n50,52, 2 (52) + 20, 2(52) + 30<br \/>\n= 50, 52, 124, 134 degrees<br \/>\nd)<br \/>\nThe number of sides (n ) = 4<br \/>\nSo,<br \/>\nThe sum of angles ( S ) = 180 ( n &#8211; 2 )<br \/>\n= 180 ( 4 &#8211; 2 )<br \/>\n= 180 ( 2 )<br \/>\n= 360<br \/>\nNow,<br \/>\nThe given sides of a polygon are: x, x + 42, x + 35, x &#8211; 17<br \/>\nSo,<br \/>\nx + x + 42 + x + 35 + x &#8211; 17 = 360<br \/>\n60 + 4x = 360<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4x = 360 &#8211; 60<br \/>\n4x = 300<br \/>\nx = 300 \u00f7 4<br \/>\nx = 75<br \/>\nHence, from the above,<br \/>\nThe angle measures of the given polygon are:<br \/>\n75,\u00a0 75 + 42,\u00a0 75 + 35 , 75 &#8211; 17<br \/>\n= 75, 117, 110, 58 degrees<br \/>\ne)<br \/>\nThe number of sides (n ) = 5<br \/>\nSo,<br \/>\nThe sum of angles ( S ) = 180 ( n &#8211; 2 )<br \/>\n= 180 ( 5 &#8211; 2 )<br \/>\n= 180 ( 3 )<br \/>\n= 540<br \/>\nNow,<br \/>\nThe given sides of a polygon are: (4x + 15), (5x + 10), (8x + 8), (3x + 5), (5x + 2)<br \/>\nSo,<br \/>\n(4x + 15)+ (5x + 10)+ (8x + 8)+ (3x + 5)+ (5x + 2) = 540<br \/>\n40 + 25x = 540<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n25x = 540 &#8211; 40<br \/>\n25x = 500<br \/>\nx = 500 \u00f7 25<br \/>\nx = 20<br \/>\nHence, from the above,<br \/>\nThe angle measures of the given polygon are:<br \/>\n(4. 20 + 15)+ (5. 20 + 10)+ (8.20 + 8)+ (3. 20 + 5)+ (5. 20 + 2)<br \/>\n= 95, 110, 168, 65, 102 degrees<br \/>\nf)<br \/>\nThe number of sides (n ) = 5<br \/>\nSo,<br \/>\nThe sum of angles ( S ) = 180 ( n &#8211; 2 )<br \/>\n= 180 ( 5 &#8211; 2 )<br \/>\n= 180 ( 3 )<br \/>\n= 540<br \/>\nNow,<br \/>\nThe given sides of a polygon are: (2x + 25), (3x + 16), (2x + 8), (4x &#8211; 18), (3x &#8211; 7)<br \/>\nSo,<br \/>\n(2x + 25) + (3x + 16) + (2x + 8) + (4x &#8211; 18) + (3x &#8211; 7) = 540<br \/>\n24 + 14x = 540<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n14x = 540 &#8211; 24<br \/>\n14x = 516<br \/>\nx = 540 \u00f7 14<br \/>\nx = 38.5<br \/>\nx = 39<br \/>\nHence, from the above,<br \/>\nThe angle measures of the given polygon are:<br \/>\n(2. 39 + 25), (3.39 + 16), (2.39 + 8), (4.39 &#8211; 18), (3.39 &#8211; 7)<br \/>\n= 103, 133, 86, 138, 110 degrees<\/p>\n<p><b>EXPLORATION 2<br \/>\nWork with a partner.<\/b><br \/>\na. Draw an irregular polygon.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-12.jpg\" alt=\"\" width=\"390\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-12.jpg 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-12-300x168.jpg 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\nb. Measure the angles of the polygon. Record the measurements on a separate sheet of paper.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-13.jpg\" alt=\"\" width=\"390\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-13.jpg 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-13-300x168.jpg 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\nc. Choose a value for x. Then, using this value, work backward to assign a variable expression to each angle measure, as in Exploration 1.<br \/>\nd. Trade polygons with your partner.<br \/>\ne. Solve an equation to find the angle measures of the polygon your partner drew. Do your answers seem reasonable? Explain.<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you use multi-step equations to solve real-life problems?<\/p>\n<p>Question 4.<br \/>\nIn Exploration 1, you were given the formula for the sum S of the angle measures of a polygon with n sides. Explain why this formula works.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe sum of the angles in a triangle is: 180 degrees<br \/>\nThe triangle is also a quadrilateral<br \/>\nSo,<br \/>\nA quadrilateral can be formed by the minimum of the three lines<br \/>\nSo,<br \/>\nThe minimum sum of all the angles in a quadrilateral is: 180 degrees<br \/>\nNow,<br \/>\nLet suppose we form a quadrilateral with 4 sides.<br \/>\nSo,<br \/>\nThe sum of all the angles in a quadrilateral = 360 degrees = 180 degrees \u00d7 2<br \/>\n= 180 degrees ( 4 sides -2 )<br \/>\nLet suppose we form a quadrilateral with 5 sides<br \/>\nSo,<br \/>\nThe sum of all the angles in a quadrilateral = 540 degrees = 180 degrees \u00d7 3<br \/>\n= 180 degrees ( 5 -2 )<br \/>\nHence, in general,<br \/>\nWe can conclude that the sum of all the angles with n sides in a quadrilateral = 180 degrees ( n-2 )<\/p>\n<p>Question 5.<br \/>\nThe sum of the angle measures of a polygon is 1080\u00ba. How many sides does the polygon have? Explain how you found your answer.<br \/>\nAnswer:<br \/>\nThe number of sides the polygon with 1080\u00b0 have: 6<\/p>\n<p>Explanation:<br \/>\nIt is given that the sum of all angle measures of a polygon is: 1080\u00b0<br \/>\nWe know that,<br \/>\nThe sum of angle measures with n sides in a polygon = 180\u00b0 ( n &#8211; 2 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n1080\u00b0 =180\u00b0 ( n &#8211; 2 )<br \/>\nn &#8211; 2 = 1080 \u00f7 180<br \/>\nn &#8211; 2 = 6<br \/>\nn = 6 + 2<br \/>\nn = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of sides of the polygon with sum of the angles 1080\u00b0 is: 6<\/p>\n<p><b>1.2 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\n-2n + 3 = 9<br \/>\nAnswer:<br \/>\nThe value of n is: -3<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-2n + 3 = 9<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-2n + 3 = 9<br \/>\n-2n = 9 \u2013 (+3 )<br \/>\nn = 6 \u00f7 ( -2 )<br \/>\n= -3<br \/>\nHence from the above,<br \/>\nWe can conclude that the value of n is: -3<\/p>\n<p>Question 2.<br \/>\n-21 = \\(\\frac{1}{2}\\) &#8211; 11<\/p>\n<p>Question 3.<br \/>\n-2x &#8211; 10x + 12 = 18<br \/>\nAnswer:<br \/>\nThe value of x is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-2x &#8211; 10x + 12 = 18<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-( 2x + 10x ) = 18 &#8211; 12<br \/>\n-12x = 6<br \/>\nx = 6 \u00f7 ( -12 )<br \/>\nx = &#8211;\\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 4.<br \/>\n3(x + 1) + 6 = -9<br \/>\nAnswer:<br \/>\nThe value of x is: -6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3 ( x + 1 ) + 6 = -9<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n3 ( x + 1 ) = -9 &#8211; (+6 )<br \/>\nBy using the Distributive property,<br \/>\n3 ( x + 1 ) = 3x + 3<br \/>\nSo,<br \/>\n3x + 3 = -15<br \/>\n3x = -15 &#8211; ( +3 )<br \/>\n3x = -18<br \/>\nx = -18 \u00f7 3<br \/>\nx = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -6<\/p>\n<p>Question 5.<br \/>\n15 = 5 + 4(2d &#8211; 3)<br \/>\nAnswer:<br \/>\nThe value of d is:\\(\\frac{11}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n15 = 5 + 4 ( 2d &#8211; 3 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\n4 ( 2d &#8211; 3 ) = 15 -5<br \/>\n4 ( 2d &#8211; 3 ) = 10<br \/>\nBy using the Distributive property,<br \/>\n4 ( 2d &#8211; 3 ) = 4 (2d ) -4 (3 )<br \/>\n= 8d &#8211; 12<br \/>\nSo,<br \/>\n8d &#8211; 12 = 10<br \/>\n8d = 10 + 12<br \/>\n8d = 22<br \/>\nd = 22 \u00f7 8<br \/>\nd = \\(\\frac{11}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of d is: \\(\\frac{11}{4}\\)<\/p>\n<p>Question 6.<br \/>\n13 = -2(y &#8211; 4) + 3y<br \/>\nAnswer:<br \/>\nThe value of y is: 5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n13 = -2 ( y &#8211; 4 ) + 3y<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nBy using the Distributive Property,<br \/>\n-2 ( y &#8211; 4 ) = -2y + 8<br \/>\nSo,<br \/>\n13 = -2y + 8 + 3y<br \/>\n13 = y + 8<br \/>\ny = 13 &#8211; 8<br \/>\ny = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 5<\/p>\n<p>Question 7.<br \/>\n2x(5 &#8211; 3) &#8211; 3x = 5<br \/>\nAnswer:<br \/>\nThe value of x is: 5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2x ( 5 &#8211; 3 ) &#8211; 3x = 5<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2x ( 2 ) &#8211; 3x = 5<br \/>\n4x &#8211; 3x = 5<br \/>\nx = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 5<\/p>\n<p>Question 8.<br \/>\n-4(2m + 5) &#8211; 3m = 35<br \/>\nAnswer:<br \/>\nThe value of m is: -5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-4 ( 2m + 5 ) &#8211; 3m = 35<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nNow,<br \/>\nBy using the Distributive Property,<br \/>\n-4 ( 2m + 5 ) = -4 (2m ) + 5 ( -4 )<br \/>\n= -8m -20<br \/>\nSo,<br \/>\n-8m -20 -3m = 35<br \/>\n-11m &#8211; 20 = 35<br \/>\n-11m = 35 + 20<br \/>\n-11m = 55<br \/>\nm = 55 \u00f7 ( -11 )<br \/>\nm = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is: -5<\/p>\n<p>Question 9.<br \/>\n5(3 &#8211; x) + 2(3 &#8211; x) = 14<br \/>\nAnswer:<br \/>\nThe value of x is: 1<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n5 ( 3 &#8211; x ) + 2 ( 3 &#8211; x ) = 14<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nNow,<br \/>\nBy using the Distributive property,<br \/>\n5 ( 3 &#8211; x ) = 5 (3 ) -5 (x)<br \/>\n= 15 &#8211; 5x<br \/>\n2 ( 3 &#8211; x ) = 2 (3) &#8211; 2 ( x)<br \/>\n= 6 &#8211; 2x<br \/>\nSo,<br \/>\n15 &#8211; 5x + 6 &#8211; 2x = 14<br \/>\n21 &#8211; 7x = 14<br \/>\n7x = 21 &#8211; 14<br \/>\n7x = 7<br \/>\nx = 7 \u00f7 7<br \/>\nx = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 1<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 10.<br \/>\nThe formula d = \\(\\frac{1}{2}\\)n + 26 relates the nozzle pressure n (in pounds per square inch) of a fire hose and the maximum horizontal distance the water reaches d (in feet). How much pressure is needed to reach a fire 50 feet away?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-28.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 28\" width=\"345\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-28.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-28-300x113.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nAnswer:<br \/>\nThe pressure needed to reach a fire 50 feet away (n ) is: 48 pounds per square inch<\/p>\n<p>Explanation:<br \/>\nIt is given that the formula<br \/>\nd = \\(\\frac{1}{2}\\)n + 26<br \/>\nrelates the nozzle pressure n (in pounds per square inch) of a fire hose and the maximum horizontal distance the water reaches d (in feet).<br \/>\nSo,<br \/>\nThe given equation is:<br \/>\nd = \\(\\frac{1}{2}\\)n + 26<br \/>\nWhere,<br \/>\nd is the maximum horizontal distance<br \/>\nn is the pressure<br \/>\nIt is also given that the maximum horizontal distance is: 50 feet<br \/>\nSo,<br \/>\n50 = \\(\\frac{1}{2}\\)n + 26<br \/>\n\\(\\frac{1}{2}\\)n = 50 &#8211; 26<br \/>\n\\(\\frac{1}{2}\\)n = 24<br \/>\n\\(\\frac{1}{2}\\) \u00d7 n = 24<br \/>\nn = 24 \u00d7 2<br \/>\nn = 48 pounds per square inch<br \/>\nHence, from the above<br \/>\nWe can conclude that the pressure needed to reach 50 feet away is: 48 pounds per square inch<\/p>\n<p>Question 11.<br \/>\n<b>Monitoring Progress<\/b><br \/>\nYou have 96 feet of fencing to enclose a rectangular pen for your dog. To provide sufficient running space for your dog to exercise, the pen should be three times as long as it is wide. Find the dimensions of the pen.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-29.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 29\" width=\"136\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nThe dimensions of the pen are:<br \/>\nlength of the pen: 12 feet<br \/>\nWidth of the pen: 36 feet<\/p>\n<p>Explanation;<br \/>\nIt is given that you\u00a0 have 96 feet of fencing to enclose a rectangular pen for your dog. To provide sufficient running space for your dog to exercise, the pen should be three times as long as it is wide.<br \/>\nSo,<br \/>\nThe perimeter of the rectangular pen is: 96 feet<br \/>\nWe know that,<br \/>\nThe perimeter of the rectangle = 2 (Length + Width )<br \/>\nIt is also given that the pen is three times as long as it is wide<br \/>\nSo,<br \/>\nWidth = 3 \u00d7 Length<br \/>\nSo,<br \/>\nThe perimeter of the rectangular pen =2 (\u00a0 Length + (\u00a03 \u00d7 Length ) )<br \/>\n96 = 2 ( 4 \u00d7 Length )<br \/>\n4 \u00d7 Length = 96 \u00f7 2<br \/>\n4 \u00d7 Length = 48<br \/>\nLength = 48 \u00f7 4<br \/>\nLength = 12 feet<br \/>\nSo,<br \/>\nWidth = 3 \u00d7 Length<br \/>\n= 3 \u00d7 12 = 36 feet<br \/>\nhence, from the above,<br \/>\nWe can conclude that<br \/>\nThe dimensions of the rectangular pen are:<br \/>\nLength of the pen is: 12 feet<br \/>\nWidth of the pen is: 36 feet<\/p>\n<h3><a id=\"Solving_Multi-step_Equations_1.2_Exercises\"><\/a>Solving Multi-step Equations 1.2 Exercises<\/h3>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u221214, solve the equation. Check your solution.<\/b><\/p>\n<p><b>Vocabulary and Core ConceptCheck<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> To solve the equation 2x + 3x = 20, first combine 2x and 3x because they are _________.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n2x + 3x = 20<br \/>\nAs 2x and 3x are combined by the symbol &#8220;+&#8221;, add 2x and 3x<br \/>\nSo,<br \/>\n2x + 3x = 5x<br \/>\nSo,<br \/>\n5x = 20<br \/>\nx = 20 \u00f7 4<br \/>\nx = 5<\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b> Describe two ways to solve the equation 2(4x &#8211; 11) = 10.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n2 (4x &#8211; 11) = 10<br \/>\nWay-1:<br \/>\n2 \u00d7 (4x &#8211; 11) = 10<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4x &#8211; 11 = 10 \u00f7 2<br \/>\n4x &#8211; 11 = 5<br \/>\n4x = 5 + 11<br \/>\n4x = 16<br \/>\nx = 16 \u00f7 4<br \/>\nx = 4<br \/>\nHence,<br \/>\nThe value of x is: 4<\/p>\n<p>Way-2:<br \/>\nBy using the Distributive Property,<br \/>\n2 (4x &#8211; 11) = 2 (4x) &#8211; 2 (11)<br \/>\n= 8x &#8211; 22<br \/>\nSo,<br \/>\n8x &#8211; 22 = 10<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n8x = 10 + 22<br \/>\n8x = 32<br \/>\nx = 32 \u00f7 8<br \/>\nx = 4<br \/>\nHence,<br \/>\nThe value of x is: 4<\/p>\n<p>Question 3.<br \/>\n3w + 7 = 19<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q3.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q3\" width=\"230\" height=\"370\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q3.png 230w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q3-186x300.png 186w\" sizes=\"(max-width: 230px) 100vw, 230px\" \/><\/p>\n<p>Question 4.<br \/>\n2g &#8211; 13 = 3<br \/>\nAnswer:<br \/>\nThe value of g is: 8<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2g &#8211; 13 = 3<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2g = 3 + 13<br \/>\n2g = 16<br \/>\n2 \u00d7 g = 16<br \/>\ng = 16 \u00f7 2<br \/>\ng = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of g is: 8<\/p>\n<p>Question 5.<br \/>\n11 = 12 &#8211; q<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q5.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q5\" width=\"249\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q5.png 249w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q5-213x300.png 213w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><\/p>\n<p>Question 6.<br \/>\n10 = 7 &#8211; m<br \/>\nAnswer:<br \/>\nThe value of m is: -3<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n10 = 7 &#8211; m<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-m = 10 &#8211; 7<br \/>\n-m = 3<br \/>\nMultiply with &#8220;-&#8221; on both sides<br \/>\n&#8211; (-m ) = -3<br \/>\nm = -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is: -3<\/p>\n<p>Question 7.<br \/>\n5 = \\(\\frac{z}{-4}\\) &#8211; 3<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q7.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q7\" width=\"237\" height=\"494\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q7.png 237w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q7-144x300.png 144w\" sizes=\"(max-width: 237px) 100vw, 237px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{a}{3}\\) + 4 = 6<br \/>\nAnswer:<br \/>\nThe value of a is: 6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{a}{3}\\) + 4 = 6<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n\\(\\frac{a}{3}\\) = 6 &#8211; 4<br \/>\n\\(\\frac{a}{3}\\) = 2<br \/>\na = 2 \u00d7 3<br \/>\na = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: 6<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{h + 6}{5}\\) = 2<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q9.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q9\" width=\"214\" height=\"485\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q9.png 214w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q9-132x300.png 132w\" sizes=\"(max-width: 214px) 100vw, 214px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{d &#8211; 8}{-2}\\) = 12<br \/>\nAnswer:<br \/>\nThe value of d is: -16<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{d &#8211; 8}{-2}\\) = 12<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nd &#8211; 8 = 12 \u00d7 (-2)<br \/>\nd &#8211; 8 = -24<br \/>\nd = -24 + 8<br \/>\nd = -16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of d is: -16<\/p>\n<p>Question 11.<br \/>\n8y + 3y = 44<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q11.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q11\" width=\"232\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q11.png 232w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q11-193x300.png 193w\" sizes=\"(max-width: 232px) 100vw, 232px\" \/><\/p>\n<p>Question 12.<br \/>\n36 = 13n &#8211; 4n<br \/>\nAnswer:<br \/>\nThe value of n is: 4<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n36 = 13n &#8211; 4n<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n36 = 9n<br \/>\n9n = 36<br \/>\nn = 36 \u00f7 9<br \/>\nn = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n is: 4<\/p>\n<p>Question 13.<br \/>\n12v + 10v + 14 = 80<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q13.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q13\" width=\"309\" height=\"440\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q13.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q13-211x300.png 211w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Question 14.<br \/>\n6c &#8211; 8 &#8211; 2c = -16<br \/>\nAnswer:<br \/>\nThe value of c is: -2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n6c &#8211; 8 &#8211; 2c = -16<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4c &#8211; 8 = -16<br \/>\n4c = -16 + 8<br \/>\n4 \u00d7 c = -8<br \/>\nc = -8 \u00f7 4<br \/>\nc = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of c is: -2<\/p>\n<p>Question 15.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe altitude a (in feet) of a plane in minutes after liftoff is given by a = 3400t + 600. How many minutes after liftoff is the plane at an altitude of 21,000 feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-30.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 30\" width=\"237\" height=\"105\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q15.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q15\" width=\"581\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q15.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q15-300x140.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 16.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car.<br \/>\nAnswer:<br \/>\nThe number of hours of labor spent repairing the car is: 6 hours<\/p>\n<p>Explanation:<br \/>\nIt is given that a repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour.<br \/>\nLet the number of hours of labor spent repairing the car be: x<br \/>\nSo,<br \/>\nThe total bill to repair your car = ( The labor cost per hour ) \u00d7 ( The number of hours of labor spent repairing the car ) +\u00a0 (The cost of the parts )<br \/>\n553 = 48x + 265<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n48x = 553 &#8211; 265<br \/>\n48x = 288<br \/>\n48 \u00d7 x = 288<br \/>\nx = 288 \u00f7 48<br \/>\nx = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of hours of labor spent repairing the car is: 6 hours<\/p>\n<p><b>In Exercises 17\u221224, solve the equation. Check your solution.<\/b><\/p>\n<p>Question 17.<br \/>\n4(z + 5) = 32<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q17.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q17\" width=\"244\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q17.png 244w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q17-161x300.png 161w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/p>\n<p>Question 18.<br \/>\n-2(4g &#8211; 3) = 3018.<br \/>\nAnswer:<br \/>\nThe value of g is: 378<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-2 (4g &#8211; 3) = 3018<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-2 \u00d7 ( 4g &#8211; 3 ) = 3018<br \/>\n4g &#8211; 3 = 3018 \u00f7 2<br \/>\n4g &#8211; 3 = 1,509<br \/>\n4g = 1,509 +3<br \/>\n4 \u00d7 g = 1,512<br \/>\ng = 1,512 \u00f7 4<br \/>\ng = 378<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of g is: 378<\/p>\n<p>Question 19.<br \/>\n6 + 5(m + 1) = 26<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q19.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q19\" width=\"291\" height=\"519\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q19.png 291w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q19-168x300.png 168w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><\/p>\n<p>Question 20.<br \/>\n5h+ 2(11 &#8211; h) = -5<br \/>\nAnswer:<br \/>\nThe value of h is: -9<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n5h + 2 ( 11-h ) = -5<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n2 ( 11 &#8211; h ) = 2 (11 ) &#8211; 2 ( h )<br \/>\n= 22 &#8211; 2h<br \/>\nSo,<br \/>\n5h + 22 &#8211; 2h = -5<br \/>\n3h + 22 = -5<br \/>\n3h = -5 &#8211; (+22)<br \/>\n3h = -5 -22<br \/>\n3h = -27<br \/>\nh = -27 \u00f7 3<br \/>\nh = -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: -9<\/p>\n<p>Question 21.<br \/>\n27 = 3c &#8211; 3(6 &#8211; 2c)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q21.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q21\" width=\"323\" height=\"595\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q21.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q21-163x300.png 163w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 22.<br \/>\n-3 = 12y &#8211; 5(2y &#8211; 7)<br \/>\nAnswer:<br \/>\nThe value of y is: -19<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-3 = 12y &#8211; 5 (2y &#8211; 7)<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n12y &#8211; 5 (2y &#8211; 7) = -3<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n5 ( 2y &#8211; 7 ) = 5 (2y ) &#8211; 5 (7 )<br \/>\n= 10y &#8211; 35<br \/>\nSo,<br \/>\n12y &#8211; ( 10y &#8211; 35 ) = -3<br \/>\n12y &#8211; 10y + 35 = -3<br \/>\n2y + 35 = -3<br \/>\n2y = -3 &#8211; (+35 )<br \/>\n2y = -3 &#8211; 35<br \/>\n2y = -38<br \/>\ny = -38 \u00f7 2<br \/>\ny = -19<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: -19<\/p>\n<p>Question 23.<br \/>\n-3(3 + x) + 4(x &#8211; 6) = -4<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q23.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q23\" width=\"380\" height=\"433\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q23.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q23-263x300.png 263w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 24.<br \/>\n5(r + 9) &#8211; 2(1 &#8211; r) = 1<br \/>\nAnswer:<br \/>\nThe value of r is: -6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n5 ( r + 9 ) &#8211; 2 ( 1 &#8211; r ) = 1<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n5 ( r + 9 ) = 5 ( r ) + 5 ( 9 )<br \/>\n= 5r + 45<br \/>\n2 ( 1 &#8211; r ) = 2 ( 1 ) &#8211; 2 ( r )<br \/>\n= 2 &#8211; 2r<br \/>\nSo,<br \/>\n5r + 45 &#8211; ( 2 &#8211; 2r ) = 1<br \/>\n5r + 45 &#8211; 2 + 2r = 1<br \/>\n7r + 43 = 1<br \/>\n7r = 1 &#8211; 43<br \/>\n7r = -42<br \/>\nr = -42 \u00f7 7<br \/>\nr = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of r is: -6<\/p>\n<p><b>USING TOOLS<br \/>\nIn Exercises 25\u221228, find the value of the variable. Then find the angle measures of the polygon. Use a protractor to check the reasonableness of your answer.<\/b><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations 31\" width=\"141\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q25.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q25\" width=\"553\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q25.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q25-300x160.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-32.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 32\" width=\"114\" height=\"168\" \/><br \/>\nAnswer:<br \/>\nThe angle measures of the rhombus are:<br \/>\n60\u00b0, 60\u00b0, 120\u00b0, 120\u00b0<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-32.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 32\" width=\"114\" height=\"168\" \/><br \/>\nFrom the above figure,<br \/>\nThe angle measures of the rhombus are: a\u00b0, 2a\u00b0, a\u00b0, 2a\u00b0<br \/>\nIt is also given that the sum of all the angle measures is: 360\u00b0<br \/>\nSo,<br \/>\na\u00b0 + 2a\u00b0 + a\u00b0 + 2a\u00b0 = 360\u00b0<br \/>\n6a\u00b0 = 360\u00b0<br \/>\na = 360\u00b0 \u00f7 6<br \/>\na = 60\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle measures of the rhombus are:<br \/>\na\u00b0, 2a\u00b0, a\u00b0, 2a\u00b0 = 60\u00b0, 2 ( 60\u00b0 ), 60\u00b0, 2 ( 60\u00b0 )<br \/>\n= 60\u00b0, 60\u00b0, 120\u00b0, 120\u00b0<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-33.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 33\" width=\"125\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q27.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q27\" width=\"570\" height=\"395\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q27.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q27-300x208.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-34.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 34\" width=\"176\" height=\"163\" \/><br \/>\nAnswer:<br \/>\nThe angle measures of the hexagon are:<br \/>\n120\u00b0, 120\u00b0, 100\u00b0, 120\u00b0, 250\u00b0, 260\u00b0<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-34.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 34\" width=\"176\" height=\"163\" \/><br \/>\nFrom the given figure,<br \/>\nThe angle measures of the hexagon are:<br \/>\n120\u00b0, 120\u00b0, 100\u00b0, 120\u00b0, x\u00b0, (x + 10)\u00b0<br \/>\nIt is also given that the sum of the angle measures of the hexagon is: 720\u00b0<br \/>\nSo,<br \/>\n120\u00b0 + 120\u00b0 + 100\u00b0 + 120\u00b0 + x\u00b0 + (x + 10)\u00b0 = 720\u00b0<br \/>\n470\u00b0 + x = 720\u00b0<br \/>\nx = 720\u00b0 &#8211; 470\u00b0<br \/>\nx = 250\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle measures of the hexagon are:<br \/>\n120\u00b0, 120\u00b0, 100\u00b0, 120\u00b0, x\u00b0, (x + 10)\u00b0 = 120\u00b0, 120\u00b0, 100\u00b0, 120\u00b0, 250\u00b0, (250 + 10)\u00b0<br \/>\n= 120\u00b0, 120\u00b0, 100\u00b0, 120\u00b0, 250\u00b0, 260\u00b0<\/p>\n<p><b>In Exercises 29\u221234, write and solve an equation to find the number.<\/b><\/p>\n<p>Question 29.<br \/>\nThe sum of twice a number and 13 is 75.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q29.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q29\" width=\"178\" height=\"223\" \/><\/p>\n<p>Question 30.<br \/>\nThe difference of three times a number and 4 is -19.<br \/>\nAnswer:<br \/>\nThe number is: -5<\/p>\n<p>Explanation:<br \/>\nIt is given that the difference of three times of a number and 4 is -19<br \/>\nNow,<br \/>\nLet the number be x<br \/>\nSo,<br \/>\nThe three times of a number = 3 (x) = 3x<br \/>\nSo,<br \/>\n3x &#8211; 4 = -19<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n3x = -19 + 4<br \/>\n3x = -15<br \/>\nx = -15 \u00f7 3<br \/>\nx = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number is: -5<\/p>\n<p>Question 31.<br \/>\nEight plus the quotient of a number and 3 is -2.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q31.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q31\" width=\"212\" height=\"266\" \/><\/p>\n<p>Question 32.<br \/>\nThe sum of twice a number and half the number is 10.<br \/>\nAnswer:<br \/>\nThe number is: 4<\/p>\n<p>Explanation:<br \/>\nIt is given that the sum of twice of a number and half the number is 10.<br \/>\nLet the number be x.<br \/>\nSo,<br \/>\nThe twice of a number = 2 (x ) = 2x<br \/>\nHalf of the number = x \u00f7 2 = \\(\\frac{x}{2}\\)<br \/>\nSo,<br \/>\n2x + \\(\\frac{x}{2}\\) = 10<br \/>\n2x can be rewritten as: \\(\\frac{4x}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{4x}{2}\\) + \\(\\frac{x}{2}\\) = 10<br \/>\n\\(\\frac{4x + x}{2}\\) = 10<br \/>\n\\(\\frac{5x}{2}\\) = 10<br \/>\n5x = 10 \u00d7 2<br \/>\n5x = 20<br \/>\nx = 20 \u00f7 5<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the numebr is: 4<\/p>\n<p>Question 33.<br \/>\nSix times the sum of a number and 15 is -42.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q33.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q33\" width=\"217\" height=\"298\" \/><\/p>\n<p>Question 34.<br \/>\nFour times the difference of a number and 7 is 12.<br \/>\nAnswer:<br \/>\nThe number is: 4<\/p>\n<p>Explanation:<br \/>\nIt is given that the four times the difference of a number and 7 is 12<br \/>\nLet the number be x<br \/>\nSo,<br \/>\nFour times of the number = 4 ( x ) = 4x<br \/>\nSo,<br \/>\n4x &#8211; x = 12<br \/>\n3x = 12<br \/>\nx = 12 \u00f7 3<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number is: 4<\/p>\n<p><b>USING EQUATIONS<br \/>\nIn Exercises 35\u221237, write and solve an equation to answer the question. Check that the units on each side of the equation balance.<\/b><\/p>\n<p>Question 35.<br \/>\nDuring the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours must you work as a landscaper?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q35.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q35\" width=\"607\" height=\"636\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q35.png 607w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q35-286x300.png 286w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><\/p>\n<p>Question 36.<br \/>\nThe area of the surface of the swimming pool is 210 square feet. What is the length d of the deep end (in feet)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-35.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 35\" width=\"306\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-35.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-35-300x149.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Answer:<br \/>\nThe length d of the deep end is: 12 feet<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-35.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 35\" width=\"306\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-35.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-35-300x149.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nIt is given that the area of the surface of the swimming pool is 210 square feet<br \/>\nFrom the above figure,<br \/>\nWe can observe that the shape of the swimming pool is a rectangle.<br \/>\nSo,<br \/>\nLength of the swimming pool = 10 ft<br \/>\nWidth of the swimming pool = d + 9 ft<br \/>\nSo,<br \/>\nThe area of the swimming pool = Length \u00d7 Width<br \/>\n= 10 \u00d7 ( d + 9 )<br \/>\nNow,<br \/>\n210 = 10 \u00d7 ( d + 9 )<br \/>\nd + 9 = 210 \u00f7 10<br \/>\nd + 9 = 21<br \/>\nd = 21 &#8211; 9<br \/>\nd = 12 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length d of the deep end is: 12 feet<\/p>\n<p>Question 37.<br \/>\nYou order two tacos and a salad. The salad costs $2.50. You pay 8% sales tax and leave a $3 tip. You pay a total of $13.80. How much does one taco cost?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q37.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q37\" width=\"638\" height=\"683\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q37.png 638w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q37-280x300.png 280w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p><b>JUSTIFYING STEPS<br \/>\nIn Exercises 38 and 39, justify each step of the solution.<\/b><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-36.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 36\" width=\"306\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-36.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-36-300x202.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Answer:<br \/>\n&#8211;\\(\\frac{1}{2}\\) ( 5x &#8211; 8 ) &#8211; 1 = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Write the equation<br \/>\n&#8211;\\(\\frac{1}{2}\\) ( 5x &#8211; 8 ) = 6 + 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Arrange the similar terms<br \/>\n&#8211;\\(\\frac{1}{2}\\) ( 5x &#8211; 8 ) = 7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Simplify<br \/>\n&#8211; ( 5x &#8211; 8 ) = 7 \u00d7 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Divide by 2 on both sides<br \/>\n&#8211; ( 5x &#8211; 8 ) = 14\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Simplify<br \/>\n5x &#8211; 8 = -14\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Multiply with &#8220;-&#8221; on both sides<br \/>\n5x = -14 + 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Arrange the similar terms<br \/>\n5x = -6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Divide by 6 on both sides<br \/>\nx = &#8211;\\(\\frac{6}{5}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 The result<br \/>\nHence,<br \/>\nThe solution is: x = &#8211;\\(\\frac{6}{5}\\)<\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-37.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 37\" width=\"304\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-37.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-37-300x207.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q39.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q39\" width=\"531\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q39.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q39-300x116.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 40 and 41, describe and correct the error in solving the equation.<\/b><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-38.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 38\" width=\"243\" height=\"166\" \/><\/p>\n<p>Answer:<br \/>\nThe given equation is:<br \/>\n-2 ( 7 &#8211; y ) + 4 = -4<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-2 ( 7 &#8211; y ) = -4 &#8211;\u00a0 (+4 )<br \/>\n-2 ( 7 &#8211; y ) = -4 &#8211; 4<br \/>\n-2 ( 7 &#8211; y ) = -8<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n2 ( 7 &#8211; y ) = 2 ( 7 ) &#8211; 2 ( y )<br \/>\n= 14 &#8211; 2y<br \/>\nSo,<br \/>\n&#8211; ( 14 &#8211; 2y ) = -8<br \/>\n2y &#8211; 14 = -8<br \/>\n2y = -8 + 14<br \/>\n2y = 6<br \/>\ny = 6 \u00f7 2<br \/>\ny = 3<br \/>\nHence,<br \/>\nThe value of y is: 3<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-39.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 39\" width=\"240\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q41.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q41\" width=\"574\" height=\"443\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q41.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q41-300x232.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 42\u221244, write and solve an equation to answer the question.<\/b><\/p>\n<p>Question 42.<br \/>\nThe perimeter of the tennis court is 228 feet. What are the dimensions of the court?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-40.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 40\" width=\"236\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\nThe dimensions of the court are:<br \/>\nThe Length of the court is: 36 feet<br \/>\nThe width of the court is: 78 feet<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-40.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 40\" width=\"236\" height=\"140\" \/><br \/>\nIt is given that the perimeter of the tennis court is: 228 feet<br \/>\nFrom the above figure,<br \/>\nWe can observe that the shape of the tennis court is the rectangle<br \/>\nSo,<br \/>\nThe length of the tennis court = w feet<br \/>\nThe width of the tennis court =\u00a0 (2w + 6 ) feet<br \/>\nWe know that,<br \/>\nThe perimeter of the rectangle = 2 ( Length + Width )<br \/>\nSo,<br \/>\nThe perimeter of the tennis court = 2 ( Length + Width )<br \/>\n228 = 2 ( w + 2w + 6 )<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n2 ( w + 2w + 6 ) = 2 ( 3w + 6 )<br \/>\n= 2 ( 3w ) + 2 ( 6 )<br \/>\n= 6w + 12<br \/>\nSo,<br \/>\n228 = 6w + 12<br \/>\n6w = 228 &#8211; 12<br \/>\n6w = 216<br \/>\nw = 216 \u00f7 6<br \/>\nw = 36<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe length of the tennis court is: 36 feet<br \/>\nThe width of the tennis court is: 2w + 6\u00a0 = 2 ( 36 ) + 6 = 78 feet<\/p>\n<p>Question 43.<br \/>\nThe perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-41.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 41\" width=\"177\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q43.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q43\" width=\"433\" height=\"466\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q43.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q43-279x300.png 279w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>Question 44.<br \/>\nThe perimeter of the school crossing sign is 102 inches. What is the length of each side?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-42.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 42\" width=\"172\" height=\"157\" \/><\/p>\n<p>Answer:<br \/>\nThe length of each side is: 15 inches<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-42.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 42\" width=\"172\" height=\"157\" \/><br \/>\nIt is given that the perimeter of the crossing sign is 102 inches<br \/>\nWe know that,<br \/>\nThe perimeter of any polygon is the sum of all the sides of that polygon<br \/>\nSo,<br \/>\nThe perimeter of the crossing sign = s + ( s + 6 ) + ( s + 6 ) + s + 2s<br \/>\n102 = 6s + 12<br \/>\n102 &#8211; 12 = 6s<br \/>\n6s = 90<br \/>\ns = 90 \u00f7 6<br \/>\ns = 15 inches<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of each side is: 15 inches<\/p>\n<p>Question 45.<br \/>\n<b>COMPARING METHODS<\/b><br \/>\nSolve the equation 2(4 &#8211; 8x) + 6 = -1 using (a) Method 1 from Example 3 and (b) Method 2 from Example 3. Which method do you prefer? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45\" width=\"273\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45.png 273w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45-249x300.png 249w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45-i.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45-i\" width=\"554\" height=\"596\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45-i.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q45-i-279x300.png 279w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>PROBLEM &#8211; SOLVING<\/b><br \/>\nAn online ticket agency charges the amounts shown for basketball tickets. The total cost for an order is $220.70. How many tickets are purchased?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-43.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 43\" width=\"283\" height=\"117\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 47.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYou have quarters and dimes that total $2.80. Your friend says it is possible that the number of quarters is 8 more than the number of dimes. Is your friend correct? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q47.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q47\" width=\"572\" height=\"629\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q47.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q47-273x300.png 273w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nYou teach a math class and assign a weight to each component of the class. You determine final grades by totaling the products of the weights and the component scores. Choose values for the remaining weights and find the necessary score on the final exam for a student to earn an A (90%) in the class, if possible. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-44.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 44\" width=\"352\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-44.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-44-300x170.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><\/p>\n<p>Answer:<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-15.jpg\" alt=\"\" width=\"374\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-15.jpg 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-15-300x168.jpg 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nFrom the above table,<br \/>\nThe weights can be calculated by the difference between the total participation and the class participation and divide the total value by 100.<br \/>\nSo,<br \/>\nThe weight of homework = [ ( 100 &#8211; 95 ) \u00f7 100]<br \/>\n= 5 \u00f7 100<br \/>\n= 0.50<br \/>\nThe weight of midterm exam = ( 100 &#8211; 88 ) \u00f7 100<br \/>\n= 12 \u00f7 100<br \/>\n= 0.12<br \/>\nSo,<br \/>\nThe necessary score of the final exam = ( 92 + 95 + 88 ) % \u00f7 3<br \/>\n= 275 % \u00f7 3<br \/>\n= 91.6 %<\/p>\n<p>Question 49.<br \/>\n<b>REASONING<\/b><br \/>\nAn even integer can be represented by the expression 2n, where n is an integer. Find three consecutive even integers that have a sum of 54. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q49-1.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q49\" width=\"561\" height=\"574\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q49-1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q49-1-293x300.png 293w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe scatter plot shows the attendance for each meeting of a gaming club.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-45.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 45\" width=\"244\" height=\"182\" \/><br \/>\na. The mean attendance for the first four meetings is 20. Is the number of students who attended the fourth meeting greater than or less than 20? Explain.<br \/>\nAnswer:<br \/>\nThe number of students who attended the fourth meeting is greater than 20<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-45.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 45\" width=\"244\" height=\"182\" \/><br \/>\nWe know that<br \/>\nThe mean = ( Sum of the given numbers ) \u00f7 (The total number of the numbers)<br \/>\nFrom the above graph,<br \/>\nThe attendance of the 1st meeting = 18<br \/>\nThe attendance of the 2nd meeting = 21<br \/>\nThe attendance of the 3rd meeting = 17<br \/>\nLet the attendance of the 4th meeting be: x<br \/>\nSo,<br \/>\nThe mean attendance\u00a0 of the first four meetings = ( The attendance of the 4 meetings ) \u00f7\u00a0 ( The total number of meetings )<br \/>\n= ( 18 + 21 + 17 + x ) \u00f7 4<br \/>\nIt is given that the mean attendance of the first four meetings is: 20<br \/>\nSo,<br \/>\n20 =\u00a0 ( 18 + 21 + 17 + x ) \u00f7 4<br \/>\n( 56 + x ) \u00f7 4 = 20<br \/>\n56 + x = 20 \u00d7 4<br \/>\n56 + x = 80<br \/>\nx = 80 &#8211; 56<br \/>\nx = 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the attendance of the 4th meeting is greater than 20<\/p>\n<p>b. Estimate the number of students who attended the fourth meeting.<br \/>\nAnswer:<br \/>\nThe number of students who attended the fourth meeting is: 24<\/p>\n<p>Explanation:<br \/>\nThe mean attendance\u00a0 of the first four meetings = ( The attendance of the 4 meetings ) \u00f7\u00a0 ( The total number of meetings )<br \/>\n= ( 18 + 21 + 17 + x ) \u00f7 4<br \/>\nIt is given that the mean attendance of the first four meetings is: 20<br \/>\nSo,<br \/>\n20 =\u00a0 ( 18 + 21 + 17 + x ) \u00f7 4<br \/>\n( 56 + x ) \u00f7 4 = 20<br \/>\n56 + x = 20 \u00d7 4<br \/>\n56 + x = 80<br \/>\nx = 80 &#8211; 56<br \/>\nx = 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of students who attended the 4th meeting is: 24<\/p>\n<p>c. Describe a way you can check your estimate in part (b).<br \/>\nAnswer:<br \/>\nThe estimate in part (b) can be checked by using the property of the mean<br \/>\nSo,<br \/>\nThe mean attendance of the four meetings = ( The attendance of the four meetings ) \u00f7 ( The total number of meetings )<br \/>\n= ( 18 + 21 + 17 + 24 ) \u00f7 4<br \/>\n= 80 \u00f7 4<br \/>\n= 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the mean attendance of the four meetings is the same as given above.<\/p>\n<p><b>REASONING<br \/>\nIn Exercises 51\u221256, the letters a, b, and c represent nonzero constants. Solve the equation for x.<\/b><\/p>\n<p>Question 51.<br \/>\nbx = -7<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q51.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q51\" width=\"109\" height=\"151\" \/><\/p>\n<p>Question 52.<br \/>\nx + a = \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\nThe value of x is: \\(\\frac{3}{4}\\) &#8211; a<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx + a = \\(\\frac{3}{4}\\)<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx =\u00a0 \\(\\frac{3}{4}\\) &#8211; a<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: \\(\\frac{3}{4}\\) &#8211; a<\/p>\n<p>Question 53.<br \/>\nax &#8211; b = 12.5<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q53.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q53\" width=\"198\" height=\"221\" \/><\/p>\n<p>Question 54.<br \/>\nax + b = c<br \/>\nAnswer:<br \/>\nThe value of x is: \\(\\frac{c &#8211; b}{a}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nax + b = c<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nax = c &#8211; b<br \/>\nx = \\(\\frac{c &#8211; b}{a}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{c &#8211; b}{a}\\)<\/p>\n<p>Question 55.<br \/>\n2bx &#8211; bx = -8<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q55.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q55\" width=\"177\" height=\"219\" \/><\/p>\n<p>Question 56.<br \/>\ncx &#8211; 4b = 5b<br \/>\nAnswer<br \/>\nThe value of x is: \\(\\frac{9b}{c}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ncx &#8211; 4b = 5b<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\ncx = 5b + 4b<br \/>\ncx = 9b<br \/>\nx = \\(\\frac{9b}{c}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{9b}{c}\\)<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Simplify the expression.<\/b><\/p>\n<p>Question 57.<br \/>\n4m + 5 &#8211; 3m<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q57.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q57\" width=\"290\" height=\"65\" \/><\/p>\n<p>Question 58.<br \/>\n9 &#8211; 8b + 6b<br \/>\nAnswer:<br \/>\n9 &#8211; 8b + 6b<br \/>\n= 9 &#8211; (8b &#8211; 6b )<br \/>\n= 9 &#8211; 2b<\/p>\n<p>Question 59.<br \/>\n6t + 3(1 &#8211; 2t) &#8211; 5<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q59.png\" alt=\"\" width=\"421\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q59.png 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q59-300x119.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p><b>Determine whether (a) x = \u22121 or (b) x = 2 is a solution of the equation.<\/b><\/p>\n<p>Question 60.<br \/>\nx &#8211; 8 = -9<br \/>\nAnswer:<br \/>\nx = -1 is a solution to the given equation<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx &#8211; 8 = -9<br \/>\na) Let x = -1<br \/>\nSo,<br \/>\n-1 &#8211; 8 = -9<br \/>\n-9 = -9<br \/>\nAs LHS is equal to RHS<br \/>\nx = -1 is a solution of the given equation<br \/>\nb) Let x = 2<br \/>\nSo,<br \/>\n2 &#8211; 8 = -9<br \/>\n-6 = -9<br \/>\nAs LHS is not equal to RHS,<br \/>\nx = 2 is not a solution of the given equation<\/p>\n<p>Question 61.<br \/>\nx + 1.5 = 3.5<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q61.png\" alt=\"\" width=\"471\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q61.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q61-300x91.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p>Question 62.<br \/>\n2x &#8211; 1 = 3<br \/>\nAnswer:<br \/>\nx = 2 is a solution to the given equation<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2x &#8211; 1 = 3<br \/>\na) Let x = -1<br \/>\nSo,<br \/>\n2 ( -1 ) &#8211; 1 = 3<br \/>\n-2 &#8211; 1 = 3<br \/>\n-3 = 3<br \/>\nAs LHS is not equal to RHS<br \/>\nx = -1 is not a solution to the given equation<br \/>\nb) Let x = 2<br \/>\nSo,<br \/>\n2 ( 2 ) -1 = 3<br \/>\n4 &#8211; 1 = 3<br \/>\n3 = 3<br \/>\nAs LHS is equal to RHS,<br \/>\nx = 2\u00a0 is a solution to the given equation<\/p>\n<p>Question 63.<br \/>\n3x + 4 = 1<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q63.png\" alt=\"\" width=\"505\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q63.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q63-300x110.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 64.<br \/>\nx + 4 = 3x<br \/>\nAnswer:<br \/>\nx = 2 is a solution to the given equation<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx + 4 = 3x<br \/>\na) Let x = -1<br \/>\nSo,<br \/>\n-1 + 4 = 3 ( -1 )<br \/>\n= 3 = -3<br \/>\nAs LHS is not equal to RHS,<br \/>\nx = -1 is not a solution to the given equation<br \/>\nb) Let x = 2<br \/>\nSo,<br \/>\n2 + 4 = 3 ( 2 )<br \/>\n6 = 6<br \/>\nAs LHS is equal to RHS,<br \/>\nx = 2 is a solution to the given equation.<\/p>\n<p>Question 65.<br \/>\n-2(x &#8211; 1) = 1 &#8211; 3x<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q65.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q65\" width=\"504\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q65.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.2-Q65-300x110.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<h3><a id=\"Lesson_1.3_Solving_Equations_with_Variables_on_Both_Sides\"><\/a>Lesson 1.3 Solving Equations with Variables on Both Sides<\/h3>\n<p><b>EXPLORATION 1<\/b><br \/>\n<b>Perimeter<\/b><\/p>\n<p><b>Work with a partner. <\/b>The two polygons have the same perimeter. Use this information to write and solve an equation involving x. Explain the process you used to find the solution. Then find the perimeter of each polygon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-46.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 46\" width=\"377\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-46.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-46-300x129.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer:<br \/>\nThe perimeter of the hexagon is: 6<br \/>\nThe perimeter of the square is: 6<\/p>\n<p>Explanation:<br \/>\nThe given figures are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-46.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 46\" width=\"377\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-46.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-46-300x129.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nBased on the number of sides (n) in the polygon,<br \/>\nWe can say the name of that polygon<br \/>\nSo,<br \/>\nIn the first figure,<br \/>\nThe number of sides is: 6<br \/>\nSo,<br \/>\nIt is Hexagon<br \/>\nIn the second figure,<br \/>\nThe number of sides is: 4<br \/>\nSo,<br \/>\nIt is square ( As all the angles are 90\u00b0 )<br \/>\nIt is given that the two polygons have the same perimeter<br \/>\nWe know that,<br \/>\n&#8220;Perimeter&#8221; of a polygon is defined as the sum of all the sides in the polygon<br \/>\nSo,<br \/>\nThe sum of all sides in the hexagon = 5 + 2 + 5 + 2 + x + x<br \/>\n= 14 + 2x<br \/>\nThe sum of all sides in the square = \\(\\frac{3x}{2}\\) + 3 + 4 + 5<br \/>\n= \\(\\frac{3x}{2}\\) + 12<br \/>\nIt is given that the perimeter of both the polygons are equal<br \/>\nSo,<br \/>\n14 + 2x = \\(\\frac{3x}{2}\\) + 12<br \/>\n14 &#8211; 12 = \\(\\frac{3x}{2}\\) &#8211; 2x<br \/>\n\\(\\frac{3x}{2}\\) &#8211; 2x = 2<br \/>\nWe can write 2x as \\(\\frac{4x}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3x}{2}\\) &#8211; \\(\\frac{4x}{2}\\) = 2<br \/>\n\\(\\frac{3x &#8211; 4x}{2}\\) = 2<br \/>\n\\(\\frac{-x}{2}\\) = 2<br \/>\n&#8211; \\(\\frac{x}{2}\\) = 2<br \/>\n-x = 2 \u00d7 2<br \/>\n-x = 4<br \/>\nx = -4<br \/>\nHence,<br \/>\nThe perimeter of the Hexagon = 14 + 2x = 14 + 2 ( -4 )<br \/>\n= 14 &#8211; 8 = 6<br \/>\nThe perimeter of the square = \\(\\frac{3x}{2}\\) + 12<br \/>\n\\(\\frac{3 \u00d7 -4}{2}\\) + 12<br \/>\n= \\(\\frac{-12}{2}\\) + 12<br \/>\n= \\(\\frac{-12}{2}\\) + \\(\\frac{24}{2}\\)<br \/>\n= \\(\\frac{24 &#8211; 12}{2}\\)<br \/>\n= \\(\\frac{12}{2}\\)<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe perimeter of the Hexagon is: 6<br \/>\nThe perimeter of the square is: 6<\/p>\n<p><b>EXPLORATION 2<br \/>\nPerimeter and Area<\/b><\/p>\n<p><b>Work with a partner.<\/b><\/p>\n<ul>\n<li>Each figure has the unusual property that the value of its perimeter (in feet) is equal to the value of its area (in square feet). Use this information to write an equation for each figure.<\/li>\n<li>Solve each equation for x. Explain the process you used to find the solution.<\/li>\n<li>Find the perimeter and area of each figure.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-47.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 47\" width=\"751\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-47.png 751w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-47-300x95.png 300w\" sizes=\"(max-width: 751px) 100vw, 751px\" \/><\/p>\n<p>Question 3.<br \/>\nHow can you solve an equation that has variables on both sides?<br \/>\nAnswer:<br \/>\nIf the variable is the same on both sides in an equation, then rearrange the like terms<br \/>\nSo,<br \/>\nSeparate the variables and the numbers and simplify the variables and the numbers<br \/>\nIn this way,<br \/>\nWe can solve an equation with a single variable<\/p>\n<p>Question 4.<br \/>\nWrite three equations that have the variable x on both sides. The equations should be different from those you wrote in Explorations 1 and 2. Have your partner solve the equations.<br \/>\nAnswer:<br \/>\nLet the three equations that have variable x on both sides and different from Explorations 1 and 2 are:<br \/>\na) 6x + 2 = 5x-6<br \/>\nb) 16x = 18x &#8211; 2<br \/>\nc) 12x = 15x + 63<br \/>\nNow,<br \/>\na)<br \/>\nThe given equation is:<br \/>\n6x + 2 = 5x &#8211; 6<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n6x &#8211; 5x = -6 &#8211; 2<br \/>\nx = -8<br \/>\nHence,<br \/>\nThe value of x is: -8<br \/>\nb) The given equation is:<br \/>\n9x = 18x &#8211; 2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n18x &#8211; 16x = 2<br \/>\n2x = 2<br \/>\nx = 2 \u00f7 2<br \/>\nx = 1<br \/>\nHence,<br \/>\nThe value of x is: 1<br \/>\nc) The given equation is:<br \/>\n12x = 15x + 63<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n12x -15x = 63<br \/>\n-3x = 63<br \/>\nx = 63 \u00f7 ( -3 )<br \/>\nx = -63 \u00f7 3<br \/>\nx = -21<br \/>\nHence,<br \/>\nThe value of x is: -21<\/p>\n<p><b>1.3 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\n-2x = 3x + 10<br \/>\nAnswer:<br \/>\nThe value of x is: -2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-2x = 3x + 10<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-2x &#8211; 3x = 10<br \/>\n-5x = 10<br \/>\nx = 10 \u00f7 (-5)<br \/>\nx = -10 \u00f7 5<br \/>\nx = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -2<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2}\\)(6h &#8211; 4) = -5h + 1<br \/>\nAnswer:<br \/>\nThe value of h is: \\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{1}{2}\\) ( 6h &#8211; 4 ) = -5h + 1<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n6h &#8211; 4 = 2 ( -5h + 1 )<br \/>\n6h &#8211; 4 = 2 ( -5h ) + 2 ( 1 ) [ By using the Distributive Property of Multiplication )<br \/>\n6h &#8211; 4 = -10h + 2<br \/>\n6h + 10h = 2 + 4<br \/>\n16h = 6<br \/>\nh = \\(\\frac{6}{16}\\)<br \/>\nh= \\(\\frac{3}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: \\(\\frac{3}{8}\\)<\/p>\n<p>Question 3.<br \/>\n&#8211;\\(\\frac{3}{4}\\)(8n + 12) = 3(n &#8211; 3)<br \/>\nAnswer:<br \/>\nThe value of n is: 0<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n&#8211;\\(\\frac{3}{4}\\) ( 8n + 12 ) = 3 ( n &#8211; 3 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n8n + 12 = &#8211;\\(\\frac{4}{3}\\) \u00d7 3 ( n &#8211; 3 )<br \/>\n8n + 12 = &#8211;\\(\\frac{4}{3}\\) \\(\\frac{3}{1}\\) ( n &#8211; 3 )<br \/>\n8n + 12 = &#8211;\\(\\frac{3 \u00d7 4}{3 \u00d7 1}\\) ( n &#8211; 3 )<br \/>\n8n + 12 = -4 ( n &#8211; 3 )<br \/>\n8n + 12 = -4n &#8211; 4 ( -3 )<br \/>\n8n + 12 = -4n + 12<br \/>\n8n + 4n =12 &#8211; 12<br \/>\n12n = 0<br \/>\nn = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n is: 0<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation.<\/b><\/p>\n<p>Question 4.<br \/>\n4(1 &#8211; p) = 4p &#8211; 4<br \/>\nAnswer:<br \/>\nThe value of p is: 1<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n4 ( 1 -p ) = 4p &#8211; 4<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4 ( 1 ) &#8211; 4 ( p ) = 4p &#8211; 4<br \/>\n4 &#8211; 4p = 4p &#8211; 4<br \/>\n4p + 4p = 4 + 4<br \/>\n8p = 8<br \/>\np = 8 \u00f7 8<br \/>\np = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of p is: 1<\/p>\n<p>Question 5.<br \/>\n6m &#8211; m = &#8211;\\(\\frac{5}{6}\\)(6m &#8211; 10)<br \/>\nAnswer:<br \/>\nThe value of m is: \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n6m &#8211; m = &#8211;\\(\\frac{5}{6}\\) ( 6m &#8211; 10 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5m = &#8211;\\(\\frac{5}{6}\\) ( 6m &#8211; 10 )<br \/>\n5m = &#8211;\\(\\frac{5}{6}\\) ( 6m ) &#8211; ( &#8211;\\(\\frac{5}{6}\\) ( 10 ) )<br \/>\n5m = &#8211;\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{6m}{1}\\) + \\(\\frac{5}{6}\\) \\(\\frac{10}{1}\\)<br \/>\n5m = &#8211;\\(\\frac{5 \u00d7 6m}{6 \u00d7 1}\\) + \\(\\frac{5 \u00d7 10}{6 \u00d7 1}\\)<br \/>\n5m = -5m + \\(\\frac{25}{3}\\)<br \/>\n5m + 5m = \\(\\frac{25}{3}\\)<br \/>\n10m = \\(\\frac{25}{3}\\)<br \/>\nm = \\(\\frac{25}{3}\\) \u00f7 \\(\\frac{10}{1}\\)<br \/>\nm = \\(\\frac{25}{3}\\) \u00d7 \\(\\frac{1}{10}\\)<br \/>\nm = \\(\\frac{25}{30}\\)<br \/>\nm = \\(\\frac{5}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is: \\(\\frac{5}{6}\\)<\/p>\n<p>Question 6.<br \/>\n10k + 7 = -3 &#8211; 10k<br \/>\nAnswer:<br \/>\nThe value of k is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n10k + 7 = -3 &#8211; 10k<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n10k + 10k = -3 &#8211; ( +7 )<br \/>\n20k = -3 &#8211;<br \/>\n20k = -10<br \/>\nk = -10 \u00f7 20<br \/>\nk = &#8211;\\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of k is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Question 7.<br \/>\n3(2a &#8211; 2) = -2(3a &#8211; 3)<br \/>\nAnswer:<br \/>\nThe value of a is: 1<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3 ( 2a &#8211; 2 ) = -2 ( 3a &#8211; 3 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n3 ( 2a ) &#8211; 3 ( 2 ) = -2 ( 3a ) + 2 ( 3 )<br \/>\n6a &#8211; 6 = -6a + 6<br \/>\n6a + 6a = 6 + 6<br \/>\n12a = 12<br \/>\na = 12 \u00f7 12<br \/>\na = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: 1<\/p>\n<p><b>Concept Summary<\/b><\/p>\n<p><b>Steps for Solving Linear Equations<\/b><br \/>\nHere are several steps you can use to solve a linear equation. Depending on the equation, you may not need to use some steps.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-48.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 48\" width=\"225\" height=\"136\" \/><br \/>\n<b>Step 1<\/b><br \/>\nUse the Distributive Property to remove any grouping symbols.<br \/>\n<b>Step 2<\/b><br \/>\nSimplify the expression on each side of the equation.<br \/>\n<b>Step 3<\/b><br \/>\nCollect the variable terms on one side of the equation and the constant terms on the other side.<br \/>\n<b>Step 4<\/b><br \/>\nIsolate the variable.<br \/>\n<b>Step 5<\/b><br \/>\nCheck your solution.<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 8.<br \/>\nA boat travels upstream on the Mississippi River for 3.5 hours. The return trip only takes 2.5 hours because the boat travels 2 miles per hour faster downstream due to the current. How far does the boat travel upstream? Answer:<br \/>\nThe distance the boat travel upstream is: 17.5 miles<\/p>\n<p>Explanation:<br \/>\nIt is given that a boat travels upstream on the Mississippi River for 3.5 hours. The return trip only takes 2.5 hours because the boat travels 2 miles per hour faster downstream due to the current.<br \/>\nNow,<br \/>\nLet x be the speed of the boat traveled upstream<br \/>\nWe know that,<br \/>\nSpeed = Distance \u00f7 Time<br \/>\nDistance = Speed \u00d7 Time<br \/>\nIt is given that the time taken by the boat traveled upstream is: 3.5 hours<br \/>\nSo,<br \/>\nDistance traveled upstream = 3.5 \u00d7 x = 3.5x<br \/>\nNow,<br \/>\nIt is also given that the speed of the boat is 2 miles per hour faster downstream<br \/>\nSo,<br \/>\nDistance traveled downstream by boat = 2.5 ( x + 2 )<br \/>\nSO,<br \/>\nAs both the distances are the same,<br \/>\n3.5x = 2.5 ( x + 2 )<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n3.5x = 2.5 ( x) + 2.5 ( 2 )<br \/>\n3.5x = 2.5x + 5<br \/>\n3.5x &#8211; 2.5x = 5<br \/>\nx = 5<br \/>\nSo,<br \/>\nThe distance traveled upstream by boat = 3.5x = 3.5 ( 5 )<br \/>\n= 17.5 miles per hour<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance traveled upstream by boat is: 17.5 miles per hour<\/p>\n<h3><a id=\"Solving_Equations_with_Variables_on_Both_Sides_1.3_Exercises\"><\/a>Solving Equations with Variables on Both Sides 1.3 Exercises<\/h3>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201316, solve the equation. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY <\/b>Is the equation -2(4 &#8211; x) = 2x + 8 an identity? Explain your reasoning.<br \/>\nAnswer:<br \/>\n-2 ( 4 &#8211; x ) = 2x + 8 is not an identity<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-2 ( 4 &#8211; x ) = 2x + 8<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n-2 ( 4 ) + 2 ( x ) = 2x + 8<br \/>\n-8 + 2x = 2x + 8<br \/>\n2x &#8211; 8 = 2x + 8<br \/>\nAs<br \/>\nLHS \u2260 RHS<br \/>\n-2 ( 4 &#8211; x ) = 2x + 8\u00a0 is not an identity<\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b> Describe the steps in solving the linear equation 3(3x &#8211; 8) = 4x + 6<br \/>\nAnswer:<br \/>\nThe value of x is: 6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3 ( 3x &#8211; 8 ) = 4x + 6<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n3 ( 3x ) &#8211; 3 ( 8 ) = 4x + 6<br \/>\n9x &#8211; 24 = 4x + 6<br \/>\n9x &#8211; 4x = 6 + 24<br \/>\n5x = 30<br \/>\nx = 30 \u00f7 5<br \/>\nx = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 6<\/p>\n<p>Question 3.<br \/>\n15 &#8211; 2x = 3x<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q3.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q3\" width=\"223\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q3.png 223w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q3-172x300.png 172w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/><\/p>\n<p>Question 4.<br \/>\n26 &#8211; 4s = 9s<br \/>\nAnswer:<br \/>\nThe value of s is: 2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n26 &#8211; 4s = 9s<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n26 = 9s + 4s<br \/>\n13s = 26<br \/>\ns = 26 \u00f7 13<br \/>\ns = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of s is: 2<\/p>\n<p>Question 5.<br \/>\n5p &#8211; 9 = 2p + 12<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q5.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q5\" width=\"279\" height=\"465\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q5.png 279w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q5-180x300.png 180w\" sizes=\"(max-width: 279px) 100vw, 279px\" \/><\/p>\n<p>Question 6.<br \/>\n8g + 10 = 35 + 3g<br \/>\nAnswer:<br \/>\nThe value of g is: 5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n8g + 10 = 35 + 3g<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n8g &#8211; 3g = 35 &#8211; 10<br \/>\n5g = 25<br \/>\ng = 25 \u00f7 5<br \/>\ng = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of g is: 5<\/p>\n<p>Question 7.<br \/>\n5t + 16 = 6 &#8211; 5t<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q7.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q7\" width=\"283\" height=\"446\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q7.png 283w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q7-190x300.png 190w\" sizes=\"(max-width: 283px) 100vw, 283px\" \/><\/p>\n<p>Question 8.<br \/>\n-3r + 10 = 15r &#8211; 8<br \/>\nAnswer:<br \/>\nThe value of r is: 1<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-3r + 10 = 15r &#8211; 8<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-3r &#8211; 15r = -10 &#8211; 8<br \/>\n-18r = -18<br \/>\nr = -18 \u00f7 ( -18 )<br \/>\nr = 1 [ since &#8211; \u00f7 &#8211; = + ]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of r is: 1<\/p>\n<p>Question 9.<br \/>\n7 + 3x &#8211; 12x = 3x + 1<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q9.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q9\" width=\"318\" height=\"698\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q9.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q9-137x300.png 137w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Question 10.<br \/>\nw &#8211; 2 + 2w = 6 + 5w<br \/>\nAnswer:<br \/>\nThe value of w is: -4<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nw &#8211; 2 + 2w = 6 + 5w<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nw + 2w -5w =6 + 2<br \/>\n-2w = 8<br \/>\nw = -8 \u00f7 2<br \/>\nw = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: -4<\/p>\n<p>Question 11.<br \/>\n10(g + 5) = 2(g + 9)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q11.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q11\" width=\"302\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q11.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q11-171x300.png 171w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p>Question 12.<br \/>\n-9(t &#8211; 2) = 4(t &#8211; 15)<br \/>\nAnswer:<br \/>\nThe value of t is: 6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-9 ( t &#8211; 2 ) = 4 ( t &#8211; 15 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n-9 ( t ) +\u00a0 9 ( 2 ) = 4 ( t ) &#8211; 4 ( 15 )<br \/>\n-9t + 18 = 4t &#8211; 60<br \/>\n-9t &#8211; 4t = -60 &#8211; 18<br \/>\n-13t = -78<br \/>\nt = -78 \u00f7 ( -13 )<br \/>\nt = 6 [ Since\u00a0 -\u00f7 &#8211; = + ]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of t is: 6<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{2}{3}\\)(3x + 9) = -2(2x + 6)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q13.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q13\" width=\"373\" height=\"669\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q13.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q13-167x300.png 167w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 14.<br \/>\n2(2t + 4) = \\(\\frac{3}{4}\\)(24 &#8211; 8t)<br \/>\nAnswer:<br \/>\nThe value of t is: 1<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2 ( 2t + 4 ) = \\(\\frac{3}{4}\\) ( 24 &#8211; 8t )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n2 ( 2t ) + 2 ( 4 ) = \\(\\frac{3}{4}\\) ( 24 ) &#8211; 8t\u00a0 (\\(\\frac{3}{4}\\) )<br \/>\n4t + 8 = \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{24}{1}\\) &#8211; \\(\\frac{8t}{1}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n4t + 8 = \\(\\frac{3 \u00d7 24}{4 \u00d7 1}\\) &#8211; \\(\\frac{3 \u00d7 8t}{4 \u00d7 1}\\)<br \/>\n4t + 8 = \\(\\frac{18}{1}\\) &#8211; \\(\\frac{6t}{1}\\)<br \/>\n4t + 8 = 18 &#8211; 6t<br \/>\n4t + 6t = 18 &#8211; 8<br \/>\n10t = 10<br \/>\nt = 10 \u00f7 10<br \/>\nt = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of t is: 1<\/p>\n<p>Question 15.<br \/>\n10(2y + 2) &#8211; y = 2(8y &#8211; 8)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q15.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q15\" width=\"425\" height=\"638\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q15.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q15-200x300.png 200w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 16.<br \/>\n2(4x + 2) = 4x &#8211; 12(x &#8211; 1)<br \/>\nAnswer:<br \/>\nThe value of x is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2 ( 4x + 2 ) = 4x &#8211; 12 ( x &#8211; 1 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n2 ( 4x ) + 2 ( 2 ) = 4x &#8211; 12 ( x ) + 12 ( 1 ) [ Since &#8211; \u00d7 &#8211; = + ]<br \/>\n8x + 4 = 4x &#8211; 12x + 12<br \/>\n8x + 4 =12 &#8211; 8x<br \/>\n8x + 8x = 12 &#8211; 4<br \/>\n16x = 8<br \/>\nx = 8 \u00f7 16<br \/>\nx = \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{1}{2}\\)<\/p>\n<p>Question 17.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou and your friend drive toward each other. The equation 50h = 190 &#8211; 45h represents the number h of hours until you and your friend meet. When will you meet?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q17.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q17\" width=\"533\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q17.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q17-300x141.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 18.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe equation 1.5r + 15 = 2.25r represents the number r of movies you must rent to spend the same amount at each movie store. How many movies must you rent to spend the same amount at each movie store?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-49.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 49\" width=\"319\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-49.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-49-300x104.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Answer:<br \/>\nThe number of movies you rent to spend the same amount at each movie store is: 20<\/p>\n<p>Explanation:<br \/>\nIt is given that<br \/>\nThe equation 1.5r + 15 = 2.25r represents the number r of movies you must rent to spend the same amount at each movie store.<br \/>\nNow,<br \/>\nWe have to find the value of r to find the number f movies you must rent to spend the same amount at each movie store<br \/>\nSo,<br \/>\nThe given equation is:<br \/>\n1.5r + 15 = 2.25r<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2.25r &#8211; 1.5r = 15<br \/>\n0.75r = 15<br \/>\n\\(\\frac{75}{100}\\)r = 15<br \/>\nr = 15 \u00d7 \\(\\frac{100}{75}\\)<br \/>\nr = \\(\\frac{15}{1}\\) \u00d7 \\(\\frac{100}{75}\\)<br \/>\nr = \\(\\frac{15 \u00d7 100}{1 \u00d7 75}\\)<br \/>\nr = 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of movies you rent to spend the same amount at each movie store is: 20<\/p>\n<p><b>In Exercises 19\u201324, solve the equation. Determine whether the equation has one solution, no solution, or infinitely many solutions.<\/b><\/p>\n<p>Question 19.<br \/>\n3t + 4 = 12 + 3t<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q19.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q19\" width=\"550\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q19.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q19-300x89.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 20.<br \/>\n6d + 8 = 14 + 3d<br \/>\nAnswer:<br \/>\nThe value of d is: 2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n6d + 8 = 14 + 3d<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n6d &#8211; 3d = 14 &#8211; 8<br \/>\n3d = 6<br \/>\nd = 6 \u00f7 3<br \/>\nd = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of d is: 2<\/p>\n<p>Question 21.<br \/>\n2(h + 1) = 5h &#8211; 7<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q21.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q21\" width=\"354\" height=\"375\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q21.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q21-283x300.png 283w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 22.<br \/>\n12y + 6 = -6(2y + 1)<br \/>\nAnswer:<br \/>\nThe value of y is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n12y + 6 = -6 ( 2y + 1 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n12y + 6 = -6 ( 2y ) &#8211; 6 ( 1 )<br \/>\n12y + 6 = -12y &#8211; 6<br \/>\n12y + 12y = -6 &#8211; ( +6 )<br \/>\n24y = -6 &#8211; 6<br \/>\n24y = -12<br \/>\ny = -12 \u00f7 24<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Question 23.<br \/>\n3(4g + 6) = 2(6g + 9)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q23.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q23\" width=\"551\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q23.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q23-300x127.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 24.<br \/>\n5(1 + 2m) = \\(\\frac{1}{2}\\)(8 + 20m)<br \/>\nAnswer:<br \/>\nm has indefinite solutions<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n5 ( 1 ) + 5 ( 2m ) = \\(\\frac{1}{2}\\) ( 8 ) + \\(\\frac{1}{2}\\) ( 20m )<br \/>\n2 ( 5 + 10m ) = 8 + 20m<br \/>\n2 ( 5 ) + 2 ( 10m ) = 8 + 20m<br \/>\n10 + 20m = 8 + 20m<br \/>\n20m &#8211; 20m = 8 &#8211; 10<br \/>\n20m &#8211; 20m = -2<br \/>\nAs\u00a0 m has the same coefficients and have the opposite signs, m has indefinite solutions<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation has the indefinite solutions<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 25 and 26, describe and correct the error in solving the equation.<\/b><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-50.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 50\" width=\"258\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q25.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q25\" width=\"539\" height=\"394\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q25.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q25-300x219.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-51.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 51\" width=\"259\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\nThe given equation is:<br \/>\n6 ( 2y + 6 ) = 4 ( 9 + 3y )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n6 ( 2y ) + 6 ( 6 ) = 4 ( 9 ) + 4 ( 3y )<br \/>\n12y + 36 = 36 + 12y<br \/>\n12y &#8211; 12y = 36 &#8211; 36<br \/>\n0 = 0<br \/>\nAs the coefficients of y are zero, the equation has no solution<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is no error in the analysis of the equation.<\/p>\n<p>Question 27.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nWrite and solve an equation to find the month when you would pay the same total amount for each Internet service.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-52.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 52\" width=\"348\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-52.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-52-300x77.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q27.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q27\" width=\"577\" height=\"518\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q27.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q27-300x269.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 28.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nOne serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams of protein from other sources. How many grams of protein do you need daily?<br \/>\nAnswer:<br \/>\nThe number of grams of protein you need daily is: 50 grams<\/p>\n<p>Explanation:<br \/>\nIt is given that one serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams of protein from other sources.<br \/>\nSo,<br \/>\nLet the number of grams of protein you need daily be: x<br \/>\nSo,<br \/>\nThe number of grams of protein you need daily = 4 % of x + 48<br \/>\nWe know that,<br \/>\n100%\u00a0 = 1<br \/>\nSo,<br \/>\n4 % = 0.04<br \/>\nSo,<br \/>\nThe number of grams of protein you need daily = 0.04x + 48<br \/>\nx = 0.04x + 48<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx &#8211; 0.04x = 48<br \/>\n0.96x = 48<br \/>\n\\(\\frac{96}{100}\\)x = 48<br \/>\nx = 48 \u00d7 \\(\\frac{100}{96}\\)<br \/>\nx = \\(\\frac{48}{1}\\) \u00d7 \\(\\frac{100}{96}\\)<br \/>\nx = \\(\\frac{48 \u00d7 100}{1 \u00d7 96}\\)<br \/>\nx = \\(\\frac{50}{1}\\)<br \/>\nx = 50 grams<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of proteins you need daily is: 50 grams<\/p>\n<p><b>USING STRUCTURE<br \/>\nIn Exercises 29 and 30, find the value of r.<\/b><\/p>\n<p>Question 29.<br \/>\n8(x + 6) &#8211; 10 + r = 3(x + 12) + 5x<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q29.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q29\" width=\"435\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q29.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q29-300x213.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 30.<br \/>\n4(x &#8211; 3) &#8211; r + 2x = 5(3x &#8211; 7) &#8211; 9x<br \/>\nAnswer:<br \/>\nThe value of r is: 23<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n4 ( x &#8211; 3 ) &#8211; r + 2x = 5 ( 3x &#8211; 7 ) &#8211; 9x<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n4x &#8211; 4 ( 3 ) &#8211; r + 2x = 5 ( 3x ) &#8211; 5 ( 7 ) &#8211; 9x<br \/>\n4x &#8211; 12 &#8211; r + 2x = 15x &#8211; 35 &#8211; 9x<br \/>\n6x &#8211; 12 &#8211; r = 6x &#8211; 35<br \/>\nr = 6x &#8211; 6x &#8211; 12 + 35<br \/>\nr = 23<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of r is: 23<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 31 and 32, the value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x. Then find the surface area and volume of the cylinder.<\/b><\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-53.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 53\" width=\"107\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q31.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q31\" width=\"561\" height=\"567\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q31.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q31-297x300.png 297w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-54.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 54\" width=\"129\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nThe Surface Area of the cylinder is: 461.49 cm\u00b2<br \/>\nThe volume of the cylinder is: 488.58 cm\u00b3<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-54.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 54\" width=\"129\" height=\"137\" \/><br \/>\nFrom the above figure,<br \/>\nThe radius of the cylinder is: 7\\(\\frac{1}{5}\\) feet<br \/>\nThe height of the cylinder is: x feet<br \/>\nIt is given that the Total Surface Area of the cylinder and the volume of the cylinder are equal.<br \/>\nWe know that,<br \/>\nThe Surface Area of the cylinder = 2\u03c0r\u00b2 + 2\u03c0rh<br \/>\nThe volume of the cylinder = \u03c0r\u00b2h<br \/>\nThe value of \u03c0 is: 3.1416<br \/>\nNow,<br \/>\nThe representation of 7\\(\\frac{1}{5}\\) in the improper fraction form is: \\(\\frac{36}{5}\\)<br \/>\nSo,<br \/>\n2\u03c0r\u00b2 + 2\u03c0rh = \u03c0r\u00b2h<br \/>\n[ 2 \u00d7 3.1416\u00a0\u00d7 \\(\\frac{36}{5}\\) \u00d7 \\(\\frac{36}{5}\\) ] + [ 2 \u00d7 3.1416 \u00d7 \\(\\frac{36}{5}\\) \u00d7 x ] = [3.1416 \u00d7 latex]\\frac{36}{5}[\/latex] \u00d7 \\(\\frac{36}{5}\\) \u00d7 x ]<br \/>\n325.72 + 45.23x = 162.86x<br \/>\n162.86x &#8211; 45.23x = 325.72<br \/>\n117.63x = 325.72<br \/>\nx = 2.76<br \/>\nx = 3<br \/>\nSo,<br \/>\nThe Surface Area of the cylinder = 2\u03c0r\u00b2 + 2\u03c0rh<br \/>\n= [ 2 \u00d7 3.1416\u00a0\u00d7 \\(\\frac{36}{5}\\) \u00d7 \\(\\frac{36}{5}\\) ] + [ 2 \u00d7 3.1416 \u00d7 \\(\\frac{36}{5}\\) \u00d7 x ]<br \/>\n= 325.72 + 45.23x<br \/>\n= 325.72 + 45.23 ( 3 )<br \/>\n= 461.49 cm\u00b2<br \/>\nThe volume of the cylinder = \u03c0r\u00b2h<br \/>\n= [3.1416 \u00d7 latex]\\frac{36}{5}[\/latex] \u00d7 \\(\\frac{36}{5}\\) \u00d7 x ]<br \/>\n= 162.86x<br \/>\n= 162.86 ( 3 )<br \/>\n= 488.58 cm\u00b3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe Surface Area of the cylinder is: 461.49 cm\u00b2<br \/>\nThe volume of the cylinder is: 488.58 cm\u00b3<\/p>\n<p>Question 33.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA cheetah that is running 90 feet per second is 120 feet behind an antelope that is running 60 feet per second. How long will it take the cheetah to catch up to the antelope?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q33.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q33\" width=\"572\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q33.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q33-300x222.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nA cheetah can run at top speed for only about 20 seconds. If an antelope is too far away for a cheetah to catch it in 20 seconds, the antelope is probably safe. Your friend claims the antelope in Exercise 33 will not be safe if the cheetah starts running 650 feet behind it. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYour friend is not correct<\/p>\n<p>Explanation:<br \/>\nIt is given that a cheetah can run at top speed for only about 20 seconds. If an antelope is too far away for a cheetah to catch it in 20 seconds, the antelope is probably safe. Your friend claims the antelope in Exercise 33 will not be safe if the cheetah starts running 650 feet behind it.<br \/>\nLet the distance of running antelope be x.<br \/>\nLet &#8216;t&#8217; be the time taken<br \/>\nSo,<br \/>\nThe distance of running Antelope is:<br \/>\nx = 650 + 60t<br \/>\nThe cheetah must arrive at the same position to catch the antelope<br \/>\nSo,<br \/>\nx = 90t<br \/>\nNow,<br \/>\n90t = 650 + 60t<br \/>\n90t &#8211; 60t = 650<br \/>\n30t = 650<br \/>\nt = 650 \u00f7 30<br \/>\nt = 21.7 seconds<br \/>\nBut it is given that the cheetah has to reach the same position as the antelope in 20 seconds<br \/>\nBut according to the calculation, it takes 21.7 seconds<br \/>\nSo,<br \/>\nAccording to your friend, the antelope is not safe if the cheetah is running 650 meters behind it.<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct.<\/p>\n<p><b>REASONING<br \/>\nIn Exercises 35 and 36, for what value of a is the equation an identity? Explain your reasoning.<\/b><\/p>\n<p>Question 35.<br \/>\na(2x + 3) = 9x + 15 + x<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q35.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q35\" width=\"579\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q35.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q35-300x201.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 36.<br \/>\n8x &#8211; 8 + 3ax = 5ax &#8211; 2a<br \/>\nAnswer:<br \/>\nThe given equation becomes an identity at a = 4<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n8x &#8211; 8 + 3ax = 5ax &#8211; 2a<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5ax &#8211; 3ax = 8x &#8211; 8 &#8211; 2a<br \/>\n2ax = 8 ( x &#8211; 1 ) &#8211; 2a<br \/>\n2ax + 2a = 8x &#8211; 8<br \/>\nEquate the like coefficients of x and the like constants in both LHS and RHS<br \/>\nSo,<br \/>\n2ax = 8x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02a = -8<br \/>\na = 8x \u00f7 2x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = -8 \u00f7 2<br \/>\na = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = -4<br \/>\nNow,<br \/>\nAt a = 4,<br \/>\nThe equation becomes<br \/>\n8x &#8211; 8 + 3ax = 5ax &#8211; 2a<br \/>\n8x &#8211; 8 + 3x ( 4 ) = 5x ( 4 ) -2 ( 4 )<br \/>\n8x &#8211; 8 + 12x = 20x &#8211; 8<br \/>\n20x &#8211; 8 = 20x &#8211; 8<br \/>\nHence,<br \/>\nAt a =4,<br \/>\nThe given equation is an Identity<br \/>\nAt a = -4,<br \/>\nThe equation becomes<br \/>\n8x &#8211; 8 + 3ax = 5ax &#8211; 2a<br \/>\n8x &#8211; 8 + 3x ( -4 ) = 5x ( -4 ) -2 ( -4 )<br \/>\n8x &#8211; 8 &#8211; 12x = -20x + 8<br \/>\n-4x &#8211; 8 = -20x + 8<br \/>\nHence,<br \/>\nAt a = -4, the given equation is not an Identity<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation is an Identity at a = 4<\/p>\n<p>Question 37.<br \/>\n<b>REASONING<\/b><br \/>\nTwo times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q37.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q37\" width=\"572\" height=\"494\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q37.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q37-300x259.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe table and the graph show information about students enrolled in Spanish and French classes at a high school.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 55\" width=\"334\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55-150x150.png 150w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\na. Use the graph to determine after how many years there will be equal enrollment in Spanish and French classes.<br \/>\nAnswer:<br \/>\nThe year where there will be equal enrollment in Spanish and French classes is: 6<\/p>\n<p>Explanation:<br \/>\nThe given table and the graph of the students for the Spanish and French classes are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 55\" width=\"334\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-55-150x150.png 150w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nSo,<br \/>\nFrom the above table,<br \/>\nTo find the year where there is equal enrollment in both Spanish and French, we have to find the point in the graph that the two points of Spanish and French intersect<br \/>\nSo,<br \/>\nFrom the above graph,<br \/>\nThe point that is intersecting is at 6th year<br \/>\nHence, from the above,<br \/>\nWe can conclude that there is an equal enrollment of students in the 6th year in both Spanish and French classes<\/p>\n<p>b. How does the equation 355 &#8211; 9x = 229 + 12x relate to the table and the graph? How can you use this equation to determine whether your answer in part (a) is reasonable?<br \/>\nAnswer:<br \/>\nThe given equation<br \/>\n355 &#8211; 9x = 229 + 12x<br \/>\nrepresents the total number of students enrolled in the different years in both Spanish and French classes<br \/>\nNow,<br \/>\nIn part (a),<br \/>\nWe observed that there is an equal enrollment of the students at 6th year in both Spanish and French classes<br \/>\nSo,<br \/>\nHere,<br \/>\nx is: The number of years<br \/>\nSo,<br \/>\nIn part (a),<br \/>\nx = 6<br \/>\nNow,<br \/>\nSubstitute x = 6 in the given equation.<br \/>\nNow,<br \/>\n355 &#8211; 9x = 229 + 12x<br \/>\n355 &#8211; 9 ( 6 ) = 229 + 12 ( 6 )<br \/>\n355 &#8211; 54 = 229 + 72<br \/>\n301 = 301<br \/>\nAs<br \/>\nLHS = RHS<br \/>\nWe can say that the answer is reasonable in part (a)<\/p>\n<p>Question 39.<br \/>\n<b>WRITING EQUATIONS<\/b><br \/>\nGive an example of a linear equation that has (a) no solution and (b) infinitely many solutions. Justify your answers.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q39.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q39\" width=\"523\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q39.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q39-300x287.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nDraw a different figure that has the same perimeter as the triangle shown. Explain why your figure has the same perimeter.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-56.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 56\" width=\"147\" height=\"116\" \/><\/p>\n<p>Answer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Order the values from least to greatest.<\/b><\/p>\n<p>Question 41.<br \/>\n9, | -4|, -4, 5, | 2 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q41.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q41\" width=\"260\" height=\"37\" \/><\/p>\n<p>Question 42.<br \/>\n| -32 |, 22, -16, -| 21 |, | -10 |<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| -x | = x<br \/>\n| x | = x<br \/>\nSo,<br \/>\n| -32 | = 32<br \/>\n| 21 | = 21<br \/>\n| -10 | = 10<br \/>\nHence,<br \/>\nThe order of the values from the least to the greatest is:<br \/>\n-21, -16, 10, 22, 32<\/p>\n<p>Question 43.<br \/>\n-18, | -24 |, -19, | -18 |, | 22 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q43.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q43\" width=\"450\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q43.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.3-Q43-300x25.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Question 44.<br \/>\n-| &#8211; 3 |, | 0 |, -1, | 2 |, -2<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| -x | = x<br \/>\n| x | = x<br \/>\nSo,<br \/>\n| -3 | = 3<br \/>\n| 0 | = 0<br \/>\n| 2 | = 2<br \/>\nHence,<br \/>\nThe order of the numbers from the least to the greatest is:<br \/>\n-3, -2, -1, 0, 2<\/p>\n<h3><a id=\"Solving_Linear_Equations_Study_Skills:_Completing\"><\/a>Solving Linear Equations Study Skills: Completing<\/h3>\n<p><b>1.1-1.3 What Did You Learn<\/b><\/p>\n<p><b>Core Vocabulary<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-57.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 57\" width=\"563\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-57.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-57-300x53.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p><b>Core Concepts<\/b><\/p>\n<p><b>Section 1.1<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-58.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 58\" width=\"617\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-58.png 617w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-58-300x31.png 300w\" sizes=\"(max-width: 617px) 100vw, 617px\" \/><\/p>\n<p><b>Section 1.2<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-59.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 59\" width=\"462\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-59.png 462w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-59-300x20.png 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><\/p>\n<p><b>Section 1.3<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-60.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 60\" width=\"601\" height=\"29\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-60.png 601w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-60-300x14.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow did you make sense of the relationships between the quantities in Exercise 46 on page 9?<br \/>\nAnswer:<br \/>\nIn Exercise 46 on page 9,<br \/>\nThere is a layout of the tatami mat which comprises the four identical rectangular mats and the one square mat.<br \/>\nit is also given that the area of the square mat is half of one of the rectangular mats<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe area of the square mat = Area\u00b2 [ Since all the sides of the square are equal ]<br \/>\nThe area of the rectangular mat = Length \u00d7 Width<br \/>\nSo,<br \/>\nAccording to the given condition,<br \/>\nThe relation between the area of the square mat and one of the rectangular mat is:<br \/>\nArea of the square mat = \\(\\frac{1}{2}\\) Area of one of the rectangular mat<br \/>\nSide\u00b2 = \\(\\frac{1}{2}\\) ( Length \u00d7 Width )<\/p>\n<p>Question 2.<br \/>\nWhat is the limitation of the tool you used in Exercises 25\u201328 on page 16?<br \/>\nAnswer:<br \/>\nThe limitations of the tool you used in Exercises 25 &#8211; 28 on page 16 are:<br \/>\nA) The calculated values and the values measured using the tool will be different<br \/>\nB) We won&#8217;t get the exact values of the angle measures using the tool<\/p>\n<p>Question 3.<br \/>\nWhat definition did you use in your reasoning in Exercises 35 and 36 on page 24?<br \/>\nAnswer:<br \/>\nThe definition you used in your reasoning in Exercises 35 and 36 on page 24 is:<br \/>\nMake the like coefficients of the same variable in both LHS and RHS equal so that we get the value of the variable.<\/p>\n<p><b>Study Skills<\/b><\/p>\n<p><b>Completing Homework Efficiently<\/b><\/p>\n<p>Before doing homework, review the Core Concepts and examples. Use the tutorials at BigIdeasMath.com for additional help.<\/p>\n<p>Complete homework as though you are also preparing for a quiz. Memorize different types of problems, vocabulary, rules, and so on.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-61.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 61\" width=\"394\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-61.png 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-61-300x216.png 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<h3><a id=\"Solving_Linear_Equations_1.1-1.3_Quiz\"><\/a>Solving Linear Equations 1.1-1.3 Quiz<\/h3>\n<p><b>Solve the equation. Justify each step. Check your solution. <\/b>(Section 1.1)<\/p>\n<p>Question 1.<br \/>\nx + 9 = 7<br \/>\nAnswer:<br \/>\nThe value of x is -2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx + 9 = 7<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx = 7 &#8211;\u00a0 ( +9 )<br \/>\nx = 7 &#8211; 9<br \/>\nx = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -2<\/p>\n<p>Question 2.<br \/>\n8.6 = z &#8211; 3.8<br \/>\nAnswer:<br \/>\nThe value of z is: 12.4<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n8.6 = z &#8211; 3.8<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nz = 8.6 + 3.8<br \/>\nz = 12.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of z is: 12.4<\/p>\n<p>Question 3.<br \/>\n60 = -12r<br \/>\nAnswer:<br \/>\nThe value of r is:\u00a0 -5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n60 = -12r<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nr = 60 \u00f7 ( -12 )<br \/>\nr = -60 \u00f7 12<br \/>\nr = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of r is: -5<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{3}{4}\\)p = 18<br \/>\nAnswer:<br \/>\nThe value of p is: 24<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{3}{4}\\)p = 18<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\np = 18 \u00d7 \\(\\frac{4}{3}\\)<br \/>\np = \\(\\frac{18}{1}\\) \u00d7 \\(\\frac{4}{3}\\)<br \/>\np = \\(\\frac{18 \u00d7 4}{1 \u00d7 3}\\)<br \/>\np = \\(\\frac{24}{1}\\)<br \/>\np = 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of p is: 24<\/p>\n<p><b>Solve the equation. Check your solution. <\/b>(Section 1.2)<\/p>\n<p>Question 5.<br \/>\n2m &#8211; 3 = 13<br \/>\nAnswer:<br \/>\nThe value of m is: 8<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2m &#8211; 3 = 13<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2m = 13 + 3<br \/>\n2m = 16<br \/>\nm = 16 \u00f7 2<br \/>\nm = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is: 8<\/p>\n<p>Question 6.<br \/>\n5 = 10 &#8211; v<br \/>\nAnswer:<br \/>\nThe value of v is: 5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n5 = 10 &#8211; v<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nv= 10 &#8211; 5<br \/>\nv = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of v is: 5<\/p>\n<p>Question 7.<br \/>\n5 = 7w + 8w + 2<br \/>\nAnswer:<br \/>\nThe value of w is: \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n5 = 7w + 8w + 2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5 &#8211; 2 = 7w + 8w<br \/>\n15w = 3<br \/>\nw = 3 \u00f7 15<br \/>\nw = \\(\\frac{1}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: \\(\\frac{1}{5}\\)<\/p>\n<p>Question 8.<br \/>\n-21a + 28a &#8211; 6 = -10.2<br \/>\nAnswer:<br \/>\nThe value of a is: &#8211;\\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-21a + 28a\u00a0 &#8211; 6 = -10.2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-21a + 28a = -10.2 + 6<br \/>\n7a = -4.2<br \/>\na = -4.2 \u00f7 7<br \/>\na= &#8211;\\(\\frac{42}{10}\\) \u00f7 7<br \/>\na = &#8211;\\(\\frac{42}{10}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\na = &#8211;\\(\\frac{42 \u00d7 1}{10 \u00d7 7}\\)<br \/>\na = &#8211; \\(\\frac{6}{10}\\)<br \/>\na = &#8211;\\(\\frac{3}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: &#8211;\\(\\frac{3}{5}\\)<\/p>\n<p>Question 9.<br \/>\n2k &#8211; 3(2k &#8211; 3) = 45<br \/>\nAnswer:<br \/>\nThe value of k is: -9<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2k &#8211; 3 ( 2k &#8211; 3 ) = 45<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSO,<br \/>\n2k &#8211; 3 ( 2k ) + 3 ( 3 ) = 45<br \/>\n2k &#8211; 6k + 9 = 45<br \/>\n2k &#8211; 6k = 45 &#8211; 9<br \/>\n-4k = 36<br \/>\nk = 36 \u00f7 -4<br \/>\nk = -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of k is: -9<\/p>\n<p>Question 10.<br \/>\n68 = \\(\\frac{1}{5}\\)(20x + 50) + 2<br \/>\nAnswer:<br \/>\nThe value of x is: 14<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n68 = \\(\\frac{1}{5}\\) [ 20x + 50 ] + 2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n68 &#8211; 2 = \\(\\frac{1}{5}\\) [ 20x + 50 ]<br \/>\n66 = \\(\\frac{1}{5}\\) [ 20x + 50 ]<br \/>\n66 \u00d7 5 = 20x + 50<br \/>\n330 = 20x + 50<br \/>\n20x = 330 &#8211; 50<br \/>\n20x = 280<br \/>\nx = 280 \u00f7 20<br \/>\nx = 14<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 14<\/p>\n<p><b>Solve the equation. <\/b>(Section 1.3)<\/p>\n<p>Question 11.<br \/>\n3c + 1 = c + 1<br \/>\nAnswer:<br \/>\nThe value of c is: 0<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3c + 1 = c + 1<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\n3c &#8211; c = 1 &#8211; 1<br \/>\n2c = 0<br \/>\nc = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of c is: 0<\/p>\n<p>Question 12.<br \/>\n-8 &#8211; 5n = 64 + 3n<br \/>\nAnswer:<br \/>\nThe value of n is: -9<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-8 &#8211; 5n = 64 + 3n<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-8 &#8211; 64 = 3n + 5n<br \/>\n-72 = 8n<br \/>\nn = -72 \u00f7 8<br \/>\nn = -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n is: -9<\/p>\n<p>Question 13.<br \/>\n2(8q &#8211; 5) = 4q<br \/>\nAnswer:<br \/>\nThe value of q is: \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nTe given equation is:<br \/>\n2 ( 8q &#8211; 5 ) = 4q<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2 ( 8q ) &#8211; 2 ( 5 ) = 4q<br \/>\n16q &#8211; 10 = 4q<br \/>\n16q &#8211; 4q = 10<br \/>\n12q = 10<br \/>\nq = 10 \u00f7 12<br \/>\nq = \\(\\frac{5}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of q is: \\(\\frac{5}{6}\\)<\/p>\n<p>Question 14.<br \/>\n9(y &#8211; 4) &#8211; 7y = 5(3y &#8211; 2)<br \/>\nAnswer:<br \/>\nThe value of y is: -2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n9 ( y &#8211; 4 ) &#8211; 7y = 5 ( 3y &#8211; 2 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n9 ( y ) &#8211; 9 ( 4 ) &#8211; 7y = 5 ( 3y ) &#8211; 5 ( 2 )<br \/>\n9y &#8211; 36 &#8211; 7y = 15y &#8211; 10<br \/>\n2y &#8211; 36 = 15y &#8211; 10<br \/>\n15y &#8211; 2y = 10 &#8211; 36<br \/>\n13y = -26<br \/>\ny = -26 \u00f7 13<br \/>\ny = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: -2<\/p>\n<p>Question 15.<br \/>\n4(g + 8) = 7 + 4g<br \/>\nAnswer:<br \/>\nThe given equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n4 ( g + 8 ) = 7 + 4g<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,the given equation has no solution<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4 ( g ) + 4 ( 8 ) = 7 + 4g<br \/>\n4g + 32 = 7 + 4g<br \/>\n4g &#8211; 4g + 7 = 32<br \/>\n7 = 32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation has no solution.<\/p>\n<p>Question 16.<br \/>\n-4(-5h &#8211; 4) = 2(10h + 8)<br \/>\nAnswer:<br \/>\nThe value of h is: 0<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-4 ( 5h &#8211; 4 ) = 2 ( 10h + 8 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-4 ( 5h ) + 4 ( 4 ) = 2 ( 10h ) + 2 ( 8 )<br \/>\n-20h + 16 = 20h + 16<br \/>\n-20h &#8211; 20h = 1 &#8211; 16<br \/>\n-40h =0<br \/>\nh = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: 0<\/p>\n<p>Question 17.<br \/>\nTo estimate how many miles you are from a thunderstorm, count the seconds between when you see lightning and when you hear thunder. Then divide by 5. Write and solve an equation to determine how many seconds you would count for a thunderstorm that is 2 miles away. (Section 1.1)<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nYou want to hang three equally-sized travel posters on a wall so that the posters on the ends are each 3 feet from the end of the wall. You want the spacing between posters to be equal. Write and solve an equation to determine how much space you should leave between the posters. (Section 1.2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-62.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 62\" width=\"533\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-62.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-62-300x92.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Answer:<br \/>\nThe space you should leave between the posters is: \\(\\frac{3}{2}\\) ft<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-62.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 1 Solving Linear Equations 62\" width=\"533\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-62.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-Solving-Linear-Equations-62-300x92.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><br \/>\nIt is given that you want to hang three equally-sized travel posters on a wall so that the posters on the ends are each 3 feet from the end of the wall. You want the spacing between posters to be equal.<br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nThe total space = 15 ft<br \/>\nThe total spacing covered at the ends = 3 + 3 = 6 ft<br \/>\nLet the space between the equally spaced posters be x<br \/>\nSo,<br \/>\nThe total spacing between the travel posters = 2x + 2x + 2x = 6x ft<br \/>\nSO,<br \/>\nThe total space = ( The total spacing covered at the ends ) + ( The total spacing between the travel posters )<br \/>\n15 = 6 + 6x<br \/>\n6x = 15 &#8211; 6<br \/>\n6x = 9<br \/>\nx = 9 \u00f7 6<br \/>\nx = \\(\\frac{3}{2}\\) ft<br \/>\nHence, from the above,<br \/>\nWe can conclude that the spacing between the travel posters is: \\(\\frac{3}{2}\\) ft<\/p>\n<p>Question 19.<br \/>\nYou want to paint a piece of pottery at an art studio. The total cost is the cost of the piece plus an hourly studio fee. There are two studios to choose from. (Section 1.3)<br \/>\na. After how many hours of the painting are the total costs the same at both studios? Justify your answer.<br \/>\nb. Studio B increases the hourly studio fee by $2. How does this affect your answer in part (a)? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-63.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 63\" width=\"436\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-63.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-63-300x103.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Answer:<br \/>\na)<br \/>\nIt is given that,<br \/>\nThe total cost = Cost of the vase + The hourly studio fee<br \/>\nLet the number of hours be x<br \/>\nSo,<br \/>\nThe total cost for studio A = 10 + 8x<br \/>\nThe total cost of studio B = 16 + 6x<br \/>\nIt is given that the total costs are the same<br \/>\nSo,<br \/>\n10 + 8x = 16 + 6x<br \/>\n8x &#8211; 6x = 16 &#8211; 10<br \/>\n2x = 6<br \/>\nx = 6 \u00f7 2<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the total cost will be the same after 3 hours for both the studios<\/p>\n<p>b)<br \/>\nIt is given that the studio B increases the hourly studio fee by $2<br \/>\nSo,<br \/>\nThe total hourly studio fee for studio B = 6 + 2 = $8<br \/>\nSo,<br \/>\nNow,<br \/>\nAs in part (a), the same process will be repeated but in the studio B&#8217;s hourly fee of $6, we have to put $8<br \/>\nSo,<br \/>\n10 + 8x = 16 + 8x<br \/>\n8x &#8211; 8x = 6 &#8211; 10<br \/>\n10 = 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x has no solutions<\/p>\n<h3><a id=\"Lesson_1.4_Solving_Absolute_Value_Equations\"><\/a>Lesson 1.4 Solving Absolute Value Equations<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you solve an absolute value equation?<br \/>\n<b>EXPLORATION 1<\/b><br \/>\n<b>Solving an Absolute Value Equation Algebraically<\/b><br \/>\n<b>Work with a partner.<\/b> Consider the absolute value equation<br \/>\n| x + 2 | = 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-64.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 64\" width=\"221\" height=\"176\" \/><br \/>\na. Describe the values of x + 2 that make the equation true. Use your description to write two linear equations that represent the solutions of the absolute value equation.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n-| x | = -x<br \/>\nSo,<br \/>\n| x + 2 | = 3<br \/>\nx + 2 = 3<br \/>\nx = 3 &#8211; 2<br \/>\nx = 1<br \/>\nNow,<br \/>\n-| x + 2 | = 3<br \/>\n| x + 2\u00a0 | = -3<br \/>\n-x &#8211; 2 = -3<br \/>\n-x = -3 + 2<br \/>\n-x = -1<br \/>\nx = 1<br \/>\nSo,<br \/>\nThe values of x + 2 that make the equation true is: 3 and 3<br \/>\nThe value of x is: 1 and 1<\/p>\n<p>b. Use the linear equations you wrote in part (a) to find the solutions of the absolute value equation.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n-| x | = -x<br \/>\nSo,<br \/>\n| x + 2 | = 3<br \/>\nx + 2 = 3<br \/>\nx = 3 &#8211; 2<br \/>\nx = 1<br \/>\nNow,<br \/>\n-| x + 2 | = 3<br \/>\n-| x + 2\u00a0 | = -3<br \/>\n-x &#8211; 2 = -3<br \/>\n-x = -3 + 2<br \/>\n-x = -1<br \/>\nx = 1<br \/>\nSo,<br \/>\nThe solutions of | x + 2 | are: 1 and 1<\/p>\n<p>c. How can you use linear equations to solve an absolute value equation?<br \/>\nAnswer:<br \/>\nWe use linear equations to solve an absolute value equation by using the following properties. They are:<br \/>\nA) | x | = x<br \/>\nB) -| x | = -x<\/p>\n<p><b>EXPLORATION 2<br \/>\nSolving an Absolute Value Equation Graphically<br \/>\nWork with a partner.<\/b> Consider the absolute value equation<br \/>\n| x + 2 | = 3.<br \/>\na. On a real number line, locate the point for which x + 2 = 0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-64.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 64.1\" width=\"474\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-64.1.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-64.1-300x28.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + 2 = 0<br \/>\nx = 0 &#8211; 2<br \/>\nx = -2<br \/>\nSo,<br \/>\nOn a real number line, we have to locate the point x = -2<br \/>\nHence,<br \/>\nThe point we have to locate on the real number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-17.jpg\" alt=\"\" width=\"477\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-17.jpg 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-17-300x29.jpg 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>b. Locate the points that are 3 units from the point you found in part (a). What do you notice about these points?<br \/>\nAnswer:<br \/>\nFrom part (a).<br \/>\nWe found that x = -2<br \/>\nNow,<br \/>\nTo locate the points that are 3 units away or 3 units behind from the point you found in part (a), i.e., x = -2<br \/>\nWe know that,<br \/>\n3 units away imply &#8221; Add 3 &#8221;<br \/>\n3 units behind imply &#8221; Subtract 3 &#8221;<br \/>\nNow,<br \/>\nWe have to add 3 and subtract 3 to the point we obtained in part (a)<br \/>\nSo,<br \/>\nWhen we add 3 to x = -2,<br \/>\nx = -2 + 3<br \/>\nx =1<br \/>\nWhen we subtract 3 from x = -2,<br \/>\nx = -2 &#8211; 3<br \/>\nx = -5<br \/>\nHence,<br \/>\nThe points we have to locate in the real number line are: 1 and -5<br \/>\nSo,<br \/>\nThe real number line with the located points is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-18.jpg\" alt=\"\" width=\"477\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-18.jpg 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-18-300x29.jpg 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>c. How can you use a number line to solve an absolute value equation?<br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n| x + 2 | = 3<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n-| x | = -x<br \/>\nSo,<br \/>\n| x + 2 | = 3<br \/>\nx + 2 = 3<br \/>\nx = 3 &#8211; 2<br \/>\nx = 1<br \/>\n&#8211; | x + 2 | = -3<br \/>\n-x &#8211; 2 = -3<br \/>\n-x = -3 + 2<br \/>\n-x = -1<br \/>\nx = 1<br \/>\nSo,<br \/>\nThe values we have to locate in the number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-48882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-19.jpg\" alt=\"\" width=\"477\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-19.jpg 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-19-300x29.jpg 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p><b>EXPLORATION 3<br \/>\nSolving an Absolute Value Equation Numerically<\/b><br \/>\n<b>Work with a partner. <\/b>Consider the absolute value equation<br \/>\n| x + 2 | = 3.<br \/>\na. Use a spreadsheet, as shown, to solve the absolute value equation.<br \/>\nb. Compare the solutions you found using the spreadsheet with those you found in Explorations 1 and 2. What do you notice?<br \/>\nc. How can you use a spreadsheet to solve an absolute value equation?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-65.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 65\" width=\"262\" height=\"208\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow can you solve an absolute value equation?<br \/>\nAnswer:<br \/>\nWe can solve the absolute equation by using the following properties. They are:<br \/>\nA) | x| = x<br \/>\nB) &#8211; | x | = -x<\/p>\n<p>Question 5.<br \/>\nWhat do you like or dislike about the algebraic, graphical, and numerical methods for solving an absolute value equation? Give reasons for your answers.<br \/>\nAnswer:<br \/>\nThe algebraic, numerical, and graphical methods have their own advantages in their own perspective.<br \/>\nThe algebraic methods used to solve the linear equations whereas the graphical method used to indicate the linear equations.<br \/>\nThe numerical method is applicable for mathematical operations<\/p>\n<p><b>1.4 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Graph the solutions, if possible.<\/b><\/p>\n<p>Question 1.<br \/>\n| x | = 10<br \/>\nAnswer:<br \/>\nThe value of x is: 10<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x | = 10<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\nx = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 10<\/p>\n<p>Question 2.<br \/>\n| x &#8211; 1 | = 4<br \/>\nAnswer:<br \/>\nThe value of x is: 5<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; 1 | = 4<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\nx &#8211; 1 = 4<br \/>\nx = 4 + 1<br \/>\nx = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 5<\/p>\n<p>Question 3.<br \/>\n| 3 + x | = -3<br \/>\nAnswer:<br \/>\nThe value of x is: -6<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 3 + x | = -3<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\nx + 3 = -3<br \/>\nx = -3 &#8211; 3<br \/>\nx = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -6<\/p>\n<p><b>Solve the equation. Check your solutions.<\/b><\/p>\n<p>Question 4.<br \/>\n| x &#8211; 2 | + 5 = 9<br \/>\nAnswer:<br \/>\nThe value of x is: 6<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; 2 | + 5 = 9<br \/>\n| x &#8211; 2 | = 9 &#8211; 5<br \/>\n| x &#8211; 2 | = 4<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\nx &#8211; 2 = 4<br \/>\nx = 4 + 2<br \/>\nx = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 6<\/p>\n<p>Question 5.<br \/>\n4 | 2x + 7 | = 16<br \/>\nAnswer:<br \/>\nThe value of x is: &#8211;\\(\\frac{3}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n4 | 2x + 7 | = 16<br \/>\n| 2x + 7 | = 16 \u00f7 4<br \/>\n| 2x + 7| = 4<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\n2x + 7 = 4<br \/>\n2x = 4 &#8211; 7<br \/>\n2x = -3<br \/>\nx = &#8211;\\(\\frac{3}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: &#8211;\\(\\frac{3}{2}\\)<\/p>\n<p>Question 6.<br \/>\n-2 | 5x &#8211; 1 | &#8211; 3 = -11<br \/>\nAnswer:<br \/>\nThe value of x is: 1<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n-2 | 5x &#8211; 1 | &#8211; 3 = -11<br \/>\n-2 | 5x &#8211; 1 | = -11 + 3<br \/>\n-2 | 5x &#8211; 1 | = -8<br \/>\n| 5x &#8211; 1 | = -8 \u00f7 ( -2 )<br \/>\n| 5x &#8211; 1 | = 4<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\n5x &#8211; 1 = 4<br \/>\n5x = 4 + 1<br \/>\n5x = 5<br \/>\nx = 5 \u00f7 5<br \/>\nx = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 1<\/p>\n<p>Question 7.<br \/>\nFor a poetry contest, the minimum length of a poem is 16 lines. The maximum length is 32 lines. Write an absolute value equation that represents the minimum and maximum lengths.<br \/>\nAnswer:<br \/>\nThe minimum value length is: 16<br \/>\nThe maximum length is: 32<\/p>\n<p>Explanation:<br \/>\nIt is given that for a poetry contest, the minimum length of a poem is 16 lines. The maximum length is 32 lines.<br \/>\nSo,<br \/>\nThe absolute value equation that represents the minimum length of a poem = | The minimum length of a poem |<br \/>\n= | 16 |<br \/>\n= 16<br \/>\nThe absolute value equation that represents the maximum length of a poem = | The maximum length of a poem |<br \/>\n= | 32 |<br \/>\n= 32<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe minimum value length is: 16<br \/>\nThe maximum length is: 32<\/p>\n<p><b>Solve the equation. Check your solutions.<\/b><\/p>\n<p>Question 8.<br \/>\n| x + 8 | = | 2x + 1 |<br \/>\nAnswer:<br \/>\nThe value of x is: 7<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x + 8 | = | 2x + 1 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\nx + 8 = 2x + 1<br \/>\n2x &#8211; x = 8 &#8211; 1<br \/>\nx = 7<br \/>\nHence from the above,<br \/>\nWe can conclude that the value of x is: 7<\/p>\n<p>Question 9.<br \/>\n3 | x &#8211; 4 | = | 2x + 5 |<br \/>\nAnswer:<br \/>\nThe value of x is: 17<\/p>\n<p>Explanation:<br \/>\nThe given absolute equation is:<br \/>\n3 | x &#8211; 4 | = | 2x + 5 |<br \/>\nWe know that,<br \/>\n| x |\u00a0 = x<br \/>\nSo,<br \/>\n3 ( x &#8211; 4 ) = 2x + 5<br \/>\n3 ( x ) &#8211; 3 ( 4 ) = 2x + 5<br \/>\n3x &#8211; 12 = 2x + 5<br \/>\n3x &#8211; 2x = 5 + 12<br \/>\nx = 17<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 17<\/p>\n<p><b>Solve the equation. Check your solutions.<\/b><\/p>\n<p>Question 10.<br \/>\n| x + 6 | = 2x<br \/>\nAnswer:<br \/>\nThe value of x is: 6<\/p>\n<p>Explanation:<br \/>\nThe absolute value equation is:<br \/>\n| x + 6 | = 2x<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\nx + 6 = 2x<br \/>\n2x &#8211; x = 6<br \/>\nx = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 6<\/p>\n<p>Question 11.<br \/>\n| 3x &#8211; 2 | = x<br \/>\nAnswer:<br \/>\nThe value of x is: 1<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 3x &#8211; 2 | = x<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\n3x &#8211; 2 = x<br \/>\nSoo,<br \/>\n3x &#8211; x = 2<br \/>\n2x = 2<br \/>\nx = 2 \u00f7 2<br \/>\nx = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 1<\/p>\n<p>Question 12.<br \/>\n| 2 + x | = | x &#8211; 8 |<br \/>\nAnswer:<br \/>\nThe given absolute value equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 2 + x | = | x &#8211; 8 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\n2 + x = x &#8211; 8<br \/>\n2 = x &#8211; x &#8211; 8<br \/>\n2 = -8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value equation has no solution<\/p>\n<p>Question 13.<br \/>\n| 5x &#8211; 2 | = | 5x + 4 |<br \/>\nAnswer:<br \/>\nThe given absolute value equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 5x &#8211; 2 | = | 5x + 4 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\nSo,<br \/>\n5x &#8211; 2 = 5x + 4<br \/>\n5x &#8211; 5x &#8211; 2 = 4<br \/>\n-2 = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value equation has no solution<\/p>\n<h3><a id=\"Solving_Absolute_Value_Equations_1.4_Exercises\"><\/a>Solving Absolute Value Equations 1.4 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b><br \/>\nWhat is an extraneous solution?<br \/>\nAnswer:<br \/>\nExtraneous solutions are values that we get when solving equations that are not really solutions to the equation.<br \/>\nExample for extraneous solution:<br \/>\n| 5x &#8211; 2 | = | 5x + 4 |<\/p>\n<p>Question 2.<br \/>\n<b>WRITING <\/b><br \/>\nWithout calculating, how do you know that the equation | 4x &#8211; 7 | = -1 has no solution?<br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n| 4x &#8211; 7 | = -1<br \/>\nWe know that,<br \/>\nAn absolute value can never equal a negative number.<br \/>\nSo,<br \/>\nBy the above,<br \/>\nWe can say that<br \/>\n| 4x &#8211; 7 | must not equal to a negative number.<br \/>\nHence, from the above,<br \/>\nWe can conclude that | 4x &#8211; 7 | = -1 has no solution without calculating its solution<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u221210, simplify the expression.<\/b><\/p>\n<p>Question 3.<br \/>\n| -9 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q3.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q3\" width=\"95\" height=\"35\" \/><\/p>\n<p>Question 4.<br \/>\n&#8211; | 15 |<br \/>\nAnswer:<br \/>\nThe value of -| 15 | is: -15<\/p>\n<p>Explanation:<br \/>\nThe given absolute value is: -| 15 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n| -x | = x<br \/>\n-| x | = -x<br \/>\nSo,<br \/>\n-| 15 | = -15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of -| 15 | is: -15<\/p>\n<p>Question 5.<br \/>\n| 14 | &#8211; | -14 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q5.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q5\" width=\"277\" height=\"37\" \/><\/p>\n<p>Question 6.<br \/>\n| -3 | + | 3 |<br \/>\nAnswer:<\/p>\n<p>The value of | -3 | + | 3 | is: 6<\/p>\n<p>Explanation:<br \/>\nThe given absolute value expression is:<br \/>\n| -3 | + | 3 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n| -x | = x<br \/>\n-| x | = -x<br \/>\nSo,<br \/>\n| -3 | + | 3 |<br \/>\n= 3 + 3<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of | -3 | + | 3 | is: 6<\/p>\n<p>Question 7.<br \/>\n&#8211; | -5 \u2022 (-7) |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q7.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q7\" width=\"291\" height=\"39\" \/><\/p>\n<p>Question 8.<br \/>\n| -0.8 \u2022 10 |<br \/>\nAnswer:<br \/>\nThe value of | -0.8 \u22c5 10 | is: 8<\/p>\n<p>Explanation:<br \/>\nThe given absolute value expression is:<br \/>\n| -0.8 \u22c5 10 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n| -x | = x<br \/>\n-| x | = -x<br \/>\nSo,<br \/>\n| -0.8 \u22c5 10 |<br \/>\n= | &#8211; ( 8 \u2044 10 ) \u22c5 ( 10 \u2044 1 ) |<br \/>\n= | &#8211; ( 8 \u00d7 10 ) \u2044 ( 10 \u00d7 1 ) |<br \/>\n= | -8 |<br \/>\n= 8<br \/>\nhence, from the above,<br \/>\nWe can conclude that the value of | -0.8 \u22c5 10 | is: 8<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-66.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 66\" width=\"57\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q9.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q9\" width=\"197\" height=\"62\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-67.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 67\" width=\"72\" height=\"46\" \/><br \/>\nAnswer:<br \/>\nThe value of | -12 \u2044 4 | is: 3<\/p>\n<p>Explanation:<br \/>\nThe given absolute value expression is: | -12 \u2044 4 |<br \/>\nWe know that,<br \/>\n| x | = x<br \/>\n| -x | = x<br \/>\n&#8211; | x | = -x<br \/>\nSo,<br \/>\n| -12 \u2044 4 | = | -3 |<br \/>\n= 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of | -12 \u2044 4 | is: 3<\/p>\n<p><b>In Exercises 11\u221224, solve the equation. Graph the solution(s), if possible.<\/b><\/p>\n<p>Question 11.<br \/>\n| w | = 6<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q11.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q11\" width=\"357\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q11.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q11-300x126.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Question 12.<br \/>\n| r | = -2<br \/>\nAnswer:<br \/>\nThe absolute value of a number must be greater than or equal to 0 and can not be equal to -2.<br \/>\nHence,<br \/>\nThe given absolute eqution has no solution<\/p>\n<p>Question 13.<br \/>\n| y | = -18<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q13.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q13\" width=\"559\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q13.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q13-300x65.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 14.<br \/>\n| x | = 13<br \/>\nAnswer:<br \/>\nThe value of x is: 13 or -13<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x | = 13<br \/>\nWe know that,<br \/>\n|x | = x<br \/>\n&#8211; | x | = -x<br \/>\nSo,<br \/>\n| x | = 13 or &#8211; 13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 13 or -13<\/p>\n<p>Question 15.<br \/>\n| m + 3 | = 7<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q15.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q15\" width=\"419\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q15.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q15-300x155.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Question 16.<br \/>\n| q &#8211; 8 | = 14<br \/>\nAnswer:<br \/>\nThe value of q is: 22 or -6<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| q &#8211; 8 | = 14<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nq &#8211; 8 = 14\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 q &#8211; 8 = -14<br \/>\nq = 14 + 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0q = -14 + 8<br \/>\nq = 22\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0q = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of q is: 22 or -6<\/p>\n<p>Question 17.<br \/>\n| -3d | = 15<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q17.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q17\" width=\"407\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q17.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q17-300x199.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-68.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 68\" width=\"66\" height=\"49\" \/><br \/>\nAnswer:<br \/>\nThe value of t is: 12 or -12<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| t \/ 2 | = 12<br \/>\nWe know that,<br \/>\n| x | = x\u00a0 for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nt \/ 2 = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0t \/ 2 = -6<br \/>\nt = 6 \u00d7 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 6 \u00d7 -2<br \/>\nt = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0t = -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of t is: 12 or -12<\/p>\n<p>Question 19.<br \/>\n| 4b &#8211; 5 | = 19<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q19.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q19\" width=\"473\" height=\"358\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q19.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q19-300x227.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 20.<br \/>\n| x &#8211; 1 | + 5 = 2<br \/>\nAnswer:<br \/>\nThe given absolute value equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; 1 | + 5 = 2<br \/>\n| x &#8211; 1 | = 2 &#8211; 5<br \/>\n| x &#8211; 1\u00a0 | = -3<br \/>\nWe know that,<br \/>\nThe absolute value of an equation must be greater than or equal to zero<br \/>\nSo,<br \/>\n| x &#8211; 1 | = -3 has no solution<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value equation has no solution<\/p>\n<p>Question 21.<br \/>\n-4 | 8 &#8211; 5n | = 13<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q21.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q21\" width=\"572\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q21.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q21-300x130.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-69.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 69\" width=\"124\" height=\"47\" \/><br \/>\nAnswer:<br \/>\nThe value of y is: -3 or 6<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n-3 | 1 &#8211; ( 2 \/ 3 ) y | = -9<br \/>\n| 1 &#8211; (2 \/ 3\u00a0 ) y | = -9 \u00f7 ( -3 )<br \/>\n| 1 &#8211; ( 2 \/ 3 ) y | = 3<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n1 &#8211; ( 2 \/ 3 ) y = 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1 &#8211; ( 2 \/3 ) y = -3<br \/>\n2\/3 y = 1 &#8211; 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02\/3 y = 1 + 3<br \/>\n2 \/ 3 y = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2 \/ 3 y = 4<br \/>\n2y = -2 \u00d7 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02y = 4 \u00d7 3<br \/>\n2y = -6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2y = 12<br \/>\ny = -6 \u00f7 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = 12 \u00f7 2<br \/>\ny = -3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: -3 or 6<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-70.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 70\" width=\"137\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q23.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q23\" width=\"271\" height=\"662\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q23.png 271w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q23-123x300.png 123w\" sizes=\"(max-width: 271px) 100vw, 271px\" \/><\/p>\n<p>Question 24.<br \/>\n9 | 4p + 2 | + 8 = 35<br \/>\nAnswer:<br \/>\nThe value of p is: 1 \/ 4 or -5 \/ 4<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n9 | 4p + 2 | + 8 = 35<br \/>\n9 | 4p + 2 | = 35 &#8211; 8<br \/>\n9 | 4p + 2 | = 27<br \/>\n| 4p + 2 | = 27 \u00f7 9<br \/>\n| 4p + 2 | = 3<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n4p + 2 = 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4p + 2 = -3<br \/>\n4p = 3 &#8211; 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04p = -3 &#8211; 2<br \/>\n4p = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04p = -5<br \/>\np = 1 \/ 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0p = -5 \/ 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of p is: 1 \/ 4 or -5 \/ 4<\/p>\n<p>Question 25.<br \/>\n<b>WRITING EQUATIONS<\/b><br \/>\nThe minimum distance from Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles.<br \/>\na. Represent these two distances on a number line.<br \/>\nb. Write an absolute value equation that represents the minimum and maximum distances.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q25.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q25\" width=\"545\" height=\"483\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q25.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q25-300x266.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 26.<br \/>\n<b>WRITING EQUATIONS<\/b><br \/>\nThe shoulder heights of the shortest and tallest miniature poodles are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-71.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 71\" width=\"273\" height=\"173\" \/><br \/>\na. Represent these two heights on a number line.<br \/>\nb. Write an absolute value equation that represents these heights.<\/p>\n<p>Answer:<br \/>\na)<br \/>\nThe number line that represents the two heights on a number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-20.jpg\" alt=\"\" width=\"556\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-20.jpg 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-20-300x117.jpg 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\nb)<br \/>\nThe minimum shoulder height = ( 15 &#8211; 10 ) \/ 2<br \/>\n= 5 \/ 2<br \/>\n= 2.5 inches<br \/>\nThe maximum shoulder height = 10 + 2.5<br \/>\n= 12.5 inches<br \/>\nNow,<br \/>\nLet the heights between poodles be x.<br \/>\nHence,<br \/>\nThe absolute value equation is:<br \/>\n| x &#8211; 12.5 | = 2.5<\/p>\n<p><b>USING STRUCTURE In Exercises 27\u221230, match the absolute value equation with its graph without solving the equation.<\/b><\/p>\n<p>Question 27.<br \/>\n| x + 2 | = 4<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q27.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q27\" width=\"562\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q27.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q27-300x30.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 28.<br \/>\n| x + 4 | = 2<br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n| x + 4 | = 2<br \/>\nTo find the halfway point, made the absolute value equation equal to 0.<br \/>\nSo,<br \/>\n| x + 4\u00a0 | = 0<br \/>\nSo,<br \/>\nx = -4<br \/>\nFrom the given absolute value equation,<br \/>\nWe can say that the distance from the halfway point to the minimum and maximum points is: 2<\/p>\n<p>Question 29.<br \/>\n| x &#8211; 2 | = 4<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q29.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q29\" width=\"553\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q29.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q29-300x30.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 30.<br \/>\n| x + 4 | = 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-72.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 72\" width=\"362\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-72.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-72-300x246.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<p>Answer:<\/p>\n<p><b>In Exercises 31\u221234, write an absolute value equation that has the given solutions.<\/b><\/p>\n<p>Question 31.<br \/>\nx = 8 and x = 18<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q31.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q31\" width=\"466\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q31.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q31-300x161.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 32.<br \/>\nx = -6 and x = 10<br \/>\nAnswer:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; 2 | = 8<\/p>\n<p>Explanation:<br \/>\nThe given values of x are:<br \/>\nx = -6 and x = 10<br \/>\nNow,<br \/>\nThe halfway point between 10 and -6 = [ 10 &#8211; ( -6 ) ] \/ 2<br \/>\n= [ 10 + 6 ] \/ 2<br \/>\n= 16 \/ 2<br \/>\n= 8<br \/>\nThe minimum distance from the halfway point = 8 &#8211; 6 = 2<br \/>\nHence,<br \/>\nThe absolute value equation is:<br \/>\n| x &#8211; 2 | = 5<\/p>\n<p>Question 33.<br \/>\nx = 2 and x = 9<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q33.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q33\" width=\"516\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q33.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q33-300x144.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 34.<br \/>\nx = -10 and x = -5<\/p>\n<p>Answer:<br \/>\nThe given values of x are:<br \/>\nx = -10 and x = -5<br \/>\nNow,<br \/>\nThe halfway point between -10 and -5 = [ 10 &#8211; ( 5 ) ] \/ 2<br \/>\n= [ 10 &#8211; 5 ] \/ 2<br \/>\n= 5 \/ 2<br \/>\n= 2.5<br \/>\nSo,<br \/>\nThe minimum value from the half-point = 2.5 + ( -10 )<br \/>\n= 2.5 &#8211; 10<br \/>\n= -7.5<br \/>\nHence,<br \/>\nThe absolute value equation is:<br \/>\n| x &#8211; ( -7.5 ) | = 2.5<br \/>\n| x + 7.5 | = 2.5<\/p>\n<p><b>In Exercises 35\u221244, solve the equation. Check your solutions.\u00a0<\/b><\/p>\n<p>Question 35.<br \/>\n| 4n &#8211; 15 | = | n |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q35.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q35\" width=\"461\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q35.png 461w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q35-291x300.png 291w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Question 36.<br \/>\n| 2c + 8 | = | 10c |<br \/>\nAnswer:<br \/>\nThe values of c are: 1 and 2 \/ 3<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 2c + 8 | = | 10c |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nNow,<br \/>\n2c + 8 = 10c\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2c + 8 = -10c<br \/>\n10c &#8211; 2c = 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02c + 10c = 8<br \/>\n8c = 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 12c = 8<br \/>\nc = 8 \/ 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 c = 8 \/ 12<br \/>\nc = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 c = 2 \/3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of c are: 1 and 2 \/ 3<\/p>\n<p>Question 37.<br \/>\n| 2b &#8211; 9 | = | b &#8211; 6 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q37.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q37\" width=\"537\" height=\"590\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q37.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q37-273x300.png 273w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 38.<br \/>\n| 3k &#8211; 2 | = 2 | k + 2 |<br \/>\nAnswer:<br \/>\nThe values of k are: 6 and -2 \/ 5<\/p>\n<p>Explanation:<br \/>\nThe given absolute equation is:<br \/>\n| 3k &#8211; 2 | = 2 | k + 2 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n2 ( k + 2 ) = 3k &#8211; 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2 ( k + 2 ) = &#8211; ( 3k &#8211; 2 )<br \/>\n2k + 4 = 3k &#8211; 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02k + 4 = -3k + 2<br \/>\n3k &#8211; 2k = 4 + 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02k + 3k = 2 &#8211; 4<br \/>\nk = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a05k = -2<br \/>\nk = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0k = -2 \/ 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of k are: 6 and -2 \/ 5<\/p>\n<p>Question 39.<br \/>\n4 | p &#8211; 3 | = | 2p + 8 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q39.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q39\" width=\"562\" height=\"738\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q39.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q39-228x300.png 228w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 40.<br \/>\n2 | 4w &#8211; 1 | = 3 | 4w + 2 |<br \/>\nAnswer:<br \/>\nThe value of w is: -2<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n2 | 4w &#8211; 1 | = 3 | 4w+ 2 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n2 ( 4w &#8211; 1 ) = 3 ( 4w + 2 )\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 -2 ( 4w &#8211; 1 ) = -3 ( 4w + 2 )<br \/>\n8w &#8211; 2 = 12w + 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 -8w + 2 = -12w -6<br \/>\n12w &#8211; 8w = -6 &#8211; 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 -12w + 8w = 6 + 2<br \/>\n4w = -8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0-4w = 8<br \/>\nw = -8 \/ 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 w = 8 \/ -4<br \/>\nw = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 w = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: -2<\/p>\n<p>Question 41.<br \/>\n| 3h + 1 | = 7h<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q41.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q41\" width=\"578\" height=\"644\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q41.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q41-269x300.png 269w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 42.<br \/>\n| 6a &#8211; 5 | = 4a<br \/>\nAnswer:<br \/>\nThe value of a is: 5 \/ 2 and 1 \/ 2<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 6a &#8211; 5 | = 4a<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n6a &#8211; 5 = 4a\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6a &#8211; 5 = -4a<br \/>\n6a &#8211; 4a = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a06a + 4a = 5<br \/>\n2a = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a010a = 5<br \/>\na = 5 \/ 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = 5 \/ 10<br \/>\na = 5 \/ 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0a = 1 \/ 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of a are: 5 \/ 2 and 1 \/ 2<\/p>\n<p>Question 43.<br \/>\n| f &#8211; 6 | = | f + 8 |<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q43.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q43\" width=\"492\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q43.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q43-283x300.png 283w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 44.<br \/>\n| 3x &#8211; 4 | = | 3x &#8211; 5 |<br \/>\nAnswer:<br \/>\nThe given absolute value equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 3x &#8211; 4 | = | 3x &#8211; 5 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n3x &#8211; 4 = 3x &#8211; 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8211; ( 3x &#8211; 4 ) = &#8211; ( 3x &#8211; 5 )<br \/>\n4 = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04 = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value equation has no solution<\/p>\n<p>Question 45.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nStarting from 300 feet away, a car drives toward you. It then passes by you at a speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds is given by the equation d = | 300 &#8211; 48t |. At what times is the car 60 feet from you?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q45.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q45\" width=\"572\" height=\"511\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q45.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q45-300x268.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYour friend says that the absolute value equation | 3x + 8 | &#8211; 9 = -5 has no solution because the constant on the right side of the equation is negative. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 3x + 8 | &#8211; 9 = -5<br \/>\nWe know that,<br \/>\nThe absolute value equation value must have greater than or equal to 0<br \/>\nBut here<br \/>\nThe value of the absolute value equation is less than 0<br \/>\nHence,<br \/>\nThe given absolute value equation has no solution.<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct.<\/p>\n<p>Question 47.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou randomly survey students about year-round school. The results are shown in the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-73.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 73\" width=\"238\" height=\"162\" \/><br \/>\nThe error given in the graph means that the actual percentage could be 5% more or 5% less than the percent reported by the survey.<br \/>\na. Write and solve an absolute value equation to find the least and greatest percents of students who could be in favor of the year-round school.<br \/>\nb. A classmate claims that \\(\\frac{1}{3}\\) of the student body is actually in favor of the year-round school. Does this conflict with the survey data? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q47.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q47\" width=\"567\" height=\"418\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q47.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q47-300x221.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.<br \/>\na. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights.<br \/>\nAnswer:<br \/>\nIt is given that the recommended weight of a soccer ball is 430 grams and the actual weight is allowed to vary up to 20 grams<br \/>\nHence,<br \/>\nThe absolute value equation that represents the minimum and maximum acceptable soccer ball weights is:<br \/>\n| x &#8211; 430 | = 20<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx &#8211; 430 = 20\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x &#8211; 430 = -20<br \/>\nx = 20 + 430\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = -20 + 430<br \/>\nx = 460 grams\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = 410 grams<br \/>\nHence, from the above,<br \/>\nWe can conclude that the maximum and minimum acceptable soccer weights respectively are: 460 grams and 410 grams<\/p>\n<p>b. A soccer ball weighs 423 grams. Due to wear and tear, the weight of the ball decreases by 16 grams. Is the weight acceptable? Explain.<br \/>\nAnswer:<br \/>\nThe weight that caused due to wear and tear is not acceptable<\/p>\n<p>Explanation:<br \/>\nFrom the above problem,<br \/>\nWe get the maximum weight of the soccer ball to be 460 grams with 20 grams increase or decreased to the weight of the ball<br \/>\nNow,<br \/>\nIt is given that the weight of the ball is decreased by 16 grams due to wear and tear<br \/>\nSo,<br \/>\nThe weight of the ball now = 460 &#8211; 16 = 444 grams<br \/>\nBut it is given that the weight of the ball becomes 423 grams due to wear and tear.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the weight is not acceptable<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 49 and 50, describe and correct the error in solving the equation.<\/b><\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-74.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 74\" width=\"323\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-74.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-74-300x161.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q49.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q49\" width=\"559\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q49.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q49-300x47.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-75.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 75\" width=\"329\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-75.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-75-300x202.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Answer:<br \/>\nThe values of x are: -2 and -4 \/ 3<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 5x + 8 | = x<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = &#8211; x for x &lt; 0<br \/>\nSo,<br \/>\n5x + 8 = x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5x + 8 = -x<br \/>\n5x &#8211; x = -8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5x + x = -8<br \/>\n4x = -8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6x = -8<br \/>\nx = -8 \/ 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = -8 \/ 6<br \/>\nx = -2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = -4 \/ 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of x are: -2 and -4 \/ 3<\/p>\n<p>Question 51.<br \/>\n<b>ANALYZING EQUATIONS<\/b><br \/>\nWithout solving completely, place each equation into one of the three categories.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-76.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 76\" width=\"329\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-76.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-76-300x180.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q51.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q51\" width=\"576\" height=\"641\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q51.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q51-270x300.png 270w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nFill in the equation <img loading=\"lazy\" class=\"alignnone size-full wp-image-33844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-77.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 77\" width=\"115\" height=\"29\" \/> with a, b, c, or d so that the equation is graphed correctly.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-77.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 77.1\" width=\"324\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-77.1.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-77.1-300x60.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Answer:<\/p>\n<p><b>ABSTRACT REASONING<br \/>\nIn Exercises 53\u221256, complete the statement with always, sometimes, or never. Explain your reasoning.<\/b><\/p>\n<p>Question 53.<br \/>\nIf x<sup>2<\/sup> = a<sup>2<\/sup>, then | x | is ________ equal to | a |.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q53.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q53\" width=\"534\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q53.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q53-300x54.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 54.<br \/>\nIf a and b are real numbers, then | a &#8211; b | is _________ equal to | b &#8211; a |.<br \/>\nAnswer:<br \/>\nIf a and b are real numbers, then<br \/>\n| a &#8211; b | is equal to | b &#8211; a |<\/p>\n<p>Explanation:<br \/>\nLet,<br \/>\n| a | = 5 and | b | = 9<br \/>\nWe know that,<br \/>\n| x | =x for\u00a0 x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n| a &#8211; b | = | 5 &#8211; 9 |<br \/>\n= | -4 | = 4<br \/>\n| b &#8211; a | = | 9 &#8211; 5 |<br \/>\n=\u00a0 | 4 |<br \/>\n= 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that value of<br \/>\n| a &#8211; b | is equal to | b &#8211; a | if a and b are real numbers<\/p>\n<p>Question 55.<br \/>\nFor any real number p, the equation | x &#8211; 4 | = p will ________ have two solutions.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q55.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q55\" width=\"519\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q55.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q55-300x72.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 56.<br \/>\nFor any real number p, the equation | x &#8211; p | = 4 will ________ have two solutions.<br \/>\nAnswer:<br \/>\nFor any real number,<br \/>\n| x &#8211; p | = 4 will have two solutions<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; p | = 4<br \/>\nLet the value of p be 1<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = &#8211; x for x &lt; 0<br \/>\nSo,<br \/>\n| x &#8211; 1 | = 4<br \/>\n| x &#8211; 1 | = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 | x &#8211; 1 | = -4<br \/>\nx = 4 + 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = -4 + 1<br \/>\nx = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\n| x &#8211; p | = 4 will have two solutions for any real number p<\/p>\n<p>Question 57.<br \/>\n<b>WRITING<\/b><br \/>\nExplain why absolute value equations can have no solution, one solution, or two solutions. Give an example of each case.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q57.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q55\" width=\"575\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q57.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q57-300x174.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 58.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nDescribe a real-life situation that can be modeled by an absolute value equation with the solutions x = 62 and x = 72.<br \/>\nAnswer:<br \/>\nSuppose in a school, an exam is conducted. In that examination, 67% of the students are passed. If the error of the pass percentage is 5 %, then what are the minimum and the maximum number of students passed in the examination?<br \/>\nNow,<br \/>\nThe absolute value equation for the given real-life situation is:<br \/>\n| x &#8211; 67 | = 5<br \/>\nWe know that,<br \/>\n| x | = x for x&gt; 0<br \/>\n| x | =-x for x &lt; 0<br \/>\nSo,<br \/>\nx &#8211; 67 = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x &#8211; 67 = -5<br \/>\nx = 5 + 67\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = -5 + 67<br \/>\nx = 72\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = 62<br \/>\nHence, from the above,<br \/>\nWe can conclude that the minimum and maximum number of students passed in the examination\u00a0 respectively are: 72 and 67<\/p>\n<p>Question 59.<br \/>\n<b>CRITICAL THINKING<\/b><br \/>\nSolve the equation shown. Explain how you found your solution(s).<br \/>\n8 | x + 2 | &#8211; 6 = 5 | x + 2 | + 3<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59\" width=\"383\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59-242x300.png 242w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59-i.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59-i\" width=\"410\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59-i.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q59-i-246x300.png 246w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/p>\n<p>Question 60.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe circle graph shows the results of a survey of registered voters on the day of an election.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-78.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 78\" width=\"276\" height=\"231\" \/><br \/>\nThe error given in the graph means that the actual percentage could be 2% more or 2% less than the percent reported by the survey.<br \/>\na. What are the minimum and maximum percents of voters who could vote Republican?<br \/>\nAnswer:<br \/>\nThe minimum percentage of voters for Republicans is: 40%<br \/>\nThe maximum percentage of voters for Republicans is: 44 %<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-78.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 78\" width=\"276\" height=\"231\" \/><br \/>\nFrom the graph,<br \/>\nThe vote percentage for Republicans is: 42 %<br \/>\nThe error percentage is: \u00b12%<br \/>\nSo,<br \/>\nThe absolute value equation for the maximum and the minimum number of voters is:<br \/>\n| x &#8211; 42 | = 2<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx &#8211; 42 = 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x &#8211; 42 = -2<br \/>\nx = 2 + 42\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = -2 + 42<br \/>\nx = 44\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe minimum percentage of voters for Republicans is: 40%<br \/>\nThe maximum percentage of voters for Republicans is: 44 %<\/p>\n<p>b. How can you use absolute value equations to represent your answers in part (a)?<br \/>\nAnswer:<br \/>\nFrom the property of absolute values,<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nFrom the part ( a ),<br \/>\nThe absolute value equation is:<br \/>\n| x &#8211; 42 | = 2<br \/>\nSo,<br \/>\nx &#8211; 42 = 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x &#8211; 42 = -2<br \/>\nx = 2 + 42\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = -2 + 42<br \/>\nx = 44\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can use absolute values in the above way to represent the answers<\/p>\n<p>c. One candidate receives 44% of the vote. Which party does the candidate belong to? Explain.<br \/>\nAnswer:<br \/>\nThe candidate of the Republican party receives 44 % of the vote.<\/p>\n<p>Explanation:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-78.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 78\" width=\"276\" height=\"231\" \/><br \/>\nFrom the above graph,<br \/>\nWe can say that,<br \/>\nThe percentage of the vote received by the candidate of the Republican party = 42 %<br \/>\nThe error percentage = \u00b1 2 %<br \/>\nSo,<br \/>\nNow,<br \/>\nThe percentage of the vote received by the Republicans = 42 + 2\u00a0 ( or ) 42 &#8211; 2<br \/>\n= 44 ( or ) 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that the candidate of the Republican party received the 44 % of the vote<\/p>\n<p>Question 61.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nHow many solutions does the equation a | x + b | + c = d have when a &gt; 0 and c = d? when a &lt; 0 and c &gt; d? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q61.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q61\" width=\"523\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q61.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q61-283x300.png 283w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Identify the property of equality that makes Equation 1 and Equation 2 equivalent. (Section 1.1)<\/b><\/p>\n<p>Question 62.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-79.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 79\" width=\"230\" height=\"80\" \/><\/p>\n<p>Answer:<br \/>\nThe given equations are:<br \/>\nEquation 1: 3x + 8 = x &#8211; 1<br \/>\nEquation 2: 3x + 9= x<br \/>\nFrom Equation 1,<br \/>\n3x + 8 = x &#8211; 1<br \/>\n3x + 8 + 1 = x<br \/>\n3x + 9 = x<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can get Equation2 by rearranging the Equation 1<\/p>\n<p>Question 63.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-80.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 80\" width=\"197\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q63.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q63\" width=\"521\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q63.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q63-300x32.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p><b>Use a geometric formula to solve the problem.<\/b><\/p>\n<p>Question 64.<br \/>\nA square has an area of 81 square meters. Find the side length.<br \/>\nAnswer:<br \/>\nThe side length of the square is: 9 meters<\/p>\n<p>Explanation:<br \/>\nThe given area of the square is: 81 square meters<br \/>\nWe know that,<br \/>\nArea of the square = Side \u00d7 Side<br \/>\n81 = Side \u00d7 Side<br \/>\nSide\u00b2 = 81<br \/>\nApply square root on both sides<br \/>\n\u221aSide\u00b2 = \u221a81<br \/>\nSide = 9 meters<br \/>\nHence, from the above,<br \/>\nWe can conclude that the side of the square is: 9 meters<\/p>\n<p>Question 65.<br \/>\nA circle has an area of 36\u03c0 square inches. Find the radius.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q65.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q65\" width=\"332\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q65.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q65-300x237.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p>Question 66.<br \/>\nA triangle has a height of 8 feet and an area of 48 square feet. Find the base.<br \/>\nAnswer:<br \/>\nThe base of the triangle is: 12 feet<\/p>\n<p>Explanation:<br \/>\nIt is given that a triangle has a height of 8 feet and an area of 48 square feet<br \/>\nWe know that,<br \/>\nThe area of the triangle = ( 1 \/\u00a0 2 ) \u00d7 Base \u00d7 Height<br \/>\n48 = ( 1 \/ 2 ) \u00d7 Base \u00d7 8<br \/>\nBase \u00d7 8 = 48 \u00d7 2<br \/>\nBase = ( 48 \u00d7 2 ) \u00f7 8<br \/>\nBase = 96 \u00f7 8<br \/>\nBase = 12 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the base of the triangle is: 12 feet<\/p>\n<p>Question 67.<br \/>\nA rectangle has a width of 4 centimeters and a perimeter of 26 centimeters. Find the length.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q67.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q67\" width=\"409\" height=\"290\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q67.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.4-Q67-300x213.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<h3><a id=\"Lesson_1.5_Rewriting_Equations_and_Formulas\"><\/a>Lesson 1.5 Rewriting Equations and Formulas<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you use a formula for one measurement to write a formula for a different measurement?<br \/>\nAnswer:<br \/>\nWrite the formula for one measurement and then solve the formula for the different measurement you want to find and use this new formula to find that measurement<br \/>\nHence, in the above way,<br \/>\nWe can use a formula for one measurement to write a formula for a different measurement<\/p>\n<p><b>EXPLORATION 1<br \/>\nUsing an Area Formula<br \/>\nWork with a partner.<\/b><br \/>\na. Write a formula for the area A of a parallelogram.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe area of the parallelogram ( A) = Base \u00d7 Height<\/p>\n<p>b. Substitute the given values into the formula. Then solve the equation for b. Justify each step.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-81.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 81\" width=\"186\" height=\"128\" \/><br \/>\nAnswer:<br \/>\nThe value of b is: 6 in<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-81.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 81\" width=\"186\" height=\"128\" \/><br \/>\nFrom the given figure,<br \/>\nArea ( A) = 30 in\u00b2<br \/>\nHeight ( h ) = 5 in<br \/>\nBase = b<br \/>\nFrom part ( a),<br \/>\nArea of the parallelogram = Base \u00d7 Height<br \/>\n30 = 5 \u00d7 b<br \/>\nb = 30 \u00f7 5<br \/>\nb = 6 in<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of b is: 6 in<\/p>\n<p>c. Solve the formula in part (a) for b without first substituting values into the formula. Justify each step.<br \/>\nAnswer:<br \/>\nFrom part ( a ),<br \/>\nArea of the parallelogram = Base \u00d7 Height<br \/>\nBase = ( Area of the parallelogram ) \u00f7 Height of the parallelogram<br \/>\nFrom the given figure,<br \/>\nBase = b<br \/>\nSo,<br \/>\nb = ( Area of the parallelogram ) \u00f7 Height of the parallelogram<\/p>\n<p>d. Compare how you solved the equations in parts (b) and (c). How are the processes similar? How are they different?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-82.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 82\" width=\"220\" height=\"281\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe area of the parallelogram = Base \u00d7 Height<br \/>\nUsing the above formula,<br \/>\nWe solved parts (b ) and ( c )<\/p>\n<p><b>EXPLORATION 2<\/b><br \/>\n<b>Using Area, Circumference, and Volume Formulas<\/b><br \/>\n<b>Work with a partner.<\/b> Write the indicated formula for each figure. Then write a new formula by solving for the variable whose value is not given. Use the new formula to find the value of the variable.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-83.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 83\" width=\"490\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-83.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-83-300x220.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nAnswer:<br \/>\nThe given geometrical figures are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-83.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 83\" width=\"490\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-83.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-83-300x220.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nNow,<br \/>\na)<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-21.jpg\" alt=\"\" width=\"197\" height=\"155\" \/><br \/>\nWe know that,<br \/>\nArea of the trapezoid = h ( a + b ) \/ 2<br \/>\nWhere,<br \/>\nh is the height between the two sides<br \/>\na + b is the sum of the parallel sides [ Here, b1 and b2 ]<br \/>\nFrom the given figure,<br \/>\nArea of the trapezoid = 63 cm\u00b2<br \/>\n1st parallel side ( b1 ) = 8 cm<br \/>\n2nd parallel side ( b2 ) = 10 cm<br \/>\nSo,<br \/>\nArea of the trapezoid = h ( 8 + 10 ) \/ 2<br \/>\n63 = h ( 18 ) \/ 2<br \/>\n63 \u00d7 2 = h \u00d7 18<br \/>\nh = ( 63 \u00d7 2 ) \u00f7 ( 18 \u00d7 1 )<br \/>\nh = 7 cm<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: 7 cm<br \/>\nb)<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-22.jpg\" alt=\"\" width=\"243\" height=\"160\" \/><br \/>\nWe know that,<br \/>\nCircumference of a circle = 2\u03c0r<br \/>\nWhere<br \/>\nr is the radius of the circle<br \/>\nFrom the above figure,<br \/>\nCircumference of the circle ( C ) = 24\u03c0 ft<br \/>\nSo,<br \/>\n24\u03c0 = 2\u03c0r<br \/>\nr = ( 24\u03c0 ) \u00f7 ( 2\u03c0 )<br \/>\nr = 12 ft<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of r is: 12 ft<br \/>\nc)<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-23.jpg\" alt=\"\" width=\"248\" height=\"186\" \/><br \/>\nWe know that,<br \/>\nThe volume of the rectangular prism ( V ) = Length \u00d7 Width \u00d7 Height<br \/>\nThe area of the rectangle ( B) = Length \u00d7 Width<br \/>\nSo,<br \/>\nThe volume of the rectangular prism (V ) = B \u00d7 Height<br \/>\nFrom the above figure,<br \/>\nThe volume of the rectangular prism ( V ) = 75 yd\u00b3<br \/>\nThe area of the rectangle ( B ) = 15 yd\u00b2<br \/>\nSo,<br \/>\n75 = 15 \u00d7 Height<br \/>\nHeight = 75 \u00f7 15<br \/>\nHeight = 15 yd<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: 15 yd<br \/>\nd)<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-24.jpg\" alt=\"\" width=\"223\" height=\"165\" \/><br \/>\nWe know that,<br \/>\nThe volume of cone ( V ) = \u03c0r\u00b2h \/ 3<br \/>\nThe area of the circle ( B ) = \u03c0r\u00b2<br \/>\nWhere,<br \/>\nr is the radius of the circle<br \/>\nh is the height of the cone<br \/>\nSo,<br \/>\nThe volume of the cone ( V ) = Bh \/ 3<br \/>\nFrom the above figure,<br \/>\nV = 24\u03c0 m\u00b3<br \/>\nB = 12\u03c0 m\u00b3<br \/>\nSo,<br \/>\n24\u03c0 = 12\u03c0 \u00d7 h \/ 3<br \/>\nh \/ 3 = 24\u03c0 \u00f7 12\u03c0<br \/>\nh \/ 3 = 2<br \/>\nh = 2 \u00d7 3<br \/>\nh = 6 m<br \/>\nHence, from the above,<br \/>\nWe can conclude that the height of the cone is: 6 m<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you use a formula for one measurement to write a formula for a different measurement? Give an example that is different from those given in Explorations 1 and 2.<br \/>\nAnswer:<br \/>\nWrite the formula for one measurement and then solve the formula for the different measurement you want to find and use this new formula to find that measurement<br \/>\nExample:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-25.jpg\" alt=\"\" width=\"485\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-25.jpg 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-25-300x134.jpg 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nWe know that,<br \/>\nThe area of the rectangle ( A ) = Length \u00d7 Width<br \/>\nFrom the above figure,<br \/>\nA = 20 cm\u00b2<br \/>\nL = 10 cm<br \/>\nLet,<br \/>\nW be the width of the rectangle<br \/>\nSo,<br \/>\n20 = 10 \u00d7 W<br \/>\nW = 20 \u00f7 10<br \/>\nW = 2 cm<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of W is: 2 cm<\/p>\n<p><b>1.5 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the literal equation for y.<\/b><\/p>\n<p>Question 1.<br \/>\n3y &#8211; x = 9<br \/>\nAnswer:<br \/>\nThe value of y is: ( x + 9 ) \/ 3<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3y &#8211; x = 9<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n3y = 9 + x<br \/>\ny = ( x + 9 ) \/ 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: ( x + 9 ) \/ 3<\/p>\n<p>Question 2.<br \/>\n2x &#8211; 2y = 5<br \/>\nAnswer:<br \/>\nThe value of y is: ( 2x &#8211; 5 ) \/ 2<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2x &#8211; 2y = 5<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n2y = 2x &#8211; 5<br \/>\ny = ( 2x &#8211; 5 ) \/ 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: ( 2x &#8211; 5 ) \/ 2<\/p>\n<p>Question 3.<br \/>\n20 = 8x + 4y<br \/>\nAnswer:<br \/>\nThe value of y is: 5 &#8211; 2x<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n20 = 8x + 4y<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4y = 20 &#8211; 8x<br \/>\ny = ( 20 &#8211; 8x ) \/ 4<br \/>\ny = ( 20 \u00f7 4 ) &#8211; ( 8x \u00f7 4 )<br \/>\ny = 5 &#8211; 2x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 5 &#8211; 2x<\/p>\n<p><b>Solve the literal equation for x.<\/b><\/p>\n<p>Question 4.<br \/>\ny = 5x &#8211; 4x<br \/>\nAnswer:<br \/>\nThe value of x is: y<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ny = 5x &#8211; 4x<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx = y<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: y<\/p>\n<p>Question 5.<br \/>\n2x + kx = m<br \/>\nAnswer:<br \/>\nThe value of x is: m \/ ( k + 2\u00a0 )<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2x + kx = m<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nx ( k + 2 ) = m<br \/>\nx = m \/ ( k + 2 )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: m \/ ( k + 2 )<\/p>\n<p>Question 6.<br \/>\n3 + 5x &#8211; kx = y<br \/>\nAnswer:<br \/>\nThe value of x is: ( y &#8211; 3 ) \/ ( 5 &#8211; k )<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3 + 5x &#8211; kx = y<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5x &#8211; kx = y &#8211; 3<br \/>\nx ( 5 &#8211; k ) = y &#8211; 3<br \/>\nx = ( y &#8211; 3 ) \/ ( 5 &#8211; k )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: ( y &#8211; 3 ) \/ ( 5 &#8211; k )<\/p>\n<p><b>Solve the formula for the indicated variable.\u00a0<\/b><\/p>\n<p>Question 7.<br \/>\nArea of a triangle: A = \\(\\frac{1}{2}\\)bh; Solve for h.<br \/>\nAnswer:<br \/>\nThe value of h is: \\(\\frac{2A}{b}\\)<\/p>\n<p>Explanation:<br \/>\nThe given area of a triangle is:<br \/>\nA = \\(\\frac{1}{2}\\) bh<br \/>\nbh = 2A<br \/>\nh = \\(\\frac{2A}{b}\\)<br \/>\nHence, from the above,<br \/>\nWe can onclude that the value of h is: \\(\\frac{2A}{b}\\)<\/p>\n<p>Question 8.<br \/>\nThe surface area of a cone: S = \u03c0r<sup>2<\/sup> + \u03c0r\u2113; Solve for \u2113.<br \/>\n<span style=\"font-size: 16px;\">Answer:<br \/>\nThe value of l is: \\(\\frac{S}{\u03c0r}\\) &#8211; r<\/span><\/p>\n<p>Explanation:<br \/>\nThe given surface area of a cone is:<br \/>\nS = \u03c0r\u00b2 + \u03c0rl<br \/>\nS= \u03c0r ( r + l )<br \/>\nr + l = \\(\\frac{S}{\u03c0r}\\)<br \/>\nl = \\(\\frac{S}{\u03c0r}\\) &#8211; r<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of l is: \\(\\frac{S}{\u03c0r}\\) &#8211; r<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 9.<br \/>\nA fever is generally considered to be a body temperature greater than 100\u00b0F. Your friend has a temperature of 37\u00b0C. Does your friend have a fever?<br \/>\nAnswer:<br \/>\nYour friend does not have a fever<\/p>\n<p>Explanation:<br \/>\nIt is given that a fever is generally considered to be a body temperature greater than 100\u00b0F.<br \/>\nWe know that,<br \/>\nTo convert Fahrenheit into Celsius,<br \/>\n\u00b0C = ( \u00b0F &#8211; 32 ) \u00d7 \\(\\frac{5}{9}\\)<br \/>\n\u00b0C = ( 100 &#8211; 32 ) \u00d7 \\(\\frac{5}{9}\\)<br \/>\n\u00b0C = 68 \u00d7 \\(\\frac{5}{9}\\)<br \/>\n\u00b0C = 37.7\u00b0<br \/>\nBut it is given that your friend has a temperature of 37\u00b0C<br \/>\nSo, for fever, the temperature has to be 37.7\u00b0C<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend does not have a fever<\/p>\n<p>Question 10.<br \/>\nHow much money must you deposit in a simple interest account to earn $500 in interest in 5 years at 4% annual interest?<br \/>\n<span style=\"font-size: 16px;\">Answer:<br \/>\nThe money you deposit in simple interest is: $2,500<\/span><\/p>\n<p>Explanation:<br \/>\nIt is given that you earned $500 in a simple interest to earn in 5 years at 4% annual interest<br \/>\nLet,<br \/>\nThe money you deposited be: $x<br \/>\nWe know that,<br \/>\nSimple interest = ( Principle \u00d7 Time \u00d7 Rate ) \/ 100<br \/>\nThe principle is the money you deposited<br \/>\nSo,<br \/>\n500 = ( x \u00d7 5 \u00d7 4 ) \/ 100<br \/>\n( x \u00d7 5 \u00d7 4 ) = 500 \u00d7 100<br \/>\nx \u00d7 20 = 500 \u00d7 100<br \/>\nx = ( 500 \u00d7 100 ) \u00f7 20<br \/>\nx = $2,500<br \/>\nHence, from the above,<br \/>\nWe can conclude that the money you deposited is: $2,500<\/p>\n<p>Question 11.<br \/>\nA truck driver averages 60 miles per hour while delivering freight and 45 miles per hour on the return trip. The total driving time is 7 hours. How long does each trip take?<br \/>\n<span style=\"font-size: 16px;\">Answer:<br \/>\nThe time taken for each trip is: 3 hours and 4 hours respectively<\/span><\/p>\n<p>Explanation:<br \/>\nIt is given that a truck driver averages 60 miles per hour while delivering freight and 45 miles per hour on the return trip. The total driving time is 7 hours.<br \/>\nWe know that,<br \/>\nSpeed = \\(\\frac{Distance}{Time}\\)<br \/>\nTime = \\(\\frac{Distance}{Speed}\\)<br \/>\nLet the distance be D<br \/>\nIt is given that the total driving time is: 7 hours<br \/>\nSo,<br \/>\n7 = \\(\\frac{D}{60}\\) + \\(\\frac{D}{45}\\)<br \/>\n7 \/ D = \\(\\frac{60 + 45}{60 \u00d7 45}\\)<br \/>\n7 \/ D = \\(\\frac{105}{2,700}\\)<br \/>\nD = 7 \/ \\(\\frac{105}{2,700}\\)<br \/>\nD = 7 \u00d7 \\(\\frac{2,700}{105}\\)<br \/>\nD = \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{2,700}{105}\\)<br \/>\nD = \\(\\frac{7 \u00d7 2,700}{1 \u00d7 105}\\)<br \/>\nD = 180 miles<br \/>\nSo,<br \/>\nThe time taken to deliver = \\(\\frac{180}{60}\\) = 3 hours<br \/>\nThe time taken to return = \\(\\frac{180}{45}\\) = 4 hours<br \/>\nHence, from the above,<br \/>\nWe can conclude that the time taken for each trip is: 3 hours and 4 hours respectively<\/p>\n<h3><a id=\"Rewriting_Equations_and_Formulas_1.5_Exercices\"><\/a>Rewriting Equations and Formulas 1.5 Exercices<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b><br \/>\nIs <img loading=\"lazy\" class=\"alignnone size-full wp-image-33851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-84.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 84\" width=\"81\" height=\"39\" \/> a literal equation? Explain.<br \/>\nAnswer:<br \/>\nThe &#8221; Literal equation&#8221; is an equation that contains only letters<br \/>\nNow,<br \/>\nThe given equation is:<br \/>\n9r + 16 = \u03c0 \/ 5<br \/>\nFrom the above definition,<br \/>\nWe can say that the given equation is a &#8221; Literal equation &#8221;<\/p>\n<p>Question 2.<br \/>\n<b>DIFFERENT WORDS, SAME QUESTION?<\/b><br \/>\nWhich is different? Find &#8220;both&#8221; answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-85.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 85\" width=\"534\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-85.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-85-300x48.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><br \/>\nAnswer:<br \/>\nThe given problems are:<br \/>\na) Solve 3x + 6y = 24 for x<br \/>\nb) Solve 24 &#8211; 3x = 6y for x<br \/>\nc) Solve 6y = 24 &#8211; 3x in terms of x<br \/>\nd) Solve 24 &#8211; 6y = 3x for x in terms of y<br \/>\nSo,<br \/>\nFrom the above-given problems,<br \/>\nWe can observe that d) is different as we have to find x in terms of y whereas in the remaining three problems, we have to find x<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201312, solve the literal equation for y.<\/b><\/p>\n<p>Question 3.<br \/>\ny &#8211; 3x = 13<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q3.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q3\" width=\"424\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q3.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q3-300x93.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 4.<br \/>\n2x + y = 7<br \/>\nAnswer:<br \/>\nThe value of y is: 7 &#8211; 2x<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n2x + y = 7<br \/>\nNow,<br \/>\ny = 7 &#8211; 2x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 7 &#8211; 2x<\/p>\n<p>Question 5.<br \/>\n2y &#8211; 18x = -26<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q5.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q5\" width=\"441\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q5.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q5-300x150.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p>Question 6.<br \/>\n20x + 5y = 15<br \/>\nAnswer:<br \/>\nThe value of y is: 3 &#8211; 4x<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n20x + 5y = 15<br \/>\nNow,<br \/>\n5y = 15 &#8211; 20x<br \/>\ny = ( 15 &#8211; 20x ) \/ 5<br \/>\ny = ( 15\u00a0 \/ 5 ) &#8211; ( 20x \/ 5 )<br \/>\ny = 3 &#8211; 4x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 3 &#8211; 4x<\/p>\n<p>Question 7.<br \/>\n9x &#8211; y = 45<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q7.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q7\" width=\"438\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q7.png 438w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q7-300x148.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<p>Question 8.<br \/>\n6 &#8211; 3y = -6<br \/>\nAnswer:<br \/>\nThe value of y is: 4<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n6 &#8211; 3y = -6<br \/>\n-3y = -6 &#8211; ( +6 )<br \/>\n-3y = -6 -6<br \/>\n-3y = -12<br \/>\ny = -12 \u00f7 ( -3 )<br \/>\ny = 12 \u00f7 3<br \/>\ny = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 4<\/p>\n<p>Question 9.<br \/>\n4x &#8211; 5 = 7 + 4y<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q9.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q9\" width=\"395\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q9.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q9-300x173.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 10.<br \/>\n16x + 9 = 9y &#8211; 2x<br \/>\nAnswer:<br \/>\nThe value of y is: 18x + 9<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n16x + 9 = y &#8211; 2x<br \/>\nSo,<br \/>\n16x + 2x + 9 = y<br \/>\n18x + 9 = y<br \/>\ny = 18x + 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 18x + 9<\/p>\n<p>Question 11.<br \/>\n2 +\\(\\frac{1}{6}\\)y = 3x + 4<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q11.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q11\" width=\"430\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q11.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q11-300x218.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p>Question 12.<br \/>\n11 &#8211; \\(\\frac{1}{2}\\)y = 3 + 6x<br \/>\nAnswer:<br \/>\nThe value of y is: 16 &#8211; 12x<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n11 &#8211; \\(\\frac{1}{2}\\)y = 3 + 6x<br \/>\nSo,<br \/>\n&#8211;\\(\\frac{1}{2}\\)y = 3 + 6x &#8211; 11<br \/>\n-y = 2 ( 3 + 6x &#8211; 11 )<br \/>\ny = -2 ( 3 + 6x &#8211; 11 )<br \/>\ny = -2 ( 3 ) -2 ( 6x ) + 2 ( 11 )<br \/>\ny = -6 &#8211; 12x + 22<br \/>\ny = 16 &#8211; 12x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 16 &#8211; 12x<\/p>\n<p><b>In Exercises 13\u201322, solve the literal equation for x.<\/b><\/p>\n<p>Question 13.<br \/>\ny = 4x + 8x<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q13.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q13\" width=\"370\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q13.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q13-300x203.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p>Question 14.<br \/>\nm = 10x &#8211; x<br \/>\nAnswer:<br \/>\nThe value of x is: m \/ 9<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\nm = 10x &#8211; x<br \/>\nm = 9x<br \/>\nx = m \/ 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: m \/ 9<\/p>\n<p>Question 15.<br \/>\na = 2x + 6xz<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q15.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q15\" width=\"410\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q15.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q15-300x171.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/p>\n<p>Question 16.<br \/>\ny = 3bx &#8211; 7x<br \/>\nAnswer:<br \/>\nThe value of x is: y \/ ( 3b &#8211; 7 )<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\ny = 3bx &#8211; 7x<br \/>\nSo,<br \/>\ny = x ( 3b &#8211; 7 )<br \/>\nx = y \/ ( 3b &#8211; 7 )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: y \/ ( 3b &#8211; 7 )<\/p>\n<p>Question 17.<br \/>\ny = 4x + rx + 6<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q17.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q17\" width=\"406\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q17.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q17-300x222.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 18.<br \/>\nz = 8 + 6x &#8211; px<br \/>\nAnswer:<br \/>\nThe value of x is: ( z &#8211; 8 ) \/ ( 6 &#8211; p )<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\nz = 8 + 6x &#8211; px<br \/>\nSo,<br \/>\nz &#8211; 8 = 6x &#8211; px<br \/>\nz &#8211; 8 = x ( 6 &#8211; p )<br \/>\nx = ( z &#8211; 8 ) \/ ( 6 &#8211; p )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: ( z &#8211; 8 ) \/ ( 6 &#8211; p )<\/p>\n<p>Question 19.<br \/>\nsx + tx = r<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q19.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q19\" width=\"392\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q19.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q19-300x170.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 20.<br \/>\na = bx + cx + d<br \/>\nAnswer:<br \/>\nThe value of x is: ( a &#8211; d ) \/ ( b + c )<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\na = bx + cx + d<br \/>\na &#8211; d = bx + cx<br \/>\na &#8211; d = x ( b + c )<br \/>\nx = ( a &#8211; d ) \/ ( b + c )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: ( a &#8211; d ) \/ ( b + c )<\/p>\n<p>Question 21.<br \/>\n12 &#8211; 5x &#8211; 4kx = y<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q21.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q21\" width=\"408\" height=\"483\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q21.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q21-253x300.png 253w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 22.<br \/>\nx &#8211; 9 + 2wx = y<br \/>\nAnswer:<br \/>\nThe value of x is: ( y &#8211; 9 ) \/ ( 1 &#8211; 2w )<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\nx &#8211; 9 + 2wx = y<br \/>\nx &#8211; 2wx = y + 9<br \/>\nx ( 1 &#8211; 2w ) = y + 9<br \/>\nx = ( y &#8211; 9 ) \/ ( 1 &#8211; 2w )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: ( y &#8211; 9 ) \/ ( 1 &#8211; 2w )<\/p>\n<p>Question 23.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe total cost C (in dollars) to participate in a ski club is given by the literal equation C = 85x + 60, where x is the number of ski trips you take.<br \/>\na. Solve the equation for x.<br \/>\nb. How many ski trips do you take if you spend a total of $315? $485?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-86.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 86\" width=\"195\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q23.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q23\" width=\"566\" height=\"422\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q23.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q23-300x224.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d = 4n &#8211; 2, where n is the length (in inches) of the nail.<br \/>\na. Solve the equation for n.<br \/>\nb. Use the equation from part (a) to find the lengths of nails with the following penny sizes: 3, 6, and 10.<br \/>\nAnswer:<br \/>\na)<br \/>\nThe given literal equation is:<br \/>\nd = 4n &#8211; 2<br \/>\nWhere,<br \/>\nn is the length ( in inches ) of the nail<br \/>\nSo,<br \/>\n4n = d + 2<br \/>\nn = ( d + 2 ) \/ 4<br \/>\nb)<br \/>\nIt is given that,<br \/>\nThe penny sizes ( d ) are: 3, 6, and 10<br \/>\nFrom part ( a ),<br \/>\nThe literal equation is:<br \/>\nn = ( d + 2\u00a0 ) \/ 4<br \/>\nPut, d= 3, 6 and 10<br \/>\nSo,<br \/>\nn = ( 3 + 2 ) \/4 = 5 \/ 4 inches<br \/>\nn = ( 6 + 2 ) \/ 4 = 2 inches<br \/>\nn = ( 10 + 2 ) \/ 4 = 3 inches<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 25 and 26, describe and correct the error in solving the equation for x.<\/b><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-87.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 87\" width=\"279\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q25.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q25\" width=\"544\" height=\"431\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q25.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q25-300x238.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-72.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 72.1\" width=\"242\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\nThe given literal equation is:<br \/>\n10 = ax &#8211; 3b<br \/>\nSo,<br \/>\nax = 10 + 3b<br \/>\nx = ( 10 + 3b ) \/ a<\/p>\n<p><b>In Exercises 27\u201330, solve the formula for the indicated variable.<\/b><\/p>\n<p>Question 27.<br \/>\nProfit: P = R &#8211; C; Solve for C.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q27.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q27\" width=\"543\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q27.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q27-300x141.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 28.<br \/>\nSurface area of a cylinder: S = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh; Solve for h.<br \/>\nAnswer:<br \/>\nThe given Surface area of a cylinder is:<br \/>\nS = 2\u03c0r\u00b2 + 2\u03c0rh<br \/>\nSo,<br \/>\nS = 2\u03c0r ( r + h )<br \/>\nS \/ 2\u03c0r = r + h<br \/>\nh = S \/ 2\u03c0r &#8211; r<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: S \/ ( 2\u03c0<\/p>\n<p>Question 29.<br \/>\nArea of a trapezoid: A = \\(\\frac{1}{2}\\)h(b<sub>1<\/sub> + b<sub>2<\/sub>); Solve for b<sub>2<\/sub>.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q29.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q29\" width=\"423\" height=\"440\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q29.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q29-288x300.png 288w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Question 30.<br \/>\nThe average acceleration of an object: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-88.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 88\" width=\"89\" height=\"44\" \/>; Solve for v<sub>1<\/sub>.<br \/>\nAnswer:<br \/>\nThe given average acceleration of an object is:<br \/>\na = ( v1 &#8211; v0 ) \/ t<br \/>\nSo,<br \/>\nat = v1 &#8211; v0<br \/>\nv1 = at + v0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of v1 is: at + v0<\/p>\n<p>Question 31.<br \/>\n<b>REWRITING A FORMULA<\/b><br \/>\nA common statistic used in professional football is the quarterback rating. This rating is made up of four major factors. One factor is the completion rating given by the formula<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-88.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 88.1\" width=\"117\" height=\"50\" \/><br \/>\nwhere C is the number of completed passes and A is the number of attempted passes. Solve the formula for C.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q31.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q31\" width=\"426\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q31.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q31-239x300.png 239w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p>Question 32.<br \/>\n<b>REWRITING A FORMULA<\/b><br \/>\nNewton\u2019s law of gravitation is given by the formula<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-89.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 89\" width=\"107\" height=\"55\" \/><br \/>\nwhere F is the force between two objects of masses m<sub>1<\/sub> and m<sub>2<\/sub>, G is the gravitational constant, and d is the distance between the two objects. Solve the formula for m<sub>1<\/sub>.<br \/>\nAnswer:<br \/>\nThe value of m1 is: Fd\u00b2 \/ Gm2<\/p>\n<p>Explanation:<br \/>\nThe given Newton&#8217;s law of gravitation is given by:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-89.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 89\" width=\"107\" height=\"55\" \/><br \/>\nwhere<br \/>\nF is the force between two objects of masses m<sub>1<\/sub> and m<sub>2<\/sub><br \/>\nG is the gravitational constant<br \/>\nd is the distance between the two objects.<br \/>\nNow,<br \/>\n( m1m2 ) = Fd\u00b2 \/ G<br \/>\nm1 = Fd\u00b2 \/ Gm2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m1 is: Fd\u00b2 \/ Gm2<\/p>\n<p>Question 33.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe sale price S (in dollars) of an item is given by the formula S = L &#8211; rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).<br \/>\na. Solve the formula for r.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-90.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 90\" width=\"150\" height=\"178\" \/><br \/>\nb. The list price of the shirt is $30. What is the discount rate?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q33.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q33\" width=\"544\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q33.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q33-300x199.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe density d of a substance is given by the formula d = \\(\\frac{m}{V}\\), where m is its mass and V is its volume.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-91.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 91\" width=\"274\" height=\"193\" \/><br \/>\na. Solve the formula for m?<br \/>\nAnswer:<br \/>\nThe given density d of a substance is given by:<br \/>\nd = \\(\\frac{m}{V}\\)<br \/>\nSo,<br \/>\nd \u00d7 V = m<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of m is: d \u00d7 V<\/p>\n<p>b. Find the mass of the pyrite sample.<br \/>\nAnswer:<br \/>\nThe mass of the pyrite sample is: 6.012 gm<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-91.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 91\" width=\"274\" height=\"193\" \/><br \/>\nFrom the above figure,<br \/>\nThe density of Pyrite = 5.01 g\/cm\u00b3<br \/>\nThe volume of Pyrite = 1.2 cm\u00b3<br \/>\nFrom part (a),<br \/>\nThe mass of Pyrite = Density \u00d7 Volume<br \/>\nSo,<br \/>\nThe mass of Pyrite ( m ) = 5.01 \u00d7 1.2<br \/>\n= 6.012 gm<br \/>\nHence, from the above,<br \/>\nWe can conclude that the mass of Pyrite is: 6.012 gm<\/p>\n<p>Question 35.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nYou deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q35.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q35\" width=\"540\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q35.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q35-300x144.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nA flight averages 460 miles per hour. The return flight averages 500 miles per hour due to a tailwind. The total flying time is 4.8 hours. How long is each flight? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-91.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 1 Solving Linear Equations 91.1\" width=\"318\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-91.1.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-1-Solving-Linear-Equations-91.1-300x93.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Answer:<br \/>\nThe time taken for flight is: 2.5 hours<br \/>\nThe time taken for return is: 2.3 hours<\/p>\n<p>Explanation:<br \/>\nIt is given that a flight averages 460 miles per hour. The return flight averages 500 miles per hour due to a tailwind. The total flying time is 4.8 hours.<br \/>\nWe know that,<br \/>\nSpeed = Distance \/ Time<br \/>\nTime = Distance \/ Speed<br \/>\nIt is also given that the total flying time is 4.8 hours<br \/>\nLet the distance be D<br \/>\nSo,<br \/>\n\\(\\frac{D}{460}\\) + \\(\\frac{D}{500}\\) = 4.8<br \/>\n\\(\\frac{460 + 500}{230,000}\\) = 4.8 \/ D<br \/>\n\\(\\frac{960}{230,000}\\) = 4.8 \/ D<br \/>\nD = 4.8 \u00d7 \\(\\frac{230,000}{960}\\)<br \/>\nD = 1,150 miles<br \/>\nHence,<br \/>\nThe time taken for flight = 1,150 \u00f7 460 = 2.5 hpurs<br \/>\nThe time taken for return = 1,150 \u00f7 500 = 2.3 hours<\/p>\n<p>Question 37.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nAn athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles, as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-92.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 92\" width=\"344\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-92.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-92-300x135.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\na. Write a formula for the perimeter of the indoor track.<br \/>\nb. Solve the formula for x.<br \/>\nc. The perimeter of the track is 660 feet, and r is 50 feet. Find x. Round your answer to the nearest foot.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q37.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q37\" width=\"525\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q37.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q37-300x202.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe distance d (in miles) you travel in a car is given by the two equations shown, where t is the time (in hours) and g is the number of gallons of gasoline the car uses.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-93.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 93\" width=\"347\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-93.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-93-300x116.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\na. Write an equation that relates g and t.<br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\nd = 55t &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; (1)<br \/>\nd = 20g &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; (2)<br \/>\nBy the law of Equality,<br \/>\n55t = 20g [ As the LHS for both the equations are equal, make the RHS equal ]<br \/>\nt \/ g = 20 \/ 55<br \/>\nt \/ g = 4 \/ 11<\/p>\n<p>b. Solve the equation for g.<br \/>\nAnswer:<br \/>\nFrom the given figure,<br \/>\nd = 20g<br \/>\nd = 55t<br \/>\nFrom part (a),<br \/>\nt \/ g = 4 \/ 11<br \/>\n11t = 4g<br \/>\ng = 11t \/ 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of g is: 11t \/ 4<\/p>\n<p>c. You travel for 6 hours. How many gallons of gasoline does the car use? How far do you travel? Explain.<br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\ng = 11t \/ 4<br \/>\nWhere,<br \/>\ng is the number of gallons of gasoline<br \/>\nIt is given that you travel for 6 hours<br \/>\nSo,<br \/>\nt = 6 hours<br \/>\nNow,<br \/>\ng = ( 11 \u00d7 6 ) \/ 4<br \/>\ng = 66\/4 gallons<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of gallons of gasoline is: 66 \/ 4 gallons<\/p>\n<p>Question 39.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nOne type of stone formation found in Carlsbad Caverns in New Mexico is called a column. This cylindrical stone formation connects to the ceiling and the floor of a cave.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-94.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 94\" width=\"268\" height=\"192\" \/><br \/>\na. Rewrite the formula for the circumference of a circle, so that you can easily calculate the radius of a column given its circumference.<br \/>\nb. What is the radius (to the nearest tenth of a foot) of a column that has a circumference of 7 feet? 8 feet? 9 feet?<br \/>\nc. Explain how you can find the area of a cross-section of a column when you know its circumference.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q39.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q39\" width=\"572\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q39.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q39-280x300.png 280w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe rectangular prism shown has bases&#8217; with equal side lengths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-95.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 95\" width=\"175\" height=\"151\" \/><br \/>\na. Use the figure to write a formula for the surface area S of the rectangular prism.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-95.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 95\" width=\"175\" height=\"151\" \/><br \/>\nFrom the above figure,<br \/>\nThe surface area of the rectangular prism ( S) = 2 ( lb + bh + lh )<br \/>\nWhere,<br \/>\nl is the length of the rectangular prism<br \/>\nb is the Width of the rectangular prism<br \/>\nh is the height of the rectangular prism<\/p>\n<p>b. Your teacher asks you to rewrite the formula by solving for one of the side lengths, b or \u2113. Which side length would you choose? Explain your reasoning.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe surface area of the rectangular prism ( S ) = 2 ( lb + bh + lh )<br \/>\nS \/ 2 = lb + bh + lh<br \/>\nS \/ 2 = b ( l + h ) + bh<br \/>\nS \/ 2 = b ( l + b + h )<br \/>\nb = S \/ 2 ( l + b + h )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of b is: S \/ 2 ( l + b + h )<\/p>\n<p>Question 41.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYour friend claims that Thermometer A displays a greater temperature than Thermometer B. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-96.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 96\" width=\"307\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-96.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-96-300x171.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q41.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q41\" width=\"573\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q41.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q41-300x57.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nGive a possible value for h. Justify your answer. Draw and label the figure using your chosen value of h.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-97.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 97\" width=\"209\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nThe completed figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-26.jpg\" alt=\"\" width=\"223\" height=\"115\" \/><br \/>\nThe value of h is: 5 cm<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-97.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 97\" width=\"209\" height=\"118\" \/><br \/>\nFrom the given figure,<br \/>\nWe can say that the geometrical figure is the parallelogram<br \/>\nWe know that,<br \/>\nArea of the parallelogram = Base \u00d7 Height<br \/>\nFrom the given figure,<br \/>\nArea of the parallelogram = 40 cm\u00b2<br \/>\nThe base of the parallelogram = 8 cm<br \/>\nSo,<br \/>\n40 = 8 \u00d7 Height<br \/>\nHeight = 40 \u00f7 8<br \/>\nHeight = 5 cm<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe completed figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-26.jpg\" alt=\"\" width=\"223\" height=\"115\" \/><br \/>\nThe value of h is: 5 cm<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 43 and 44, write a formula for the area of the regular polygon. Solve the formula for the height h.<\/b><\/p>\n<p>Question 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-98.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 98\" width=\"134\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q43.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q43\" width=\"438\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q43.png 438w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q43-300x254.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-99.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 99\" width=\"128\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nThe value of h is: A \/ 3b<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-99.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 99\" width=\"128\" height=\"138\" \/><br \/>\nFrom the above figure,<br \/>\nWe can say that the figure is Hexagon<br \/>\nNow,<br \/>\nThe Hexagon with the six triangles is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-1-27.jpg\" alt=\"\" width=\"148\" height=\"124\" \/><br \/>\nSo,<br \/>\nFrom the figure,<br \/>\nThere are 6 triangles<br \/>\nWe know that,<br \/>\nThe area of a triangle = \\(\\frac{1}{2}\\) \u00d7 Base \u00d7 Height<br \/>\nSo,<br \/>\nThe area of the Hexagon = The area of the 6 triangles<br \/>\n= 6 ( \\(\\frac{1}{2}\\) ) \u00d7 Base \u00d7 Height<br \/>\nLet,<br \/>\nThe area of the Hexagon be A<br \/>\nThe height of the hexagon be h<br \/>\nThe Base of the hexagon be b<br \/>\nSo,<br \/>\nA = 6 ( \\(\\frac{1}{2}\\) ) \u00d7 Base \u00d7 Height<br \/>\nA = 3 \u00d7 Base \u00d7 Height<br \/>\nBase \u00d7 Height = A \/ 3<br \/>\nHeight = A \/ ( 3 \u00d7 Base )<br \/>\nSo,<br \/>\nh = A \/ 3b<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: A \/ 3b<\/p>\n<p><b>REASONING<br \/>\nIn Exercises 45 and 46, solve the literal equation for a.<\/b><\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-1-Solving-Linear-Equations-100.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 1 Solving Linear Equations 100\" width=\"105\" height=\"44\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q45.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q45\" width=\"434\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q45.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q45-300x284.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-101.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 101\" width=\"100\" height=\"50\" \/><br \/>\nAnswer:<br \/>\nThe value of a is: \\(\\frac{by}{y &#8211; bx}\\)<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\ny = x [ \\(\\frac{ab}{a &#8211; b}\\)<br \/>\n\\(\\frac{ab}{a &#8211; b}\\) = y \/ x<br \/>\nx ( ab ) = y ( a &#8211; b )<br \/>\nabx = ay &#8211; by<br \/>\nby = ay &#8211; abx<br \/>\nby = a ( y &#8211; bx )<br \/>\na = \\(\\frac{by}{y &#8211; bx}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: \\(\\frac{by}{y &#8211; bx}\\)<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 47.<br \/>\n15 &#8211; 5 + 5<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q47.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q47\" width=\"272\" height=\"100\" \/><\/p>\n<p>Question 48.<br \/>\n18 \u2022 2 &#8211; 4<sup>2<\/sup> \u00f7 8<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n18 \u22c5 2 &#8211; 4\u00b2 \u00f7 8<br \/>\nWe have to remember that,<br \/>\nWhen there is an expression to solve with multiple mathematical symbols, we have to follow the BODMAS rule<br \/>\nBODMAS indicates the hierarchy we have to follow when we will solve mathematical symbols<br \/>\nIn BODMAS,<br \/>\nB &#8211; Brackets<br \/>\nO &#8211; Of<br \/>\nD &#8211; Division<br \/>\nM &#8211; Multiplication<br \/>\nA &#8211; Addition<br \/>\nS &#8211; Subtraction<br \/>\nSo,<br \/>\n18 \u22c5 2 &#8211; 4\u00b2 \u00f7 8 = 18 \u22c5 2 &#8211; ( 4 \u00d7 4 ) \u00f7 8<br \/>\n= 18 \u22c5 2 &#8211; 2<br \/>\n= 36 &#8211; 2<br \/>\n= 34<\/p>\n<p>Question 49.<br \/>\n3<sup>3<\/sup> + 12 \u00f7 3 \u2022 5<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q49.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q49\" width=\"343\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q49.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q49-300x117.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>Question 50.<br \/>\n2<sup>5<\/sup>(5 &#8211; 6) + 9 \u00f7 3<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n2<sup>5<\/sup>(5 &#8211; 6) + 9 \u00f7 3<br \/>\nWe have to remember that,<br \/>\nWhen there is an expression to solve with multiple mathematical symbols, we have to follow the BODMAS rule<br \/>\nBODMAS indicates the hierarchy we have to follow when we will solve mathematical symbols<br \/>\nIn BODMAS,<br \/>\nB &#8211; Brackets<br \/>\nO &#8211; Of<br \/>\nD &#8211; Division<br \/>\nM &#8211; Multiplication<br \/>\nA &#8211; Addition<br \/>\nS &#8211; Subtraction<br \/>\nSo,<br \/>\n2<sup>5<\/sup>(5 &#8211; 6) + 9 \u00f7 3 = ( 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 ) ( 5 &#8211; 6 ) + ( 9 \u00f7 3 )<br \/>\n= ( 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 ) ( 5 &#8211; 6 ) + 3<br \/>\n= ( 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 ) ( -1 ) + 3<br \/>\n= -( 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 )\u00a0 + 3<br \/>\n= -32 + 3<br \/>\n= -29<\/p>\n<p><b>Solve the equation. Graph the solutions, if possible. <\/b>(Section 1.4)<\/p>\n<p>Question 51.<br \/>\n| x &#8211; 3 | + 4 = 9<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q51.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q51\" width=\"350\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q51.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q51-300x281.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Question 52.<br \/>\n| 3y &#8211; 12 | &#8211; 7 = 2<br \/>\nAnswer:<br \/>\nThe values of y are: 7 and 1<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 3y &#8211; 12 | &#8211; 7 = 2<br \/>\n| 3y &#8211; 12 | = 2 + 7<br \/>\n| 3y &#8211; 12 | = 9<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n3y &#8211; 12 = 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3y &#8211; 12 = -9<br \/>\n3y = 9 + 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a03y = -9 + 12<br \/>\n3y = 21\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3y = 3<br \/>\ny = 21 \/ 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y = 3 \/ 3<br \/>\ny = 7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of y are: 7 and 1<\/p>\n<p>Question 53.<br \/>\n2 | 2r + 4 | = -16<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q53.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q53\" width=\"564\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q53.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-1-Solving-Linear-Equations-Lesson-1.5-Q53-300x115.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 54.<br \/>\n-4 | s + 9 | = -24<br \/>\nAnswer:<br \/>\nThe value of s is: -3 and -15<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n-4 | s + 9 | = -24<br \/>\n| s + 9 | = -24 \u00f7 ( -4 )<br \/>\n| s + 9 | = 6 [ Since &#8211; \u00f7 &#8211; = + ]<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\ns + 9 = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s + 9 = -6<br \/>\ns = 6 &#8211; 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = -6 &#8211; 9<br \/>\ns = -3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0s = -15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of s are: -3 and -15<\/p>\n<h3><a id=\"Solving_Linear_Equations_Performance_Task:_Magic_of_Mathematics\"><\/a>Solving Linear Equations Performance Task: Magic of Mathematics<\/h3>\n<p><b>1.4\u20131.5 What Did You Learn?<\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-102.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 102\" width=\"476\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-102.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-102-300x33.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 1.4<br \/>\n<\/b><img loading=\"lazy\" class=\"alignnone size-full wp-image-33904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-103.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 103\" width=\"326\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-103.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-103-300x75.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\n<b>Section 1.5<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-104.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 104\" width=\"215\" height=\"45\" \/><\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow did you decide whether your friend\u2019s argument in Exercise 46 on page 33 made sense?<br \/>\nAnswer:<br \/>\nOn page 33 in Exercise 46,<br \/>\nThe given absolute equation is:<br \/>\n| 3x + 8 | &#8211; 9 = -5<br \/>\n| 3x + 8 | = -5 + 9<br \/>\n| 3x + 8 | = 4<br \/>\nSo, from the absolute equation,<br \/>\nWe can say that the given absolute value equation has a solution<br \/>\nBut, according to your friend,<br \/>\nThe argument is that the absolute value equation has no solution<\/p>\n<p>Question 2.<br \/>\nHow did you use the structure of the equation in Exercise 59 on page 34 to rewrite the equation?<br \/>\nAnswer:<br \/>\nThe given absolute value equation in Exercise 59 on page 34 is:<br \/>\n8 | x + 2 | &#8211; 6 = 5 | x + 2 | + 3<br \/>\nThe above equation can be re-written as:<br \/>\n8 | x + 2\u00a0 | &#8211; 5\u00a0 | x + 2 | = 3 + 6<br \/>\n3 | x + 2\u00a0 | = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the re-written form of the given absolute value equation is:<br \/>\n3 | x + 2 | = 9<\/p>\n<p>Question 3.<br \/>\nWhat entry points did you use to answer Exercises 43 and 44 on page 42?<br \/>\nAnswer:<br \/>\nIn Exercises 43 and 44 on page 42,<br \/>\nWe used the triangles as an entry point<br \/>\nIn Exercise 43,<br \/>\nThe given figure is a pentagon<br \/>\nUsing the above entry point,<br \/>\nWe divided the pentagon into 5 triangles<br \/>\nIn Exercise 44,<br \/>\nThe given figure is a Hexagon<br \/>\nUsing the above entry point,<br \/>\nWe divided the hexagon into 6 triangles.<\/p>\n<p><b>Performance Task<\/b><\/p>\n<p><b>Magic of Mathematics<\/b><\/p>\n<p>Have you ever watched a magician perform a number trick? You can use algebra to explain how these types of tricks work.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-105.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 105\" width=\"268\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-105.png 268w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-105-265x300.png 265w\" sizes=\"(max-width: 268px) 100vw, 268px\" \/><br \/>\nTo explore the answers to these questions and more, go to <img loading=\"lazy\" class=\"alignnone size-full wp-image-33908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-106.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 106\" width=\"83\" height=\"84\" \/><\/p>\n<h3><a id=\"Solving_Linear_Equations_Chapter_Review\"><\/a>Solving Linear Equations Chapter Review<\/h3>\n<p><b>1.1 Solving Simple Equations <\/b>(pp. 3\u201310)<\/p>\n<p>a. Solve x \u2212 5 = \u22129. Justify each step.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-106.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 106.1\" width=\"443\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-106.1.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-106.1-300x77.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>b. Solve 4x = 12. Justify each step.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-107.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 107\" width=\"458\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-107.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-107-300x85.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p><b>Solve the equation. Justify each step. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\nz + 3 = -6<br \/>\nAnswer:<br \/>\nThe value of z is: -9<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nz + 3 = -6<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nz = -6 &#8211; ( +3 )<br \/>\nz = -6 &#8211; 3<br \/>\nz = -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of z is: -9<\/p>\n<p>Question 2.<br \/>\n2.6 = -0.2t<br \/>\nAnswer:<br \/>\nThe value of t is: -13<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2.6 = -0.2t<br \/>\n\\(\\frac{26}{10}\\) = &#8211;\\(\\frac{2}{10}\\)t<br \/>\nt = \\(\\frac{26}{10}\\) \u00f7 ( &#8211;\\(\\frac{2}{10}\\) )<br \/>\nt = &#8211; \\(\\frac{26}{10}\\) \u00d7 \\(\\frac{10}{2}\\)<br \/>\nt = -13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of t is: -13<\/p>\n<p>Question 3.<br \/>\n&#8211; \\(\\frac{n}{5}\\) = -2<br \/>\nAnswer:<br \/>\nThe value of n is: 10<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n&#8211;\\(\\frac{n}{5}\\) = -2<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-n = -2 \u00d7 5<br \/>\n-n = -10<br \/>\nn = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n is: 10<\/p>\n<p><b>1.2 Solving Multi-Step Equations<\/b> (pp. 11\u201318)<\/p>\n<p>Solve \u22126x + 23 + 2x = 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-108.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 108\" width=\"494\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-108.png 494w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-108-300x101.png 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p><b>Solve the equation. Check your Solution.<\/b><\/p>\n<p>Question 4.<br \/>\n3y + 11 = -16<br \/>\nAnswer:<br \/>\nThe value of y is: -9<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3y + 11 = -16<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n3y = -16 &#8211; 11<br \/>\n3y = -27<br \/>\ny = -27 \u00f7 3<br \/>\ny = -9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: -9<\/p>\n<p>Question 5.<br \/>\n6 = 1 &#8211; b<br \/>\nAnswer:<br \/>\nThe value of b is: -5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n6 = 1 &#8211; b<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\nb = 1 &#8211; 6<br \/>\nb = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of b is: -5<\/p>\n<p>Question 6.<br \/>\nn + 5n + 7 = 43<br \/>\nAnswer:<br \/>\nThe value of n is: 6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nn + 5n + 7 = 43<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n6n + 7 = 43<br \/>\n6n = 43 &#8211; 7<br \/>\n6n = 36<br \/>\nn = 36 \u00f7 6<br \/>\nn = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n is: 6<\/p>\n<p>Question 7.<br \/>\n-4(2z + 6) &#8211; 12 = 4<br \/>\nAnswer:<br \/>\nThe value of z is: -5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-4 ( 2z + 6 ) &#8211; 12 = 4<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n-4 ( 2z + 6 ) = 4 + 12<br \/>\n-4 ( 2z + 6 ) = 16<br \/>\n-4 ( 2z ) &#8211; 4 ( 6 ) = 16<br \/>\n-8z &#8211; 24 = 16<br \/>\n-8z = 16 + 24<br \/>\n-8z = 40<br \/>\nz = 40 \u00f7 ( -8 )<br \/>\nz = -5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of z is: -5<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{3}{2}\\)(x &#8211; 2) &#8211; 5 = 19<br \/>\nAnswer:<br \/>\nThe value of x is: 18<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{3}{2}\\) ( x &#8211; 2 ) &#8211; 5 = 19<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n\\(\\frac{3}{2}\\) ( x &#8211; 2 ) = 19 + 5<br \/>\n\\(\\frac{3}{2}\\) ( x &#8211; 2 ) = 24<br \/>\nx &#8211; 2 = 24 \u00d7 \\(\\frac{2}{3}\\)<br \/>\nx &#8211; 2 = \\(\\frac{24}{1}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\nx &#8211; 2 = 16<br \/>\nx = 16 + 2<br \/>\nx = 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 18<\/p>\n<p>Question 9.<br \/>\n6 = \\(\\frac{1}{5}\\)w + \\(\\frac{7}{5}\\)w &#8211; 4<br \/>\nAnswer:<br \/>\nThe value of w is: \\(\\frac{25}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n6 = \\(\\frac{1}{5}\\)w + \\(\\frac{7}{5}\\)w &#8211; 4<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n6 + 4 = \\(\\frac{1}{5}\\)w + \\(\\frac{7}{5}\\)w<br \/>\n10 = w [ \\(\\frac{1 + 7}{5}\\) ]<br \/>\n10 = \\(\\frac{8}{5}\\)w<br \/>\nw = 10 \u00d7 \\(\\frac{5}{8}\\)<br \/>\nw = \\(\\frac{10}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\nw = \\(\\frac{25}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: \\(\\frac{25}{4}\\)<\/p>\n<p><b>Find the value of x. Then find the angle measures of the polygon.<\/b><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-109.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 109\" width=\"203\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\nThe angle measures of the given polygon are: 110\u00b0, 50\u00b0, 20\u00b0<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-109.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 109\" width=\"203\" height=\"82\" \/><br \/>\nFrom the above figure,<br \/>\nThe angle measures are: 110\u00b0, 5x\u00b0, 2x\u00b0<br \/>\nIt is also given that<br \/>\nThe sum of the angle measures = 180\u00b0<br \/>\nSo,<br \/>\n110 + 5x + 2x = 180\u00b0<br \/>\n7x = 180 &#8211; 110<br \/>\n7x = 70\u00b0<br \/>\nx = 70 \/ 7<br \/>\nx = 10\u00b0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the angle measures of the given polygon are: 110\u00b0, 50\u00b0, 20\u00b0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-110.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 110\" width=\"196\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe angle measures of the given polygon are: 126\u00b0, 126\u00b0, 96\u00b0, 96\u00b0, 96\u00b0<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-110.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 110\" width=\"196\" height=\"99\" \/><br \/>\nFrom the above figure,<br \/>\nThe angle measures of the given polygon are: ( x &#8211; 30 )\u00b0, x\u00b0, x\u00b0, ( x &#8211; 30 )\u00b0, ( x &#8211; 30 )\u00b0<br \/>\nIt is also given that,<br \/>\nThe sum of the angle measures of the given polygon = 540\u00b0<br \/>\nSo,<br \/>\n( x &#8211; 30 )\u00b0 + x\u00b0 + x\u00b0 + ( x &#8211; 30 )\u00b0 + ( x &#8211; 30 )\u00b0 = 540\u00b0<br \/>\n5x &#8211; 90\u00b0 = 540\u00b0<br \/>\n5x = 540\u00b0 + 90\u00b0<br \/>\n5x = 630\u00b0<br \/>\nx = 630 \/ 5<br \/>\nx = 126\u00b0<br \/>\nHence,f rom the above,<br \/>\nWe can conclude that the angle measures of the given polygon are: 126\u00b0, 126\u00b0, 96\u00b0, 96\u00b0, 96\u00b0<\/p>\n<p><b>1.3 Solving Equations with Variables on Both Sides<\/b> (pp. 19\u201324)<\/p>\n<p>Solve 2( y \u2212 4) = \u22124( y + 8).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-111.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 111\" width=\"419\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-111.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-111-300x121.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p><b>Solve the equation.<\/b><\/p>\n<p>Question 12.<br \/>\n3n &#8211; 3 = 4n + 1<br \/>\nAnswer:<br \/>\nThe value of n is: -4<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3n &#8211; 3 = 4n + 1<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4n &#8211; 3n = -1 &#8211; 3<br \/>\nn = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of n is: -4<\/p>\n<p>Question 13.<br \/>\n5(1 + x) = 5x + 5<br \/>\nAnswer:<br \/>\nThe given equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n5 ( 1 + x ) = 5x + 5<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n5 ( 1 ) + 5 ( x ) = 5x + 5<br \/>\n5 + 5x = 5x + 5<br \/>\n5 = 5x &#8211; 5x + 5<br \/>\n5 = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation has no solution<\/p>\n<p>Question 14.<br \/>\n3(n + 4) = \\(\\frac{1}{2}\\)(6n + 4)<br \/>\nAnswer:<br \/>\nThe given equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3 ( n + 4 ) = \\(\\frac{1}{2}\\) ( 6n + 4 )<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n3 ( n ) + 3 ( 4 ) = \\(\\frac{1}{2}\\) ( 6n + 4 )<br \/>\n3n + 12 = \\(\\frac{1}{2}\\) ( 6n + 4 )<br \/>\n2 ( 3n + 12 ) = 6n + 4<br \/>\n2 ( 3n ) + 2 ( 12 ) = 6n + 4<br \/>\n6n + 24 = 6n + 4<br \/>\n24 = 6n &#8211; 6n + 4<br \/>\n24 = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation has no solution<\/p>\n<p><b>1.4 Solving Absolute Value Equations<\/b> (pp. 27\u201334)<\/p>\n<p>a. Solve | x \u2212 5 | = 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-112.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 112\" width=\"436\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-112.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-112-300x83.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>b. Solve | 2x + 6 | = 4x. Check your solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-113.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 113\" width=\"443\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-113.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-113-300x144.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-114.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 114\" width=\"178\" height=\"266\" \/><\/p>\n<p>Check the apparent solutions to see if either is extraneous.<br \/>\nThe solution is x = 3. Reject x = -1 because it is extraneous.<\/p>\n<p><b>Solve the equation. Check your solutions.<\/b><\/p>\n<p>Question 15.<br \/>\n| y + 3 | = 17<br \/>\nAnswer:<br \/>\nThe value of y is: 14 or -20<\/p>\n<p>Explaantion:<br \/>\nThe given absolute value equation is:<br \/>\n| y + 3 | = 17<br \/>\nWe know that,<br \/>\n| x | = x for x\u00a0 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\ny + 3 = 17\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0y + 3 = -17<br \/>\ny = 17 &#8211; 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = -17 &#8211; 3<br \/>\ny = 14\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 y = -20<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 14 or -20<\/p>\n<p>Question 16.<br \/>\n-2 | 5w &#8211; 7 | + 9 = -7<br \/>\nAnswer:<br \/>\nThe value of w is: 3 or &#8211;\\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n-2 | 5w &#8211; 7 | + 9 = -7<br \/>\n-2 | 5w &#8211; 7 | = -7 &#8211; 9<br \/>\n-2 | 5w &#8211; 7 | = -16<br \/>\n| 5w &#8211; 7 | = -16 \/ ( -2 )<br \/>\n| 5w &#8211; 7 | = 8<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n5w &#8211; 7 = 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a05w &#8211; 7 = -8<br \/>\n5w = 8 + 7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5w = -8 + 7<br \/>\n5w = 15\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a05w = -1<br \/>\nw = 15 \u00f7 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0w = &#8211;\\(\\frac{1}{5}\\)<br \/>\nw = 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 w =-\\(\\frac{1}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of w is: 3 or &#8211;\\(\\frac{1}{5}\\)<\/p>\n<p>Question 17.<br \/>\n| x &#8211; 2 | = | 4 + x |<br \/>\nAnswer:<br \/>\nThe given absolute equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; 2 | = | 4 + x |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx &#8211; 2 = 4 + x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8211; ( x &#8211; 2 ) = &#8211; ( 4 + x )<br \/>\n-2 = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2 = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute equation has no solution<\/p>\n<p>Question 18.<br \/>\nThe minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds.<br \/>\nAnswer:<br \/>\nThe absolute value equation that represents the minimum and maximum speeds is:<br \/>\n| x &#8211; 84.5 | = 9.5<\/p>\n<p>Explanation:<br \/>\nIt is given that the minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour.<br \/>\nSo,<br \/>\nThe average wind speed sustained = ( 74 + 95 ) \/2<br \/>\n= 169 \/ 2<br \/>\n= 84.5 miles per hour<br \/>\nNow,<br \/>\nThe minimum wind speed from the average speed point = 84.5 &#8211; 74<br \/>\n= 9.5 miles per hour<br \/>\nSo,<br \/>\nThe absolute value equation that represents the minimum and maximum wind speed is:<br \/>\n| x &#8211; 84.5 | = 9.5<\/p>\n<p><b>1.5 Rewriting Equations and Formulas <\/b>(pp. 35\u201342)<br \/>\na. The slope-intercept form of a linear equation is y = mx + b. Solve the equation for m.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-115.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 115\" width=\"396\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-115.png 396w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-115-300x144.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p>b. The formula for the surface area S of a cylinder is S = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh. Solve the formula for the height h.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-116.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 116\" width=\"413\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-116.png 413w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-116-300x150.png 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<p><b>Solve the literal equation for y.<\/b><\/p>\n<p>Question 19.<br \/>\n2x &#8211; 4y = 20<br \/>\nAnswer:<br \/>\nThe value of y is: ( x \/ 2 ) &#8211; 5<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n2x &#8211; 4y = 20<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4y = 2x &#8211; 20<br \/>\ny = ( 2x &#8211; 20 ) \/ 4<br \/>\ny = ( 2x \/ 4 ) &#8211; ( 20 \/ 4 )<br \/>\ny = ( x \/ 2 ) &#8211; 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: ( x \/ 2 ) &#8211; 5<\/p>\n<p>Question 20.<br \/>\n8x &#8211; 3 = 5 + 4y<br \/>\nAnswer:<br \/>\nThe value of y is: 2x &#8211; 2<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\n8x &#8211; 3 = 5 + 4y<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\n4y = 8x &#8211; 3 &#8211; 5<br \/>\n4y = 8x &#8211; 8<br \/>\ny = ( 8x &#8211; 8 ) \/ 4<br \/>\ny = ( 8x \/ 4 ) &#8211; ( 8 &#8211; 4 )<br \/>\ny = 2x &#8211; 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: 2x &#8211; 2<\/p>\n<p>Question 21.<br \/>\na a = 9y + 3yx<br \/>\nAnswer:<br \/>\nThe value of y is: a\u00b2 \/ ( 3x + 9 )<\/p>\n<p>Explanation:<br \/>\nThe given literal equation is:<br \/>\na\u00b2 = 9y + 3yx<br \/>\nWhen we convert any sign from LHS, then the sign will be converted into the opposite sign in RHS,<br \/>\nSo,<br \/>\n+ in LHS is converted into \u2013 in RHS and vice-versa<br \/>\n\u00d7 in LHS is converted into \u00f7 in RHS and vice-versa<br \/>\nSo,<br \/>\na\u00b2 = y ( 3x + 9 )<br \/>\ny = a\u00b2 \/ ( 3x + 9 )<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of y is: a\u00b2 \/ ( 3x + 9 )<\/p>\n<p>Question 22.<br \/>\nThe volume V of a pyramid is given by the formula V = \\(\\frac{1}{3}\\)Bh, where B is the area of the base and h is the height.<br \/>\na. Solve the formula for h.<br \/>\nb. Find the height h of the pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-117.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 117\" width=\"202\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\na)<br \/>\nThe value of h is: \\(\\frac{3V}{B}\\)<\/p>\n<p>Explanation:<br \/>\nThe given formula is:<br \/>\nV = \\(\\frac{1}{3}\\)Bh<br \/>\nWhere,<br \/>\nB is the area of the base<br \/>\nh is the height<br \/>\nNow,<br \/>\n3V = Bh<br \/>\nh = \\(\\frac{3V}{B}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of h is: \\(\\frac{3V}{B}\\)<\/p>\n<p>b)<br \/>\nThe value of h is: 18 cm<\/p>\n<p>Explanation:<br \/>\nFrom the given figure,<br \/>\nArea of the base ( B ) = 36 cm\u00b2<br \/>\nVolume of the base ( V ) = 216 cm\u00b3<br \/>\nFrom part (a),<br \/>\nh = \\(\\frac{3V}{B}\\)<br \/>\nh = \\(\\frac{3 \u00d7 216}{36}\\)<br \/>\nh = \\(\\frac{3 \u00d7 216}{36 \u00d7 1}\\)<br \/>\nh = 18 cm<br \/>\nHence, from the above,<br \/>\nWe can conclud ethat the value of h is: 18 cm<\/p>\n<p>Question 23.<br \/>\nThe formula F = \\(\\frac{9}{5}\\)(K &#8211; 273.15) + 32 converts a temperature from kelvin K to degrees Fahrenheit F.<br \/>\na. Solve the formula for K.<br \/>\nb. Convert 180\u00b0F to kelvin K. Round your answer to the nearest hundredth.<br \/>\nAnswer:<br \/>\na)<br \/>\nThe formula for K is:<br \/>\nK = \\(\\frac{5}{9}\\) ( F &#8211; 32 ) + 273.15<\/p>\n<p>Explanation:<br \/>\nThe given formula for F is:<br \/>\nF = \\(\\frac{9}{5}\\) ( K &#8211; 273.15 ) + 32<br \/>\nNow,<br \/>\nF &#8211; 32 = \\(\\frac{9}{5}\\) ( K &#8211; 273.15 )<br \/>\n\\(\\frac{5}{9}\\) ( F &#8211; 32 ) = K &#8211; 273.15<br \/>\nK = \\(\\frac{5}{9}\\) ( F &#8211; 32 ) + 273.15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of K is: \\(\\frac{5}{9}\\) ( F &#8211; 32 ) + 273.15<\/p>\n<h3><a id=\"Solving_Linear_Equations_Chapter_Test\"><\/a>Solving Linear Equations Chapter Test<\/h3>\n<p><b>Solve the equation. Justify each step. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\nx &#8211; 7 = 15<br \/>\nAnswer:<br \/>\nThe value of x is: 22<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\nx &#8211; 7 = 15<br \/>\nNow,<br \/>\nx = 15 + 7<br \/>\nx = 22<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 22<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{3}\\)x = 5<br \/>\nAnswer:<br \/>\nThe value of x is: \\(\\frac{15}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{2}{3}\\) x = 5<br \/>\nNow,<br \/>\nx = 5 \u00d7 \\(\\frac{3}{2}\\)<br \/>\nx = \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\nx = \\(\\frac{15}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: \\(\\frac{15}{2}\\)<\/p>\n<p>Question 3<br \/>\n11x + 1 = -1 + x<br \/>\nAnswer:<br \/>\nThe value of x is: &#8211;\\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n11x + 1 = -1 + x<br \/>\nNow,<br \/>\n11x &#8211; x = -1 &#8211; 1<br \/>\n10x = -2<br \/>\nx = &#8211;\\(\\frac{2}{10}\\)<br \/>\nx = &#8211;\\(\\frac{1}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p><b>Solve the equation.<\/b><\/p>\n<p>Question 4.<br \/>\n2 | x &#8211; 3 | &#8211; 5 = 7<br \/>\nAnswer:<br \/>\nThe value of x is: 9 or -3<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n2 | x &#8211; 3 | &#8211; 5 = 7<br \/>\n2 | x &#8211; 3 | = 7 + 5<br \/>\n2 | x &#8211; 3 | = 12<br \/>\n| x &#8211; 3 | = \\(\\frac{12}{2}\\)<br \/>\n| x &#8211; 3 | = 6<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx &#8211; 3 = 6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x &#8211; 3 = -6<br \/>\nx = 6 + 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x = -6 + 3<br \/>\nx = 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = -3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 9 or -3<\/p>\n<p>Question 5.<br \/>\n| 2x &#8211; 19 | = 4x + 1<br \/>\nAnswer:<br \/>\nThe value of x is: -10 or 3<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 2x &#8211; 19 | = 4x + 1<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\n4x + 1 = 2x &#8211; 19\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04x + 1 = &#8211; ( 2x &#8211; 19 )<br \/>\n4x &#8211; 2x = -19 &#8211; 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04x + 2x = 19 &#8211; 1<br \/>\n2x = -20\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6x = 18<br \/>\nx = \\(\\frac{-20}{2}\\)\u00a0 \u00a0 \u00a0 x = \\(\\frac{18}{6}\\)<br \/>\nx = -10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0x = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -10 or 3<\/p>\n<p>Question 6.<br \/>\n-2 + 5x &#8211; 7 = 3x &#8211; 9 + 2x<br \/>\nAnswer:<br \/>\nThe given absolute equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n-2 + 5x &#8211; 7 = 3x &#8211; 9 + 2x<br \/>\n5x &#8211; 9 = 5x &#8211; 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value equation has no solution<\/p>\n<p>Question 7.<br \/>\n3(x + 4) &#8211; 1 = -7<br \/>\nAnswer:<br \/>\nThe value of x is: -6<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3 ( x + 4 ) &#8211; 1 = -7<br \/>\nSo,<br \/>\n3 ( x ) + 3 ( 4 ) = -7 + 1<br \/>\n3x + 12 = -6<br \/>\n3x = -6 &#8211; 12<br \/>\n3x = -18<br \/>\nx = &#8211;\\(\\frac{18}{3}\\)<br \/>\nx = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: -6<\/p>\n<p>Question 8.<br \/>\n| 20 + 2x | = | 4x + 4 |<br \/>\nAnswer:<br \/>\nThe value of x is: 8<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| 20 + 2x | = | 4x + 4 |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\n20 + 2x = 4x + 4<br \/>\n4x &#8211; 2x = 20 &#8211; 4<br \/>\n2x = 16<br \/>\nx = \\(\\frac{16}{2}\\)<br \/>\nx = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x is: 8<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{3}\\)(6x + 12) &#8211; 2(x &#8211; 7) = 19<br \/>\nAnswer:<br \/>\nThe given equation has no solution<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n\\(\\frac{1}{3}\\) ( 6x + 12 ) &#8211; 2 ( x &#8211; 7 ) = 19<br \/>\nNow,<br \/>\n\\(\\frac{1}{3}\\) ( 6x &#8211; 12 ) = 19 + 2 ( x &#8211; 7 )<br \/>\n\\(\\frac{1}{3}\\) ( 6x &#8211; 12 ) = 19 + 2x &#8211; 14<br \/>\n\\(\\frac{1}{3}\\) ( 6x &#8211; 12 ) = 2x + 5<br \/>\n1 ( 6x &#8211; 12 ) = 3 ( 2x + 5 )<br \/>\n6x &#8211; 12 = 6x + 15<br \/>\n6x &#8211; 6x = 15 + 12<br \/>\n15 = -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation has no solution<\/p>\n<p><b>Describe the values of c for which the equation has no solution. Explain your reasoning.<\/b><\/p>\n<p>Question 10.<br \/>\n3x &#8211; 5 = 3x &#8211; c<br \/>\nAnswer:<br \/>\nThe value of c is: 5<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n3x &#8211; 5 = 3x &#8211; c<br \/>\nIt is given that the equation has no solution<br \/>\nSo,<br \/>\n3x &#8211; 3x &#8211; 5 =-c<br \/>\n-c = -5<br \/>\nc = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of c is: 5<\/p>\n<p>Question 11.<br \/>\n| x &#8211; 7 | = c<br \/>\nAnswer:<br \/>\nThe value of c is: -7<\/p>\n<p>Explanation:<br \/>\nThe given absolute value equation is:<br \/>\n| x &#8211; 7 | = c<br \/>\nIt is given that the equation has no solution i.e., x = 0<br \/>\nSo,<br \/>\n0 &#8211; 7 = c<br \/>\nc = -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of c is: -7<\/p>\n<p>Question 12.<br \/>\nA safety regulation states that the minimum height of a handrail is 30 inches. The maximum height is 38 inches. Write an absolute value equation that represents the minimum and maximum heights.<br \/>\nAnswer:<br \/>\nThe absolute value expression that represents the minimum and maximum heights is:<br \/>\n| x &#8211; 64 | = 34<\/p>\n<p>Explanation:<br \/>\nIt is given that a safety regulation states that the minimum height of a handrail is 30 inches. The maximum height is 38 inches.<br \/>\nSo,<br \/>\nThe average height of a handrail = ( 30 + 38 ) \/ 2<br \/>\n= 68 \/ 2<br \/>\n= 34 inches<br \/>\nNow,<br \/>\nThe minimum height from the average height of a handrail = 34 + 30<br \/>\n= 64 inches<br \/>\nHence,<br \/>\nThe absolute value equation that represents the minimum and maximum height of a handrail is:<br \/>\n| x &#8211; 64 | = 34<\/p>\n<p>Question 13.<br \/>\nThe perimeter P (in yards) of a soccer field is represented by the formula P = 2\u2113 + 2w, where \u2113 is the length (in yards) and w is the width (in yards).<br \/>\na. Solve the formula for w.<br \/>\nAnswer:<br \/>\nThe given formula is:<br \/>\nP = 2l + 2w<br \/>\nWhere,<br \/>\nP is perimeter ( in yards )<br \/>\nl is the length ( in yards )<br \/>\nw is the width ( in yards )<br \/>\nSo,<br \/>\n2w = P &#8211; 2l<br \/>\nw = ( P &#8211; 2l ) \/ 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the formula for w is:<br \/>\nw = ( P &#8211; 2l ) \/ 2<\/p>\n<p>b. Find the width of the field.<br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-117.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 117.1\" width=\"248\" height=\"180\" \/><br \/>\nFrom the above figure,<br \/>\nPerimeter ( P ) = 330 yd<br \/>\nLength ( l) = 100 yd<br \/>\nFrom part (a),<br \/>\nw = ( P &#8211; 2l ) \/2<br \/>\nw = ( 330 &#8211; 100 ) \/ 2<br \/>\nw = 230 \/ 2<br \/>\nw = 115 yd<br \/>\nHence, from the above,<br \/>\nWe can conclude that the width of the field is: 115 yd<\/p>\n<p>c. About what percent of the field is inside the circle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-117.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 117.1\" width=\"248\" height=\"180\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nYour car needs new brakes. You call a dealership and a local mechanic for prices.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-118.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 118\" width=\"439\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-118.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-118-300x63.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><br \/>\na. After how many hours are the total costs the same at both places? Justify your answer.<br \/>\nAnswer:<br \/>\nFrom the given table,<br \/>\nLet the total labor hours be x<br \/>\nSo,<br \/>\nThe total cost at the Dealership = ( Cost of parts ) + ( Labor cost per hour ) \u00d7 ( Total labor hours )<br \/>\n= 24 + 99x<br \/>\nThe total cost at the local mechanic = ( Cost of parts ) + ( Labor cost per hour ) \u00d7 ( Total labor hours )<br \/>\n= 45 + 89x<br \/>\nIt is given that the total cost is the same in both places<br \/>\nSo,<br \/>\n24 + 99x = 45 + 89x<br \/>\n99x &#8211; 89x = 45 &#8211; 24<br \/>\n10x = 21<br \/>\nx = 21 \/ 10<br \/>\nx = 2.1 hours<br \/>\nHence, from the above,<br \/>\nWe can conclude that after 2.1 hours, the total cost will be the same in both places<\/p>\n<p>b. When do the repairs cost less at the dealership? at the local mechanic? Explain.<br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-118.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 118\" width=\"439\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-118.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-118-300x63.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><br \/>\nFrom the above table,<br \/>\nCompare the labor cost per hour<br \/>\nBy comparison,<br \/>\nWe can say that the labor cost per hour is less at the local mechanic<br \/>\nHence, from the above,<br \/>\nWe can conclude that the repair cost less at the local mechanic<\/p>\n<p>Question 15.<br \/>\nConsider the equation | 4x + 20 | = 6x. Without calculating, how do you know that x = -2 is an extraneous solution?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe absolute value equations only accept the values greater than or equal to 0<br \/>\nHence,<br \/>\nFor the given absolute value equation,<br \/>\n| 4x + 20 | = 6x<br \/>\nx = -2 is an extraneous solution<\/p>\n<p>Question 16.<br \/>\nYour friend was solving the equation shown and was confused by the result \u201c-8 = -8.\u201d Explain what this result means.<br \/>\n4(y &#8211; 2) &#8211; 2y = 6y &#8211; 8 &#8211; 4y<br \/>\n4y &#8211; 8 &#8211; 2y = 6y &#8211; 8 &#8211; 4y<br \/>\n2y &#8211; 8 = 2y &#8211; 8<br \/>\n-8 = -8<br \/>\nAnswer:<br \/>\nThe result &#8221; -8 = -8 &#8221; means that the solved equation has no solution<\/p>\n<h3><a id=\"Solving_Linear_Equations_Cumulative_Assessment\"><\/a>Solving Linear Equations Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nA mountain biking park has 48 trails, 37.5% of which are beginner trails. The rest are divided evenly between intermediate and expert trails. How many of each kind of trail are there?<br \/>\nA. 12 beginner, 18 intermediate, 18 expert<br \/>\nB. 18 beginner, 15 intermediate, 15 expert<br \/>\nC. 18 beginner, 12 intermediate, 18 expert<br \/>\nD. 30 beginner, 9 intermediate, 9 expert<\/p>\n<p>Answer:<br \/>\nThe correct option is: B<br \/>\nThe number of beginner trials is: 18<br \/>\nThe number of intermediate trials is: 15<br \/>\nThe number of expert trials is: 15<\/p>\n<p>Explanation:<br \/>\nIt is given that a mountain biking park has 48 trails, 37.5% of which are beginner trails. The rest are divided evenly between intermediate and expert trials.<br \/>\nSo,<br \/>\nThe number of beginner trials is 3.5 % of the total number of trials<br \/>\nIt is given that the total number of trials is: 48<br \/>\nWe know that,<br \/>\nThe value of 37.5 % is: \\(\\frac{3}{8}\\) [ 37.5 % = 50 % &#8211; 12.5 % ]<br \/>\nSo,<br \/>\nThe number of beginner trials = \\(\\frac{3}{8}\\) \u00d7 48<br \/>\n= \\(\\frac{3}{8}\\) \u00d7 \\(\\frac{48}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 48}{8 \u00d7 1}\\)<br \/>\n= 18<br \/>\nSo,<br \/>\nThe number\u00a0 of intermediate and expert trials = ( The total number of trials ) &#8211; ( The number of beginner trials )<br \/>\n= 48 &#8211; 18<br \/>\n= 30 trials<br \/>\nIt is also given that the intermediate trials and expert trails are divided evenly<br \/>\nSo,<br \/>\n30 \u00f7 2 = 15 trials each<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe number of beginner trials is: 18<br \/>\nThe number of intermediate trials is: 15<br \/>\nThe number of expert trials is: 15<\/p>\n<p>Question 2.<br \/>\nWhich of the equations are equivalent to cx &#8211; a = b?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-119.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 119\" width=\"436\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-119.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-119-300x84.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Answer:<br \/>\nThe given equations are:<br \/>\na) cx &#8211; a + b = 2b<br \/>\nb) 0 = cx &#8211; a + b<br \/>\nc) 2cx &#8211; 2a = b \/ 2<br \/>\nd) x &#8211; a = b \/ 2<br \/>\ne) x = ( a + b ) \/ c<br \/>\nf) b + a = cx<br \/>\nNow,<br \/>\nWe have to find the equations from above that is equivalent to the given equation cx &#8211; a = b<br \/>\nNow,<br \/>\na)<br \/>\nThe given equation is:<br \/>\ncx &#8211; a + b = 2b<br \/>\nSo,<br \/>\ncx &#8211; a = b &#8211; b<br \/>\ncx &#8211; a = b<br \/>\nb)<br \/>\nThe given equation is:<br \/>\n0 = cx &#8211; a + b<br \/>\nSo,<br \/>\ncx &#8211; a = -b<br \/>\nc)<br \/>\nThe given equation is:<br \/>\n2cx &#8211; 2a = b \/ 2<br \/>\nSo,<br \/>\ncx &#8211; a = b \/ 4<br \/>\nd )<br \/>\nThe given equation is:<br \/>\ncx &#8211; a = b \/ 2<br \/>\nSo,<br \/>\n2 ( cx &#8211; a ) = b<br \/>\ne)<br \/>\nThe given equation is:<br \/>\nx = ( a + b ) \/ c<br \/>\nSo,<br \/>\ncx = a + b<br \/>\ncx &#8211; a = b<br \/>\nf)<br \/>\nThe given equation is:<br \/>\nb + a = cx<br \/>\nSo,<br \/>\ncx &#8211; a = b<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equations that are equivalent to cx &#8211; a = b is: a, e, f<\/p>\n<p>Question 3.<br \/>\nLet N represent the number of solutions of the equation 3(x &#8211; a) = 3x &#8211; 6. Complete each statement with the symbol &lt;, &gt;, or =.<br \/>\na. When a = 3, N ____ 1.<br \/>\nb. When a = -3, N ____ 1.<br \/>\nc. When a = 2, N ____ 1.<br \/>\nd. When a = -2, N ____ 1.<br \/>\ne. When a = x, N ____ 1.<br \/>\nf. When a = -x, N ____ 1.<\/p>\n<p>Answer:<br \/>\nThe given equation is:<br \/>\n3 ( x &#8211; a ) = 3x &#8211; 6<br \/>\nSo,<br \/>\n3x &#8211; 3a = 3x &#8211; 6<br \/>\nNow,<br \/>\na) When a = 3,<br \/>\n3x &#8211; 3 ( 3 ) = 3x &#8211; 6<br \/>\n3x &#8211; 9 = 3x &#8211; 6<br \/>\n9 = 6<br \/>\nHence,<br \/>\nWhen a = 3 there is no solution<br \/>\nHence,<br \/>\nN &lt; 1<br \/>\nb) When a = -3<br \/>\n3x + 3 ( 3 ) =3 x &#8211; 6<br \/>\n9 = -6<br \/>\nHence,<br \/>\nWhen a = -3, there is no solution<br \/>\nHence,<br \/>\nN &lt; 1<br \/>\nc) When a = 2<br \/>\n3x &#8211; 3 ( 2 ) = 3x &#8211; 6<br \/>\n3x &#8211; 6 =3x &#8211;<br \/>\n6 = 6<br \/>\nHence,<br \/>\nWhen a= 2, there is no solution<br \/>\nHence,<br \/>\nN &lt; 1<br \/>\nd) When a = -2<br \/>\n3x + 3 ( 2 ) = 3x &#8211; 6<br \/>\n3x + 6 = 3x &#8211; 6<br \/>\n6 = -6<br \/>\nHence,<br \/>\nWhen a = -2, thereis no solution<br \/>\nHence,<br \/>\nN &lt; 1<br \/>\ne) When a = x<br \/>\n3x &#8211; 3 ( x ) = 3x &#8211; 6<br \/>\n3x = 6<br \/>\nx = 6 \/ 3<br \/>\nx = 2<br \/>\nHence,<br \/>\nWhen a\u00a0 x, theer is 1 solution<br \/>\nHence,<br \/>\nN = 1<br \/>\nf) When a = -x<br \/>\n3x + 3 ( x ) = 3x &#8211; 6<br \/>\n6x &#8211; 3x = -6<br \/>\n3x = -6<br \/>\nx = -6 \/ 3<br \/>\nx = -2<br \/>\nHence,<br \/>\nWhen a = -x, there is 1 solution<br \/>\nHence,<br \/>\nN = 1<\/p>\n<p>Question 4.<br \/>\nYou are painting your dining room white and your living room blue. You spend $132 on 5 cans of paint. The white paint costs $24 per can, and the blue paint costs $28 per can.<br \/>\na. Use the numbers and symbols to write an equation that represents how many cans of each color you bought.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-120.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 120\" width=\"388\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-120.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-120-300x107.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nAnswer:<br \/>\nThe number of cans of white paint is: 2<br \/>\nThe number of cans of blue paint is: 3<\/p>\n<p>Explanation:<br \/>\nIt is given that you spend $132 on 5 cans of paint<br \/>\nIt is also given that the white paint costs $24 per can and the blue paint costs $28 per can<br \/>\nNow,<br \/>\nLet<br \/>\nThe number of white cans is: x<br \/>\nThe number of blue cans be: 5 &#8211; x<br \/>\nSo,<br \/>\nThe total cost of paint = ( The number of white cans ) \u00d7 ( The cost of white paint per can ) + ( The number of blue cans ) \u00d7 ( The cost of blue paint per can )<br \/>\n132 = 24x + 28 ( 5 &#8211; x )<br \/>\n24x + 28 ( 5 ) &#8211; 28x = 132<br \/>\n140 &#8211; 4x = 132<br \/>\n4x = 140 &#8211; 132<br \/>\n4x = 8<br \/>\nx = 8 \u00f7 4<br \/>\nx = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe number of cans of white paint is: 2<br \/>\nThe number of cans of blue paint is: 3<\/p>\n<p>b. How much would you have saved by switching the colors of the dining room and living room? Explain.<br \/>\nAnswer:<br \/>\nThe money you have saved by switching the colors of the dining room and living room is: $0<\/p>\n<p>Explanation:<br \/>\nFrom part (a),<br \/>\nThe number of white cans is: 2<br \/>\nThe number of blue cans is: 3<br \/>\nIt is given that white color is used in the dining room and the blue color is used in the living room<br \/>\nSo,<br \/>\nThe cost of white paint after interchanging the color in the living room = 24 \u00d7 2<br \/>\n= $48<br \/>\nThe cost of blue paint after interchanging the color in the dining room = 28 \u00d7 3<br \/>\n= $84<br \/>\nSo,<br \/>\nThe total cost of paint after interchanging the colors = 48 + 84<br \/>\n= $132<br \/>\nHence,<br \/>\nThe amount of money saved = ( The money you paid for the paint before interchanging ) &#8211; ( The money you paid for the paint after interchanging )<br \/>\n= 132 &#8211; 132<br \/>\n=$0<\/p>\n<p>Question 5.<br \/>\nWhich of the equations are equivalent?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-121.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 121\" width=\"333\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-121.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-121-300x103.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Answer:<br \/>\nThe given equations are:<br \/>\na ) 6x + 6 = -14<br \/>\nb ) 8x + 6 = -2x &#8211; 14<br \/>\nc ) 5x + 3 = -7<br \/>\nd ) 7x + 3 = 2x &#8211; 13<br \/>\nNow,<br \/>\nTo find the equivalent equations, find the value of x<br \/>\nSo,<br \/>\na)<br \/>\nThe given equation is:<br \/>\n6x + 6 = -14<br \/>\n6x = -14 &#8211; 6<br \/>\n6x = -20<br \/>\nx = -20 \/ 6<br \/>\nx = -10 \/ 3<br \/>\nb)<br \/>\nThe given equation is:<br \/>\n8x + 6 = -2x &#8211; 14<br \/>\n8x + 2x = -14 &#8211; 6<br \/>\n10x = -20<br \/>\nx = -20 \/ 10<br \/>\nx = -2<br \/>\nc)<br \/>\nThe given equation is:<br \/>\n5x + 3 = -7<br \/>\n5x = -7 -3<br \/>\n5x = -10<br \/>\nx= -10 \/ 5<br \/>\nx = -2<br \/>\nd)<br \/>\nThe given equation is:<br \/>\n7x + 3 = 2x &#8211; 13<br \/>\n7x &#8211; 2x = -13 &#8211; 3<br \/>\n5x = -16<br \/>\nx = -16 \/ 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equations c) and d) are equivalent<\/p>\n<p>Question 6.<br \/>\nThe perimeter of the triangle is 13 inches. What is the length of the shortest side?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-122.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 122\" width=\"221\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe length of the shortest side is: 3 inches<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nThe perimeter is the sum of all the sides of the given figure<br \/>\nIt is given that the perimeter of the triangle is: 13 inches<br \/>\nSo,<br \/>\nThe perimeter of the triangle = ( x &#8211; 5 ) + ( x \/ 2 ) + 6<br \/>\n13 = x + 1 + ( x \/ 2 )<br \/>\n13 = ( 2x \/ 2 ) + ( x \/ 2 ) + 1<br \/>\n3x \/ 2 = 13 &#8211; 1<br \/>\n3x \/ 2 = 12<br \/>\n3x = 12 \u00d7 2<br \/>\n3x = 24<br \/>\nx = 24 \/ 3<br \/>\nx = 8<br \/>\nSo,<br \/>\nThe lengths of all sides are: ( 8 &#8211; 5 ), 6, ( 8 \/ 2 ) = 3 inches, 6 inches, 4 inches<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the shortest side is: 3 inches<\/p>\n<p>Question 7.<br \/>\nYou pay $45 per month for cable TV. Your friend buys a satellite TV receiver for $99 and pays $36 per month for satellite TV. Your friend claims that the expenses for a year of satellite TV are less than the expenses for a year of cable.<br \/>\na. Write and solve an equation to determine when you and your friend will have paid the same amount for TV services.<br \/>\nAnswer:<br \/>\nIt is given that you pay $45 per month for cable TV. Your friend buys a satellite TV receiver for $99 and pays $36 per month for satellite TV<br \/>\nSo,<br \/>\nLet the number of months be x<br \/>\nNow,<br \/>\nThe time they paid the same amount for TV services is:<br \/>\n45x = 99 + 36x<br \/>\n45x &#8211; 36x = 99<br \/>\n9x= 99<br \/>\nx = 99 \/ 9<br \/>\nx = 11<br \/>\nHence, from the above,<br \/>\nWe can conclude that after 11 months, you and your friend will pay the same amount for TV services<\/p>\n<p>b. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYour friend is correct<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n1 year = 12 months<br \/>\nSo,<br \/>\nThe expenses paid by you for TV services = 45x = 45 \u00d7 12 = $540<br \/>\nThe expenses paid by your friend for TV services = 99 + 36x<br \/>\n= 99 + 36 ( 12 )<br \/>\n= 99 + 432<br \/>\n= $531<br \/>\nBy comparing the expenses of you and your friend,<br \/>\nWe can conclude that your friend is correct<\/p>\n<p>Question 8.<br \/>\nPlace each equation into one of the four categories.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-123.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 123\" width=\"660\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-123.png 660w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-123-300x83.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>Question 9.<br \/>\nA car travels 1000 feet in 12.5 seconds. Which of the expressions do not represent the average speed of the car?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-1-Solving-Linear-Equations-124.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 1 Solving Linear Equations 124\" width=\"286\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nWe know that,<br \/>\nAverage speed = ( Distance ) \u00f7 ( Time )<br \/>\nIt is given that a car travels 1000 feet in 12.5 seconds<br \/>\nSo,<br \/>\nAverage speed = 1000 \/ 12.5<br \/>\n= 80\\(\\frac{feet}{second}\\)<br \/>\nNow,<br \/>\nThe given options are:<br \/>\nA) 80\\(\\frac{second}{feet}\\) B) 80\\(\\frac{feet}{second}\\) C) \\(\\frac{80 feet}{second}\\)<br \/>\nD) \\(\\frac{second}{ 80 feet}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that option B) represents the average speed<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations available here are free of cost. Students can seek homework help and solve the questions covered in the Ch 1 lessons. Also, these solutions of BIM Algebra 1 Ch 1 Answer Book improve their math skills and become math proficient in the future. Choosing &#8230; <a title=\"Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-1\/\" aria-label=\"More on Big Ideas Math Algebra 1 Answers Chapter 1 Solving Linear Equations\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/33786"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=33786"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/33786\/revisions"}],"predecessor-version":[{"id":90349,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/33786\/revisions\/90349"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=33786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=33786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=33786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}