{"id":28878,"date":"2022-04-03T16:00:06","date_gmt":"2022-04-03T10:30:06","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=28878"},"modified":"2022-04-07T10:57:27","modified_gmt":"2022-04-07T05:27:27","slug":"big-ideas-math-answers-grade-7-chapter-3","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-3\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 3 Expressions"},"content":{"rendered":"<p><strong>Big Ideas Math 7th Grade Chapter 3 Expressions Answer Key: <\/strong>Download free step-by-step problem and solution pdf of Big Ideas Math Grade 7 Chapter 3 Expressions from here. Follow the various concepts and topics involved in this chapter and make your preparation easy and efficient. We are providing the free Big Ideas Math Book 7th Grade Answer Key Chapter 3 Expressions pdf links in the below sections.<\/p>\n<p>Refer to the <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7\/\">Big Ideas Math Answers Grade 7 <\/a>Chapter 3 Expressions and finish your preparation and assignment. The solutions for 7th-grade chapter 3 expressions give you a clear idea of how to solve and understand the problems. With the help of experts, we have given all the problems of a chapter in a single pdf. To avoid time waste, download the pdf and start your preparation.<\/p>\n<h2>Big Ideas Math Book 7th Grade Answer Key Chapter 3 Expressions<\/h2>\n<p>There are various topics available in the Expressions Chapter. Those are Adding and Subtracting Linear Expressions, The Distributive Property, Algebraic Expressions, Factoring Expressions, and so on. Find out the solutions and problems involved in these chapters. To understand the concept more clearly, compare the problems with real-life situations.<\/p>\n<p>Follow<strong> BIM 7th Grade Chapter 3 Expressions Solution Ke<\/strong>y and know your strengths and weaknesses. First of all, know the syllabus of expressions and then based on the various concepts, prepare the timetable. Involve the number of concepts, time remaining to learn all the topics, etc, and prepare the timetable according to it. Know the example problems and formulae in the below sections.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Expressions_STEAM_VIDEO\/Performance\">Expressions STEAM VIDEO\/Performance<\/a><\/li>\n<li><a href=\"#Expressions_Getting_Ready_for_Chapter_3\">Expressions Getting Ready for Chapter 3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Algebraic Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.1_Algebraic_Expressions\">Lesson 3.1 Algebraic Expressions<\/a><\/li>\n<li><a href=\"#Algebraic_Expressions_Homework_&amp;_Practice_3.1\">Algebraic Expressions Homework &amp; Practice 3.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Adding and Subtracting Linear Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.2_Adding_and_Subtracting_Linear_Expressions\">Lesson 3.2 Adding and Subtracting Linear Expressions<\/a><\/li>\n<li><a href=\"#Adding_and_Subtracting_Linear_Expressions_Homework_&amp;_Practice_3.2\">Adding and Subtracting Linear Expressions Homework &amp; Practice 3.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 The Distributive Property<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.3_The_Distributive_Property\">Lesson 3.3 The Distributive Property<\/a><\/li>\n<li><a href=\"#The_Distributive_Property_Homework_&amp;_Practice_3.3\">The Distributive Property Homework &amp; Practice 3.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Factoring Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.4_Factoring_Expressions\">Lesson 3.4 Factoring Expressions<\/a><\/li>\n<li><a href=\"#Factoring_Expressions_Homework_&amp;_Practice_3.4\">Factoring Expressions Homework &amp; Practice 3.4<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 3 &#8211; Expressions\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Expressions_Connecting_Concepts\">Expressions Connecting Concepts<\/a><\/li>\n<li><a href=\"#Expressions_Chapter_Review\">Expressions Chapter Review<\/a><\/li>\n<li><a href=\"#Expressions_Practice_Test\">Expressions Practice Test<\/a><\/li>\n<li><a href=\"#Expressions_Cumulative_Practice\">Expressions Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Expressions_STEAM_VIDEO\/Performance\"><\/a>Expressions STEAM VIDEO\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p><strong>Trophic Status<\/strong><\/p>\n<p>In an ecosystem, energy and nutrients \ufb02ow between abiotic and components. Biotic components are the living parts of an ecosystem. Abiotic components are the non-living parts of an ecosystem. What is an example of an ecosystem?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 1\" width=\"219\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-1.png 219w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-1-199x300.png 199w\" sizes=\"(max-width: 219px) 100vw, 219px\" \/><\/p>\n<p><strong>Watch the STEAM video \u201cTrophic Status.\u201d Then answer the following questions.<\/strong><\/p>\n<p>Question 1.<br \/>\nGive examples of both biotic and abiotic components in an ecosystem. Explain.<\/p>\n<p>Answer:<br \/>\nExamples of biotic components are plants, animals, bacteria, fungi. Examples of abiotic components are water, soil, sunlight, gases, etc.<\/p>\n<p>Explanation:<br \/>\nBiotic components are the living organisms in an ecosystem. Examples of biotic components are plants, animals, bacteria, fungi. Abiotic components are the non-living physical and chemical factors in the environment that affect ecosystems. Examples of abiotic components are water, soil, sunlight, gases, etc. Abiotic factors affect the ability of organisms to reproduce, survive, help determine the types and number of organisms able to exist in the environment. Limiting factors restrict growth. Biotic factors are the living things that directly or indirectly affect organisms in the environment.<\/p>\n<p>Question 2.<br \/>\nWhen an organism is eaten, its energy \ufb02ows into the organism that consumes it. Explain how to use an expression to represent the total energy that a person gains from eating each of the items shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 2\" width=\"422\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-2.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-2-300x114.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Answer:<br \/>\nbx + lx + fx<\/p>\n<p>Explanation:<br \/>\nLet us take the energy gained by eating a banana is bx, by eating leaves is lx, by eating fish is fx.<br \/>\nSo, the expression becomes the sum of all those energies.<br \/>\nbx + lx + fx<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Chlorophyll in Plants<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the STEAM concepts you learned to answer the questions in the Video Performance Task. You will be given the numbers of atoms found in molecules involved in photosynthesis.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 3\" width=\"168\" height=\"117\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 4\" width=\"288\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-4.png 288w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-4-233x300.png 233w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><br \/>\nYou will be asked to determine the total cost for a model of a molecule given the costs of different types of atom models. How can you \ufb01nd the total cost of purchasing several identical objects?<\/p>\n<h3><a id=\"Expressions_Getting_Ready_for_Chapter_3\"><\/a>Expressions Getting Ready for Chapter 3<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p><strong>Work with a partner. Rewrite the algebraic expression so that it has fewer symbols x but still has the same value when evaluated for any value of x.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 5\" width=\"563\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-5.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-5-300x80.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Answer:<br \/>\n1. 3x + 4<br \/>\n2. 3x &#8211; 1<br \/>\n3. 2x &#8211; 3<br \/>\n4. 2(1 + x)<br \/>\n5. 3x &#8211; 1<br \/>\n6. x + 5<\/p>\n<p>Explanation:<br \/>\n1. Original expression is 2x + 4 + x<br \/>\nSimplified expression is 3x + 4<br \/>\n2. Original expression is 3(x + 1) &#8211; 4<br \/>\n3x + 3 &#8211; 4 = 3x &#8211; 1<br \/>\nSimplified expression is 3x &#8211; 1<br \/>\n3. Original expression is x &#8211; (3 &#8211; x)<br \/>\nx &#8211; 3 + x<br \/>\nSimplified expression is 2x &#8211; 3<br \/>\n4. Original expression is 5 + 2x &#8211; 3<br \/>\nSimplified expression is 2 + 2x = 2(1 + x)<br \/>\n5. Original expression is x + 3 + 2x &#8211; 4<br \/>\nSimplified expression is 3x &#8211; 1<br \/>\n6. Original expression is 2x + 2 &#8211; x + 3<br \/>\nSimplified expression is x + 5<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING GUIDELINES<\/strong><br \/>\nWork with a partner. Use your answers in Exercises 1-6 to write guidelines for simplifying an expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 6\" width=\"444\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-6.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-6-300x150.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Answer:<br \/>\nFirst, you need to take the given original expression as it is.<br \/>\nIf there are any braces, then eliminate them by expanding the expression<br \/>\nThen, add or subtract variables and constants together to get the solution<\/p>\n<p>Explanation:<br \/>\nLet us take question 2. 3(x + 1) &#8211; 4<br \/>\nExpand 3<br \/>\n3x + 3 &#8211; 4<br \/>\nSimplify<br \/>\n3x &#8211; 1<\/p>\n<p><strong>APPLYING A DEFINITION<\/strong><br \/>\n<strong>Work with a partner. Two expressions are equivalent if x they have the same value when evaluated for any value of x. Decide which two expressions are equivalent. Explain your reasoning.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 7\" width=\"469\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-7.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-7-300x87.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Answer:<br \/>\n8. x &#8211; (2x + 1) is equivalent to -x &#8211; 1<br \/>\n9. 2x + 3 &#8211; x + 4 is equivalent to x + 7 in expression B<br \/>\n10. 3 + x -2(x + 1) is equivalent to -x + 1<br \/>\n11. 2 &#8211; 2x &#8211; (x + 2) is equivalent to -3x<\/p>\n<p>Explanation:<br \/>\n8. x &#8211; (2x + 1) = x &#8211; 2x &#8211; 1<br \/>\n= -x &#8211; 1<br \/>\nSo, x &#8211; (2x + 1) is equivalent to -x &#8211; 1<br \/>\n9. 2x + 3 &#8211; x + 4 = x + 7<br \/>\nSo, 2x + 3 &#8211; x + 4 is equivalent to x + 7 in expression B<br \/>\n10. 3 + x -2(x + 1) = 3 + x -2x &#8211; 2<br \/>\n= 1 &#8211; x<br \/>\nSo, 3 + x -2(x + 1) is equivalent to -x + 1<br \/>\n11. 2 &#8211; 2x &#8211; (x + 2) = 2 &#8211; 2x &#8211; x &#8211; 2<br \/>\n= -3x<br \/>\nSo, 2 &#8211; 2x &#8211; (x + 2) is equivalent to -3x<\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 8\" width=\"575\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-8.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-8-300x17.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<h3><a id=\"Lesson_3.1_Algebraic_Expressions\"><\/a>Lesson 3.1 Algebraic Expressions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Simplifying Algebraic Expressions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Choose a value of other than 0 or 1 for the last column in the table. Complete the table by evaluating each algebraic expression for each value of x. What do you notice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 9\" width=\"620\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-9.png 620w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-9-300x225.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><br \/>\nb. How can you use properties of operations to justify your answers in part(a)? Explain your reasoning.<br \/>\nc. To subtract a number, you can add its opposite. Does a similar rule apply to the terms of an algebraic expression? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-38506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-1.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 1\" width=\"491\" height=\"585\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-1.jpg 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-1-252x300.jpg 252w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nb. Just simplify the expression and put the values of x in simplified expression<br \/>\nc. Yes<\/p>\n<p>Explanation:<br \/>\na.<br \/>\nA. -1\/3 + x + 7\/3 = (-1 + 7)\/3 + x<br \/>\n= -6\/3 + x = -2 + x<br \/>\nIf x = 0, then -2 + 0 = -2<br \/>\nIf x = 1, then -2 + 1 = -1<br \/>\nIf x = 4, then -2 + 4 = 2<br \/>\nB. 0.5x + 3 &#8211; 1.5x &#8211; 1 = -x + 4<br \/>\nIf x = 0, then -0 + 4 = 4<br \/>\nIf x = 1, then -1 + 4 = 3<br \/>\nIf x = 4, then -4 + 4 = 0<br \/>\nC. 2x + 6<br \/>\nIf x = 0, then 2(0) + 6 = 6<br \/>\nIf x = 1, then 2(1) + 6 = 8<br \/>\nIfx = 4, then 2(4) + 6 = 14<br \/>\nD. x + 4<br \/>\nIf x = 0, then 0 + 4 = 4<br \/>\nIf x = 1, then 1 + 4 = 5<br \/>\nIf x = 4, then 4 + 4 = 8<br \/>\nE. -2x + 2<br \/>\nIf x = 0, then -2(0) + 2 = 2<br \/>\nIf x = 1, then -2(1) + 2 = 0<br \/>\nIf x = 4, then -2(4) + 2 = -6<br \/>\nF. 1\/2 x &#8211; x + 3\/2 x + 4 = 4\/2 x &#8211; x + 4<br \/>\n= 2x &#8211; x + 4 = x + 4<br \/>\nIf x = 0, then 0 + 4 = 4<br \/>\nIf x = 1, then 1 + 4 = 5<br \/>\nIf x = 4, then 4 + 4 = 8<br \/>\nG. -4.8x + 2 &#8211; x + 3.8x = -2x + 2<br \/>\nIf x = 0, then -2(0) + 2 = 2<br \/>\nIf x = 1, then -2(1) + 2 = 0<br \/>\nIf x = 4, then -2(4) + 2 = -6<br \/>\nH. x + 2<br \/>\nIf x = 0, then 0 + 2 = 2<br \/>\nIf x = 1, then 1 + 2 = 3<br \/>\nIf x = 4, then 4 + 2 = 6<br \/>\nI. -x + 2<br \/>\nIf x = 0, then -0 + 2 = 2<br \/>\nIf x = 1, then -1 + 2 =1<br \/>\nIf x = 4, then -4 + 2 = -2<br \/>\nJ. 3x + 2 &#8211; x + 4 = 2x + 6<br \/>\nIf x = 0, then 2(0) + 6 = 6<br \/>\nIf x = 1, then 2(1) + 6 = 8<br \/>\nIf x = 4, then 2(4) + 6 = 14<\/p>\n<p><strong>3.1 Lesson<\/strong><\/p>\n<p>In an algebraic expression, are terms that have the same variables raised to the same exponents. Constant terms are also like terms. To identify terms and like terms in an expression, \ufb01rst write the expression as a sum of its terms.<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Identify the terms and like terms in the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 10\" width=\"94\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\nTerms are 10, y, -3\/2y, like terms are y, -3\/2y.<\/p>\n<p>Explanation:<br \/>\nThe given expression is y + 10 &#8211; 3\/2 y<br \/>\nLike terms are y, -3\/2y<br \/>\nBecause they have the same variable y<br \/>\nTerms are 10, y, -3\/2y<\/p>\n<p>Question 2.<br \/>\n2r<sup>2<\/sup> + 7r &#8211; r<sup>2<\/sup> &#8211; 9<\/p>\n<p>Answer:<br \/>\nThe like terms are 2r\u00b2, -r\u00b2, Terms are -9, 7r, 2r\u00b2, -r\u00b2<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2r\u00b2 + 7r -r\u00b2 &#8211; 9<br \/>\nThe like terms are 2r\u00b2, -r\u00b2<br \/>\nTerms are -9, 7r, 2r\u00b2, -r\u00b2<\/p>\n<p>Question 3.<br \/>\n7 + 4p &#8211; 5 + p + 2q<\/p>\n<p>Answer:<br \/>\nThe like terms are 4p, p<br \/>\nThe terms are 7, -5, 2q, 4p, p<\/p>\n<p>Explanation:<br \/>\nGiven expression is 7 + 4p &#8211; 5 + p + 2q<br \/>\nThe like terms are 4p, p<br \/>\nThe terms are 7, -5, 2q, 4p, p<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n-10y + 15y<\/p>\n<p>Answer:<br \/>\n-10y + 15y = 5y<\/p>\n<p>Explanation:<br \/>\nGiven expression is -10y + 15y<br \/>\n5y<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 11\" width=\"73\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\n3\/8 b &#8211; 3\/4 b = -3\/8 b<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3\/8 b &#8211; 3\/4 b<br \/>\nL.C.M of 8, 4 is 8<br \/>\n(3 &#8211; 6)\/8 b = -3\/8 b<\/p>\n<p>Question 6.<br \/>\n2.4g &#8211; 2.4g &#8211; 9.8g<\/p>\n<p>Answer:<br \/>\n-9.8g<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2.4g &#8211; 2.4g &#8211; 9.8g<br \/>\n-9.8g<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 7.<br \/>\n14 &#8211; 3z + 8 + z<\/p>\n<p>Answer:<br \/>\n22 &#8211; 2z<\/p>\n<p>Explanation:<br \/>\nGiven expression is 14 &#8211; 3z + 8 + z<br \/>\nAdd constants and like terms<br \/>\n22 &#8211; 2z<\/p>\n<p>Question 8.<br \/>\n2.5x + 4.3x &#8211; 5<\/p>\n<p>Answer:<br \/>\n6.8x &#8211; 5<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2.5x + 4.3x &#8211; 5<br \/>\n6.8x &#8211; 5<\/p>\n<p>Question 9.<br \/>\n2s &#8211; 9s + 8t &#8211; t<\/p>\n<p>Answer:<br \/>\n7(t &#8211; s)<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2s &#8211; 9s + 8t &#8211; t<br \/>\n-7s + 7t = 7(t &#8211; s)<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to identify the terms and like terms of 3y &#8211; 4 &#8211; 5y.<\/p>\n<p>Answer:<br \/>\nThe like terms are 3y, -5y<br \/>\nTerms are -4, 3y, -5y<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3y &#8211; 4 &#8211; 5y<br \/>\nLike terms are the terms in the expression which have the same variable<br \/>\nThe following are the like terms because each term contains a variable y and numeric coefficient<br \/>\n3y, -5y<br \/>\nOther than like terms are called the terms<br \/>\nTerms are -4, 3y, -5y<\/p>\n<p><strong>SIMPLIFYING ALGEBRAIC EXPRESSIONS<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 11.<br \/>\n7p + 6p<\/p>\n<p>Answer:<br \/>\n13p<\/p>\n<p>Explanation:<br \/>\nGiven expression is 7p + 6p<br \/>\n13p<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 12\" width=\"109\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n3n\/2 &#8211; 3<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4\/5 n &#8211; 3 + 7\/10 n<br \/>\n(8n + 7n)\/10 &#8211; 3<br \/>\n= 15n\/10 &#8211; 3<br \/>\n= 3n\/2 &#8211; 3<\/p>\n<p>Question 13.<br \/>\n2w &#8211; g &#8211; 7w + 3g<\/p>\n<p>Answer:<br \/>\n-5w + 2g<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2w &#8211; g &#8211; 7w + 3g<br \/>\nPerform the arithmetic operations between the like terms<br \/>\n-5w + 2g<\/p>\n<p>Question 14.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIs the expression 3x + 2x &#8211; 4 in simplest form? Explain.<\/p>\n<p>Answer:<br \/>\nThe expression 3x + 2x &#8211; 4 is not in the simplest form.<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3x + 2x &#8211; 4<br \/>\n= 5x &#8211; 4<br \/>\nThe simplest form of 3x + 2x &#8211; 4 is 5x &#8211; 4<\/p>\n<p>Question 15.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 13\" width=\"303\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-13.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-13-300x102.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>Answer:<br \/>\n5x &#8211; 10 &#8211; 2x does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\nThe first expression is -4 + 6 + 3x = 2 + 3x<br \/>\nThe second expression is 3x + 9 &#8211; 7 = 3x + 2<br \/>\nThe third expression is 5x &#8211; 10 &#8211; 2x = 3x &#8211; 10<br \/>\nFourth expression is 5x &#8211; 4 + 6 &#8211; 2x = 3x + 2<br \/>\nSo, out of all 5x &#8211; 10 &#8211; 2x does not belong with the other three.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nAn exercise mat is 3.3 times as long as it is wide. Write expressions in simplest form that represent the perimeter and the area of the exercise mat.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 14\" width=\"288\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nThe perimeter of the exercise mat is 8.6l, Area of the exercise mat is 3.3l\u00b2<\/p>\n<p>Explanation:<br \/>\nLet us take the l is the length of the exercise mat<br \/>\nThen, the width of the exercise mat = 3.3l<br \/>\nPerimeter of exercise mat = 2(length + width)<br \/>\n= 2(l + 3.3l)<br \/>\n= 2(4.3l) = 8.6 l<br \/>\nArea of the exercise mat = length x width<br \/>\n= l x 3.3l<br \/>\n= 3.3l\u00b2<br \/>\nTherefore, the perimeter of the exercise mat is 8.6l, Area of the exercise mat is 3.3l\u00b2<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA group of friends visits the movie theater in Example 4. Each person buys a daytime ticket and a small drink. The group shares 2 large popcorns. What is the average cost per person when there are 4 people in the group?<\/p>\n<p>Answer:<br \/>\nThe total cost for a group of 4 people is $35.<\/p>\n<p>Explanation:<br \/>\nNumber of tickets . cost per ticket + number of small drinks . cost per small drink + Number of large popcorns . Cost per large popcorn<br \/>\nThe same number of tickets, small drinks are purchased. So, can represent the number of tickets, the number of small drinks.<br \/>\n5x + 1.75x + $8 = x(5 + 1.75) + $8<br \/>\n= 6.75x + $8<br \/>\n2 popcorns cost is 2 x 4 = $8<br \/>\nThe expression 6.75x + $8 indicates that the cost per person is $6.75 + $8 = 14.75<br \/>\nTo find the cost for a group of 4 people, evaluate the expression when x = 4<br \/>\n= 6.75 (4 ) + 8 = 27 + 8 = 35<br \/>\nThe total cost for a group of 4 people is $35.<\/p>\n<h3><a id=\"Algebraic_Expressions_Homework_&amp;_Practice_3.1\"><\/a>Algebraic Expressions Homework &amp; Practice 3.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product or quotient. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 15\" width=\"66\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n-1\/2<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n-2\/7 x 7\/4 = -2\/4<br \/>\n= -1\/2<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 16\" width=\"77\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n3\/5<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n-2\/3(-9\/10) = 2\/3 x 9\/10<br \/>\n= 6\/10 = 3\/5<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 17\" width=\"88\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n-13\/6<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n1(4\/9) \u00f7 (-2\/3) = 13\/9 \u00f7 (-2\/3)<br \/>\n= 13\/9 x (-3\/2) = -13\/6<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 18\" width=\"148\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n3\/4, 78%, 0.85, 87%, 7\/8<\/p>\n<p>Explanation:<br \/>\nGiven that<br \/>\n7\/8 = 0.875, 0.85, 87% = 87\/100 = 0.87 3\/4 = 0.75, 78% = 78\/100 = 0.78<br \/>\nSo, the numbers are 0.875, 0.85, 0.87, 0.75, 0.78<br \/>\nOrdering from the least to the greatest is 0.75,0.78,0.85,0.87,0.875<br \/>\ni.e 3\/4, 78%, 0.85, 87%, 7\/8<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 19\" width=\"160\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n15%, 1450%, 14.8, 15(4\/5)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n15% = 15\/100 = 0.15, 14.8, 15(4\/5) = 79\/5 = 15.8, 1450% = 1450\/100 = 14.5<br \/>\nSo the numbers are 0.15, 14.8, 15.8, 14.5<br \/>\nThe order of number from least to greatest is 0.15, 14.5, 14.8, 15.8<br \/>\ni.e 15%, 1450%, 14.8, 15(4\/5)<\/p>\n<p>Question 6.<br \/>\nA bird\u2019s nest is 12 feet above the ground. A mole\u2019s den is 12 inches below the ground. What is the difference in height of these two positions?<br \/>\nA. 24 in.<br \/>\nB. 11 ft<br \/>\nC. 13 ft<br \/>\nD. 24 ft<\/p>\n<p>Answer:<br \/>\nThe difference in height of these two positions is 13 feet.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe bird nest is 12 feet above the ground and a mole&#8217;s den is 12 inches below the ground.<br \/>\nSo, the mole&#8217;s den have to travel 12 inches +12 feet to reach the bird nest<br \/>\nSo, the difference in height of these two positions is 12 feet + 12 inches<br \/>\n= 12 feet + 1 feet = 13 feet<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>REASONING<\/strong><br \/>\n<strong>Determine whether the expressions are equivalent. Explain your reasoning.<\/strong> (See Exploration 1, p. 91.)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 20\" width=\"253\" height=\"78\" \/><\/p>\n<p>Answer:<br \/>\nThe expressions are not equivalent<\/p>\n<p>Explanation:<br \/>\nExpression 1 is 3 &#8211; 5x<br \/>\nExpression 2 is 4.25 &#8211; 5x &#8211; 4.25<br \/>\n= -5x<br \/>\nSo, expressions are not equivalent<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 21\" width=\"293\" height=\"80\" \/><\/p>\n<p>Answer:<br \/>\nBoth the expressions are equivalent.<\/p>\n<p>Explanation:<br \/>\nExpression 1 is 1.25x + 4 + 0.75x &#8211; 3<br \/>\n= 2x + 4 &#8211; 3 = 2x + 1<br \/>\nExpression 2 is 2x + 1<br \/>\nSo, both the expressions are equivalent.<\/p>\n<p><strong>IDENTIFYING TERMS AND LIKE TERMS<\/strong><br \/>\n<strong>Identify the terms and like terms in the expression.<\/strong><\/p>\n<p>Question 9.<br \/>\nt + 8 + 3t<\/p>\n<p>Answer:<br \/>\nLike terms are t, 3t<br \/>\nTerms are 8, t, 3t<\/p>\n<p>Explanation:<br \/>\nGiven expression is t + 8 + 3t<br \/>\nLike terms are t, 3t<br \/>\nTerms are 8, t, 3t<\/p>\n<p>Question 10.<br \/>\n3z + 4 + 2 + 4z<\/p>\n<p>Answer:<br \/>\nLike terms are 3z, 4z<br \/>\nterms are 4, 2, 3z, 4z<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3z + 4 + 2 + 4z<br \/>\nLike terms are 3z, 4z<br \/>\nterms are 4, 2, 3z, 4z<\/p>\n<p>Question 11.<br \/>\n2n &#8211; n &#8211; 4 + 7n<\/p>\n<p>Answer:<br \/>\nLike terms are 2n, -n, 7n<br \/>\nTerms are -4, 2n, -n, 7n<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2n &#8211; n &#8211; 4 + 7n<br \/>\nLike terms are 2n, -n, 7n<br \/>\nTerms are -4, 2n, -n, 7n<\/p>\n<p>Question 12.<br \/>\n-x &#8211; 9x<sup>2<\/sup> + 12x<sup>2<\/sup> + 7<\/p>\n<p>Answer:<br \/>\nLike terms are -9x\u00b2, 12x\u00b2<br \/>\nTerms are 7, -x, -9x\u00b2, 12x\u00b2<\/p>\n<p>Explanation:<br \/>\nGiven expression is -x &#8211; 9x\u00b2 + 12x\u00b2 + 7<br \/>\nLike terms are -9x\u00b2, 12x\u00b2<br \/>\nTerms are 7, -x, -9x\u00b2, 12x\u00b2<\/p>\n<p>Question 13.<br \/>\n1.4y + 5 &#8211; 4.2 &#8211; 5y<sup>2<\/sup> + z<\/p>\n<p>Answer:<br \/>\nThere are no like terms<br \/>\nTerms are 1.4y, 5, -4.2, -5y\u00b2, z<\/p>\n<p>Explanation:<br \/>\nGiven expression is 1.4y + 5 &#8211; 4.2 &#8211; 5y\u00b2 + z<br \/>\nThere are no like terms<br \/>\nTerms are 1.4y, 5, -4.2, -5y\u00b2, z<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 22\" width=\"150\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\nLike terms are 1\/2 s, 3\/4 s<br \/>\nTerms are -4, 1\/8, -s\u00b3, 1\/2 s, 3\/4 s<\/p>\n<p>Explanation:<br \/>\nGiven expression is 1\/2 s &#8211; 4 + 3\/4 s + 1\/8 &#8211; s\u00b3<br \/>\nLike terms are 1\/2 s, 3\/4 s<br \/>\nTerms are -4, 1\/8, -s\u00b3, 1\/2 s, 3\/4 s<\/p>\n<p>Question 15.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend identi\ufb01es the terms and like terms in the expression 3x &#8211; 5 &#8211; 2x + 9x. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 23\" width=\"233\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3x &#8211; 5 &#8211; 2x + 9x<br \/>\nlike terms are 3x, -2x, 9x<br \/>\nTerms are 3x, -2x, 9x, 5<\/p>\n<p><strong>SIMPLIFYING ALGEBRAIC EXPRESSIONS<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 16.<br \/>\n12g + 9g<\/p>\n<p>Answer:<br \/>\n21g<\/p>\n<p>Explanation:<br \/>\nThe given expression is 12g + 9g<br \/>\n= 21g<\/p>\n<p>Question 17.<br \/>\n11x + 9 &#8211; 7<\/p>\n<p>Answer:<br \/>\n11x + 2<\/p>\n<p>Explanation:<br \/>\nGiven expression is 11x + 9 &#8211; 7<br \/>\n= 11x + 2<\/p>\n<p>Question 18.<br \/>\n8s &#8211; 11s + 6s<\/p>\n<p>Answer:<br \/>\n3s<\/p>\n<p>Explanation:<br \/>\nGiven expression is 8s &#8211; 11s + 6s<br \/>\n= 14s &#8211; 11s = 3s<\/p>\n<p>Question 19.<br \/>\n4b &#8211; 24 + 19<\/p>\n<p>Answer:<br \/>\n4b &#8211; 5<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4b &#8211; 24 + 19<br \/>\n= 4b &#8211; 5<\/p>\n<p>Question 20.<br \/>\n4p &#8211; 5p &#8211; 30p<\/p>\n<p>Answer:<br \/>\n-31p<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4p &#8211; 5p &#8211; 30p<br \/>\n= 4p &#8211; 35p = -31p<\/p>\n<p>Question 21.<br \/>\n4.2v &#8211; 5 &#8211; 6.5v<\/p>\n<p>Answer:<br \/>\n-2.3v &#8211; 5<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4.2v &#8211; 5 &#8211; 6.5v<br \/>\n= -2.3v &#8211; 5<\/p>\n<p>Question 22.<br \/>\n8 + 4a + 6.2 &#8211; 9a<\/p>\n<p>Answer:<br \/>\n14.2 &#8211; 5a<\/p>\n<p>Explanation:<br \/>\nGiven expression is 8 + 4a + 6.2 &#8211; 9a<br \/>\n= 14.2 &#8211; 5a<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 24\" width=\"133\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n3 &#8211; 1\/2 y<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2\/5y &#8211; 4 + 7 &#8211; 9\/10y<br \/>\n= (4 &#8211; 9)\/10 y + 3<br \/>\n= -5\/10 y + 3<br \/>\n= -1\/2 y + 3<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 25\" width=\"148\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n40c\/3 &#8211; 3\/2<\/p>\n<p>Explanation:<br \/>\nGiven expression is -2\/3 c -9\/5 + 14c + 3\/10<br \/>\n= (-2 + 42)c\/3 &#8211; (18 &#8211; 3)\/10<br \/>\n= 40c\/3 &#8211; 15\/10<br \/>\n= 40c\/3 &#8211; 3\/2<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nOn a hike, each hiker carries the items shown. Write and interpret an expression in simplest form that represents the weight carried by x hikers. How much total weight is carried when there are 4 hikers?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 26\" width=\"366\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-26.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-26-300x172.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Answer:<br \/>\nWhen there are 4 hikers the total weight is 40.8 lb.<\/p>\n<p>Explanation:<br \/>\nA hiker has thw following items:<br \/>\nA sleeping bag of 3.4 lb weight, camping bag of 4.6 lb weight, and a water bottle of 2.2 lb weight<br \/>\nThe expression can be<br \/>\n3.4x + 4.6x + 2.2x = x<br \/>\nHere x is the weight each hiker is carrying<br \/>\n10.2x = x<br \/>\nSo, each hiker carries a total weight of 10.2 pounds<br \/>\nWhen there are 4 hikes, the total weight is 10.2 x 4 = 40.8<\/p>\n<p>Question 26.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nEvaluate the expression -8x + 5 &#8211; 2x &#8211; 4 + 5 when x = 2 before and after simplifying. Which method do you prefer? Explain.<\/p>\n<p>Answer:<br \/>\n-14<\/p>\n<p>Explanation:<br \/>\nGiven expression is -8x + 5 &#8211; 2x &#8211; 4 + 5<br \/>\nPut x = 2<br \/>\n-8(2) + 5 -2(2) &#8211; 4 + 5<br \/>\n= -16 + 5 &#8211; 4 &#8211; 4 + 5 = -14<br \/>\nSimplify -8x + 5 &#8211; 2x &#8211; 4 + 5<br \/>\n= -10x + 10 &#8211; 4 = -10x + 6<br \/>\nPut x = 2 in -10x + 6<br \/>\n= -10(2) + 6<br \/>\n= -20 + 6 = -14<br \/>\nI just prefer putting x = 2 after simplifying the expression.<\/p>\n<p>Question 27.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an expression with \ufb01ve different terms that is equivalent 8x<sup>2<\/sup> + 3x<sup>2<\/sup> + 3y. Justify your answer.<\/p>\n<p>Answer:<br \/>\n3x\u00b2 + 2y + y + 7x\u00b2 + x\u00b2<\/p>\n<p>Explanation:<br \/>\nGiven expression is 8x\u00b2 + 3x\u00b2 + 3y.<br \/>\nThe expression which is equivalent to 8x\u00b2 + 3x\u00b2 + 3y and having 5 different terms can be as follows<br \/>\n3x\u00b2 + 2y + y + 7x\u00b2 + x\u00b2<br \/>\nby simplifying the above expression, you will get the original expression.<\/p>\n<p>Question 28.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nWhich of the following shows a correct way of simplifying 6 + (3 &#8211; 5x)? Explain the errors made in the other choices.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-27.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 27\" width=\"651\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-27.png 651w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-27-300x41.png 300w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/p>\n<p>Answer:<br \/>\nC. 6 + (3 &#8211; 5x) = (6 + 3) &#8211; 5x = 9 &#8211; 5x<\/p>\n<p>Explanation:<br \/>\nA. 6 + (3 &#8211; 5x) = (6 + 3 &#8211; 5)x<br \/>\nHere, x is applicable to only -5x, it is not multiplied with whole expression<br \/>\nB. 6 + (3 &#8211; 5x) = 6 + (3 &#8211; 5)x<br \/>\nHere, x is the multiple of only -5x, but you have included 3 also which is false<br \/>\nC. 6 + (3 &#8211; 5x) = (6 + 3) &#8211; 5x = 9 &#8211; 5x<br \/>\nThis is true<br \/>\nD. 6 + (3 &#8211; 5x) = (6 + 3 + 5) &#8211; x<br \/>\n5 is the multiple of x, it is not constant.<\/p>\n<p>Question 29.<br \/>\n<strong>PRECISION<\/strong><br \/>\nTwo comets orbit the Sun. One comet travels 30,000 miles per hour and the other comet travels 28,500 miles per hour. What is the most efficient way to calculate the difference of the distances traveled by the comets for any given number of minutes? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-28.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 28\" width=\"265\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\nThe difference between those distances is 1500 miles for 60 minutes.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nOne comet travels 30,000 miles per hour and the other comet travels 28,500 miles per hour.<br \/>\nLet us say, the time given for the comets is 60 minutes.<br \/>\nSo, in 60 minutes, the first one travels 30,000 miles, and the second one travels 28,500 miles<br \/>\nThe difference between those distances = 30,000 &#8211; 28,500 = 1500 miles<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nFind the earnings for washing and waxing 12 cars and 8 trucks. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-29.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 29\" width=\"166\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nand waxing 12 cars and 8 trucks is $440<\/p>\n<p>Explanation:<br \/>\nThe earnings for washing and waxing 12 cars = 12(washing one car cost) + 12(waxing one car cost)<br \/>\n= 12($8) + 12($12)<br \/>\n= 12(8 + 12) = $240<br \/>\nThe earnings for washing and waxing 8 trucks = 8(washing one truck cost) + 8(waxing one truck cost)<br \/>\n= 8($10) + 8($15)<br \/>\n= 8(10 + 15) = 8(25) = $200<br \/>\nSo, the earnings for washing and waxing 12 cars and 8 trucks is $ 240 + $200 = $440<\/p>\n<p>Question 31.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou apply gold foil to a piece of red poster board to make the design shown.<br \/>\na. Find the area of the gold foil when x = 3. Justify your answer.<br \/>\nb. The pattern at the right is called \u201cSt. George\u2019s Cross.\u201d Find a country that uses this pattern as its \ufb02ag.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-30.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 30\" width=\"328\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-30.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-30-300x191.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Answer:<br \/>\na. Area of the gold foil = 87 sq in<br \/>\nb. England<\/p>\n<p>Explanation:<br \/>\nYou apply gold foil to a piece of red poster board to make the design.<br \/>\na. Area of rectangle = length x breadth<br \/>\n= 20 x 12 = 240 sq in.<br \/>\nLength of the gold foil = (12 &#8211; x) in<br \/>\nThe breadth of gold foil = (20 &#8211; x) in<br \/>\nArea of horizontal gold foil = length x breadth<br \/>\n= 20 * x = 20x sq. in<br \/>\nArea of the vertical gold foil = length x breath<br \/>\n= 12 * x = 12x sq. in<br \/>\nArea of the middle gold foil = length x breadth<br \/>\n= x * x = x\u00b2 sq. in<br \/>\nArea of the gold foil = Area of horizontal gold foil + Area of vertical gold foil &#8211; Area of the middle gold foil<br \/>\n= 20x + 12x &#8211; x\u00b2<br \/>\nThe area of gold foil when x = 3 is 20(3) + 12(3) &#8211; (3)\u00b2<br \/>\n= 60 + 36 &#8211; 9<br \/>\n= 87 sq in<br \/>\nb. The pattern at the right is called \u201cSt. George\u2019s Cross.\u201d Find a country that uses this pattern as its \ufb02ag.<br \/>\nEngland<\/p>\n<p>Question 32.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nTwo rectangles have different dimensions. Each rectangle has a perimeter of (7x + 5) inches. Draw and label diagrams that represent possible dimensions of the rectangles.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-3.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 3\" width=\"528\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-3.jpg 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-3-300x110.jpg 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><br \/>\nRectangle 1 dimensions are 3.5x and 2.5, rectangle 2 dimensions are 1\/2(5x + 1), x + 2<\/p>\n<p>Explanation:<br \/>\nPerimeter of rectangle = (7x + 5) inches<br \/>\n2(length + width) = 7x + 5<br \/>\nlength + width = (7x + 5)\/2<br \/>\nRectangle 1 dimensions can be 3.5x and 2.5<br \/>\nRectangle 2 dimensions can be 1\/2(5x + 1), x + 2<\/p>\n<h3><a id=\"Lesson_3.2_Adding_and_Subtracting_Linear_Expressions\"><\/a>Lesson 3.2 Adding and Subtracting Linear Expressions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Using Algebra Tiles<\/strong><br \/>\n<strong>Work with a partner. You can use the algebra tiles shown at the left to \ufb01nd sums and differences of algebraic expressions.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-31.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 31\" width=\"174\" height=\"132\" \/><br \/>\na. How can you use algebra tiles to model a sum of terms that equals 0? Explain your reasoning.<br \/>\nb. Write each sum or difference modeled below. Then use the algebra tiles to simplify the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-32.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 32\" width=\"562\" height=\"285\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-32.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-32-300x152.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><br \/>\nc. Write two algebraic expressions of the form ax + b, where a and b are rational numbers. Find the sum and difference of the expressions.<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Using Properties of Operations<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Do algebraic expressions, such as 2x, -3y, and 3z + 1 have additive inverses? How do you know?<br \/>\nb. How can you \ufb01nd the sums and differences modeled in Exploration 1 without using algebra tiles? Explain your reasoning.<\/p>\n<p><strong>3.2 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the sum.<\/strong><\/p>\n<p>Question 1.<br \/>\n(x + 3) + (2x &#8211; 1)<\/p>\n<p>Answer:<br \/>\n(x + 3) + (2x &#8211; 1) = 3x + 2<\/p>\n<p>Explanation:<br \/>\nThe given expression is (x + 3) + (2x &#8211; 1)<br \/>\nAdd the like terms and constant<br \/>\n= 3x + 3 &#8211; 1<br \/>\n= 3x + 2<\/p>\n<p>Question 2.<br \/>\n(-8z + 4) + (8z &#8211; 7)<\/p>\n<p>Answer:<br \/>\n(-8z + 4) + (8z &#8211; 7) = -3<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-8z + 4) + (8z &#8211; 7)<br \/>\n= -8z + 4 + 8z &#8211; 7<br \/>\n= -3<\/p>\n<p>Question 3.<br \/>\n(4.5 &#8211; n) + (-10n + 6.5)<\/p>\n<p>Answer:<br \/>\n(4.5 &#8211; n) + (-10n + 6.5) = 11(1 &#8211; n)<\/p>\n<p>Explanation:<br \/>\nThe given expression is (4.5 &#8211; n) + (-10n + 6.5)<br \/>\n= 4.5 &#8211; n &#8211; 10n + 6.5<br \/>\n= 11 &#8211; 11n<br \/>\n= 11(1 &#8211; n)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-34.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 34\" width=\"160\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n(1\/2w &#8211; 3) + (1\/4w + 3) = 3w\/4<\/p>\n<p>Explanation:<br \/>\nThe given expression is (1\/2w &#8211; 3) + (1\/4w + 3)<br \/>\n= 1\/2w &#8211; 3 + 1\/4w + 3<br \/>\n= (2w + w)\/4 = 3w\/4<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the difference.<\/strong><\/p>\n<p>Question 5.<br \/>\n(m &#8211; 3) &#8211; (-m + 12)<\/p>\n<p>Answer:<br \/>\n(m &#8211; 3) &#8211; (-m + 12) = 2m &#8211; 15<\/p>\n<p>Explanation:<br \/>\nThe given expression is (m &#8211; 3) &#8211; (-m + 12)<br \/>\n= m &#8211; 3 + m &#8211; 12<br \/>\n= 2m &#8211; 15<\/p>\n<p>Question 6.<br \/>\n(-2c + 5) &#8211; (6.3c + 20)<\/p>\n<p>Answer:<br \/>\n(-2c + 5) &#8211; (6.3c + 20) = -83c &#8211; 15<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-2c + 5) &#8211; (6.3c + 20)<br \/>\n= -2c + 5 &#8211; 6.3c &#8211; 20<br \/>\n= -83c &#8211; 15<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how to distinguish a linear expression from a nonlinear expression. Give an example of each.<\/p>\n<p>Answer:<br \/>\nAn example of a linear expression is 2x + 1.<br \/>\nAn example of a non-linear expression is 2x\u00b2 + 1<\/p>\n<p>Explanation:<br \/>\nLinear expressions are the expressions where the sum of constants and products of constants and raised to a power of 0 or 1. Non-linear expressions are the expressions where the sum of constants and products of constants and raised to a power that is not 0 or 1.<br \/>\nSo, an example of a linear expression is 2x + 1.<br \/>\nAn example of a non-linear expression is 2x\u00b2 + 1<\/p>\n<p>Question 8.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-35.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 35\" width=\"500\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-35.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-35-300x58.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Answer:<br \/>\nWhat is x more than 3x &#8211; 1 is different.<\/p>\n<p>Explanation:<br \/>\nWhat is x more than 3x &#8211; 1 = x + 3x &#8211; 1 = 4x &#8211; 1<br \/>\nFind 3x &#8211; 1 decreased by x = 3x &#8211; 1 &#8211; x = 2x &#8211; 1<br \/>\nWhat is the difference of 3x &#8211; 1 and x = 3x &#8211; 1 &#8211; x = 2x &#8211; 1<br \/>\nSubtract (x + 1) from 3x = 3x &#8211; (x + 1) = 3x &#8211; x &#8211; 1 = 2x &#8211; 1<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn a basketball game, the home team scores (2m + 39) points and the away team scores (3m + 40) points, where m is the number of minutes since halftime. Who wins the game? What is the difference in the scores minutes after halftime? Explain.<\/p>\n<p>Answer:<br \/>\nThe away team wins the game. And the difference in the scores minutes after halftime is 2m + 2.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe score of home team = 2m + 39 points<br \/>\nThe score of away team = 3m + 40 points<br \/>\nHere, m is the number of minutes since halftime<br \/>\nLet us consider the teams that score the same points after the half time<br \/>\nThe score of home team = 2m + 39 + 2m + 39 = 4m + 78<br \/>\nThe score of away team = 3m + 40 + 3m + 40 = 6m + 80<br \/>\nThe difference between those scores = 6m + 80 &#8211; (4m + 78)<br \/>\n= 6m + 80 &#8211; 4m &#8211; 78 = 2m + 2<br \/>\nThe away team wins the game.<\/p>\n<p>Question 10.<br \/>\nElectric guitar kits originally cost d dollars online. You buy the kits on sale for 50% of the original price, plus a shipping fee of $4.50 per kit. After painting and assembly, you sell each guitar online for (1.5d + 4.5) dollars. Find and interpret your pro\ufb01t on each guitar sold.<\/p>\n<p>Answer:<br \/>\nYour profit on each electric guitar kit is d dollars<\/p>\n<p>Explanation:<br \/>\nElectric guitar kits originally cost d dollars online.<br \/>\nYou buy the kits on sale for 50% of the original price. So, the purchase price of kit is = d\/2 + 4.50<br \/>\nAfter painting and assembly, you sell each guitar online for (1.5d + 4.5) dollars<br \/>\nProfit = Selling price &#8211; Purchased price<br \/>\n= 1.5d + 4.5 &#8211; (d\/2+ 4.50)<br \/>\n= 1.5d + 4.5 &#8211; 0.5d &#8211; 4.50<br \/>\n= d dollars<br \/>\nYour profit on each electric guitar kit is d dollars. You pay (0.5d + 4.50) dollars for each kit. so, you are getting 4.50 dollars less than double your money.<\/p>\n<h3><a id=\"Adding_and_Subtracting_Linear_Expressions_Homework_&amp;_Practice_3.2\"><\/a>Adding and Subtracting Linear Expressions Homework &amp; Practice 3.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n4f + 11f<\/p>\n<p>Answer:<br \/>\n4f + 11f = 15f<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4f + 11f<br \/>\nAdd the like terms<br \/>\n= 15f<\/p>\n<p>Question 2.<br \/>\nb + 4b &#8211; 9b<\/p>\n<p>Answer:<br \/>\nb + 4b &#8211; 9b = -4b<\/p>\n<p>Explanation:<br \/>\nGiven expression is b + 4b &#8211; 9b<br \/>\nPerform required operations between like terms<br \/>\n= 5b &#8211; 9b = -4b<\/p>\n<p>Question 3.<br \/>\n-4z &#8211; 6 &#8211; 7z + 3<\/p>\n<p>Answer:<br \/>\n-4z &#8211; 6 &#8211; 7z + 3 = -11z- 3<\/p>\n<p>Explanation:<br \/>\nGiven expression is -4z &#8211; 6 &#8211; 7z + 3<br \/>\nPerform required operations between like terms and constants<br \/>\n= -11z- 3<\/p>\n<p><strong>Evaluate the expression when x = \\(-\\frac{4}{5}\\) and y = \\(\\frac{1}{3}\\).<\/strong><\/p>\n<p>Question 4.<br \/>\nx + y<\/p>\n<p>Answer:<br \/>\n-7\/15<\/p>\n<p>Explanation:<br \/>\nGiven expression is x + y<br \/>\nPut x = -4\/5, y = 1\/3<br \/>\n= -4\/5 + 1\/3<br \/>\n= (-12 + 5)\/15 = -7\/15<\/p>\n<p>Question 5.<br \/>\n2x + 6y<\/p>\n<p>Answer:<br \/>\n2\/5<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2x + 6y<br \/>\nPut x = -4\/5, y = 1\/3<br \/>\n= 2(-4\/5) + 6(1\/3) = -8\/5 + 6\/3<br \/>\n= (-24 + 30)\/15 = 6\/15<br \/>\n= 2\/5<\/p>\n<p>Question 6.<br \/>\n-x + 4y<\/p>\n<p>Answer:<br \/>\n32\/15<\/p>\n<p>Explanation:<br \/>\nGiven expression is -x + 4y<br \/>\nPut x = -4\/5, y = 1\/3<br \/>\n= -(-4\/5) + 4(1\/3)<br \/>\n= 4\/5 + 4\/3<br \/>\n= (12 + 20)\/15<br \/>\n= 32\/15<\/p>\n<p>Question 7.<br \/>\nWhat is the surface area of a cube that has a side length of 5 feet?<br \/>\nA. 25 ft<sup>2<\/sup><br \/>\nB. 75 ft<sup>2<\/sup><br \/>\nC. 125 ft<sup>2<\/sup><br \/>\nD. 150 ft<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\nD. 150 ft\u00b2<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nthe side length of cube = 5 feet<br \/>\nThe surface area of a cube = 6side\u00b2<br \/>\n= 6 x (5)\u00b2 = 6 x 25<br \/>\n= 150 ft\u00b2<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING ALGEBRA TILES<\/strong><br \/>\n<strong>Write the sum or difference modeled by the algebra tiles. Then use the algebra tiles to simplify the expression.<\/strong> (See Exploration 1, p. 97.)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-36.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 36\" width=\"355\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-36.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-36-300x57.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>Answer:<br \/>\n3x &#8211; 1<\/p>\n<p>Explanation:<br \/>\nConvert the given algebra tiles to the expressions<br \/>\n(x &#8211; 1 &#8211; 1 &#8211; 1 + x &#8211; 1 &#8211; 1 &#8211; 1) + (x + 1 + 1+ 1+ 1+ 1)<br \/>\n= (2x &#8211; 6) +(x + 5)<br \/>\n= 2x &#8211; 6 + x + 5<br \/>\n= 3x &#8211; 1<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-37.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 37\" width=\"384\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-37.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-37-300x60.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Answer:<br \/>\n11<\/p>\n<p>Explanation:<br \/>\nConvert the given algebra tiles to the expressions<br \/>\n(x + 1 + 1 + 1+ 1 + 1 + x + 1 + 1) &#8211; (x &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 + x)<br \/>\n= (2x + 7) &#8211; (2x &#8211; 4)<br \/>\n= 2x + 7 &#8211; 2x + 4<br \/>\n= 11<\/p>\n<p><strong>ADDING LINEAR EXPRESSIONS<\/strong><br \/>\n<strong>Find the sum.<\/strong><\/p>\n<p>Question 10.<br \/>\n(n + 8) + (n &#8211; 12)<\/p>\n<p>Answer:<br \/>\n(n + 8) + (n &#8211; 12) = 2n &#8211; 4<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (n + 8) + (n &#8211; 12)<br \/>\n= n + 8 + n &#8211; 12<br \/>\n= 2n &#8211; 4<\/p>\n<p>Question 11.<br \/>\n(7 &#8211; b) + (3b + 2)<\/p>\n<p>Answer:<br \/>\n(7 &#8211; b) + (3b + 2) = 9 + 2b<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (7 &#8211; b) + (3b + 2)<br \/>\n= 7 &#8211; b + 3b + 2<br \/>\n= 9 + 2b<\/p>\n<p>Question 12.<br \/>\n(2w &#8211; 9) + (-4w &#8211; 5)<\/p>\n<p>Answer:<br \/>\n(2w &#8211; 9) + (-4w &#8211; 5) = -2w &#8211; 14<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (2w &#8211; 9) + (-4w &#8211; 5)<br \/>\n= 2w &#8211; 9 &#8211; 4w- 5<br \/>\n= -2w &#8211; 14<\/p>\n<p>Question 13.<br \/>\n(2x &#8211; 6) + (4x &#8211; 12)<\/p>\n<p>Answer:<br \/>\n(2x &#8211; 6) + (4x &#8211; 12) = 8x &#8211; 18<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (2x &#8211; 6) + (4x &#8211; 12)<br \/>\n= 2x &#8211; 6 + 4x &#8211; 12<br \/>\n= 8x &#8211; 18<\/p>\n<p>Question 14.<br \/>\n(-3.4k &#8211; 7) + (3k + 21)<\/p>\n<p>Answer:<br \/>\n(-3.4k &#8211; 7) + (3k + 21) = -0.4k + 14<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (-3.4k &#8211; 7) + (3k + 21)<br \/>\n= -3.4k &#8211; 7 + 3k + 21<br \/>\n= -0.4k + 14<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-38.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 38\" width=\"172\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\n(-7\/2 z+ 4) + (1\/5 z- 15) = -33z\/10 &#8211; 11<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (-7\/2 z+ 4) + (1\/5 z- 15)<br \/>\n= -7\/2 z + 4 + 1\/5 z- 15<br \/>\n= (-35z + 2z)\/10 &#8211; 11<br \/>\n= -33z\/10 &#8211; 11<\/p>\n<p>Question 16.<br \/>\n(6 &#8211; 2.7h) + (-1.3j &#8211; 4)<\/p>\n<p>Answer:<br \/>\n(6 &#8211; 2.7h) + (-1.3j &#8211; 4) = 2 &#8211; 2.7h &#8211; 1.3j<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (6 &#8211; 2.7h) + (-1.3j &#8211; 4)<br \/>\n= 6 &#8211; 2.7h &#8211; 1.3j &#8211; 4<br \/>\n= 2 &#8211; 2.7h &#8211; 1.3j<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-39.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 39\" width=\"239\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n(7\/4 x &#8211; 5) + (2y &#8211; 3.5) + (-1\/4 x + 5) = 3x\/2 + 2y &#8211; 3.5<\/p>\n<p>Explanation:<br \/>\nGiven linear expression is (7\/4 x &#8211; 5) + (2y &#8211; 3.5) + (-1\/4 x + 5)<br \/>\n= 7\/4 x &#8211; 5 + 2y &#8211; 3.5 &#8211; 1\/4x + 5<br \/>\n= (7x &#8211; x)\/4 + 2y &#8211; 3.5<br \/>\n= 6x\/4 + 2y &#8211; 3.5<br \/>\n= 3x\/2 + 2y &#8211; 3.5<\/p>\n<p>Question 18.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWhile catching \ufb01re\ufb02ies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) \ufb01re\ufb02ies and your friend has (4m + 6) \ufb01re\ufb02ies.<br \/>\na. How many total \ufb01re\ufb02ies do you and your friend catch? Explain your reasoning.<br \/>\nb. The competition lasts 3 minutes. Who has more \ufb01re\ufb02ies? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-40.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 40\" width=\"180\" height=\"210\" \/><\/p>\n<p>Answer:<br \/>\na. The total number of fireflies collected is 7m + 19<br \/>\nb. You have more fireflies when compared with your friend.<\/p>\n<p>Explanation:<br \/>\nThe number of fireflies you collected after m minutes is (3m + 13)<br \/>\nThe number of fireflies your friend collected after m minutes is (4m + 6)<br \/>\na.<br \/>\nThe number of fireflies you collected is (3m + 13)<br \/>\nThe number of fireflies your friend collected is (4m + 6)<br \/>\nThe total number of fireflies collected = (3m + 13) + (4m + 6)<br \/>\n= 3m + 13 + 4m + 6 = 7m + 19<br \/>\nb. The competition lasts 3 minutes<br \/>\nSo, The number of fireflies you collected is 3(1) + 13 = 3 + 13 = 16<br \/>\nThe number of fireflies your friend collected is 4(1) + 6 = 4 + 6 = 10<br \/>\nSo, you have more fireflies when compared with your friend.<\/p>\n<p>SUBTRACTING LINEAR EXPRESSIONS<\/p>\n<p><strong>Find the difference.<\/strong><\/p>\n<p>Question 19.<br \/>\n(-2g + 7) &#8211; (g + 11)<\/p>\n<p>Answer:<br \/>\n(-2g + 7) &#8211; (g + 11) = -3g &#8211; 4<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (-2g + 7) &#8211; (g + 11)<br \/>\n= -2g + 7 &#8211; g &#8211; 11<br \/>\n= -3g &#8211; 4<\/p>\n<p>Question 20.<br \/>\n(6d + 5) &#8211; (2 &#8211; 3d)<\/p>\n<p>Answer:<br \/>\n(6d + 5) &#8211; (2 &#8211; 3d) = 9d + 3<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (6d + 5) &#8211; (2 &#8211; 3d)<br \/>\n= 6d + 5 &#8211; 2 + 3d<br \/>\n= 9d + 3<\/p>\n<p>Question 21.<br \/>\n(4 &#8211; 5y) &#8211; (2y &#8211; 16)<\/p>\n<p>Answer:<br \/>\n(4 &#8211; 5y) &#8211; (2y &#8211; 16) = 20 &#8211; 7y<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (4 &#8211; 5y) &#8211; (2y &#8211; 16)<br \/>\n= 4 &#8211; 5y &#8211; 2y + 16<br \/>\n= 20 &#8211; 7y<\/p>\n<p>Question 22.<br \/>\n(2n &#8211; 9) &#8211; (-2.4n + 4)<\/p>\n<p>Answer:<br \/>\n(2n &#8211; 9) &#8211; (-2.4n + 4) = 4.4n &#8211; 13<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (2n &#8211; 9) &#8211; (-2.4n + 4)<br \/>\n= 2n &#8211; 9 + 2.4n &#8211; 4<br \/>\n= 4.4n &#8211; 13<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-41.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 41\" width=\"167\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n(-1\/8 c + 16) &#8211; (3\/8 + 3c) = (-25c + 125)\/8<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (-1\/8 c + 16) &#8211; (3\/8 + 3c)<br \/>\n= -1\/8 c + 16 &#8211; 3\/8 &#8211; 3c<br \/>\n= (-c &#8211; 24c)\/8 + (128 &#8211; 3)\/8<br \/>\n= -25c\/8 + 125\/8<br \/>\n= (-25c + 125)\/8<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-42.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 42\" width=\"171\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n(9\/4 x + 6) &#8211; (-5\/4 x &#8211; 24) = 7x\/2 + 30<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (9\/4 x + 6) &#8211; (-5\/4 x &#8211; 24)<br \/>\n= 9x\/4 + 6 + 5x\/4 + 24<br \/>\n= (9x + 5x)\/4 + 30<br \/>\n= 14x\/4 + 30<br \/>\n= 7x\/2 + 30<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-43.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 43\" width=\"160\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n(1\/3 &#8211; 6m) &#8211; (1\/4 n &#8211; 8) = 25\/4 &#8211; 6m &#8211; n\/4<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (1\/3 &#8211; 6m) &#8211; (1\/4 n &#8211; 8)<br \/>\n= 1\/3 &#8211; 6m &#8211; 1\/4 n + 8<br \/>\n= (1 + 24)\/3 &#8211; 6m &#8211; n\/4<br \/>\n= 25\/4 &#8211; 6m &#8211; n\/4<\/p>\n<p>Question 26.<br \/>\n(1 &#8211; 5q) &#8211; (2.5s + 8) &#8211; (0.5q + 6)<\/p>\n<p>Answer:<br \/>\n(1 &#8211; 5q) &#8211; (2.5s + 8) &#8211; (0.5q + 6) = -5.5q &#8211; 2.5s &#8211; 13<\/p>\n<p>Explanation:<br \/>\nThe given linear expression is (1 &#8211; 5q) &#8211; (2.5s + 8) &#8211; (0.5q + 6)<br \/>\n= 1 &#8211; 5q &#8211; 2.5s &#8211; 8 &#8211; 0.5q &#8211; 6<br \/>\n= 1 &#8211; 5.5q &#8211; 2.5s &#8211; 14<br \/>\n= -5.5q &#8211; 2.5s &#8211; 13<\/p>\n<p>Question 27.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the difference (4m + 9) &#8211; (2m &#8211; 5). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-44.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 44\" width=\"328\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-44.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-44-300x116.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nThe given expression is (4m + 9) &#8211; (2m &#8211; 5)<br \/>\n= 4m + 9 &#8211; 2m + 5<br \/>\n= 2m + 14<\/p>\n<p>Question 28.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe expression 17n + 11 represents the perimeter of the triangle. What is the length of the third side? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-45.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 45\" width=\"201\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the third side is 8n.<\/p>\n<p>Explanation:<br \/>\nPerimeter of the triangle = 17n + 11<br \/>\n5n + 6 + 4n + 5 + third side = 17n + 11<br \/>\n9n + 11 + third side = 17n + 11<br \/>\nthird side = 17n + 11 &#8211; (9n +11)<br \/>\n= 17n + 11 &#8211; 9n &#8211; 11<br \/>\n= 8n<br \/>\nThe length of the third side is 8n.<\/p>\n<p>Question 29.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYour friend says the sum of two linear expressions is always a linear expression. Is your friend correct? Explain.<\/p>\n<p>Answer:<br \/>\nyes, the sum of two linear expressions is always a linear expression.<\/p>\n<p>Explanation:<br \/>\nThe sum of two linear expressions is always a linear expression. But the product of linear expressions may not be the linear expression.<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou burn 265 calories running and then 7 calories per minute swimming. Your friend burns 273 calories running and then 11 calories per minute swimming. You each swim for the same number of minutes. Find and interpret the difference in the amounts of calories burned by you and your friend.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-46.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 46\" width=\"132\" height=\"226\" \/><\/p>\n<p>Answer:<br \/>\nThe difference in the amounts of calories burned by you and your friend is 8 + 4m.<\/p>\n<p>Explanation:<br \/>\nThe number of calories your burn by running and swimming is 265 + 7m<br \/>\nThe number of calories your friend burns by running and swimming is 273 + 11m<br \/>\nThe difference in amount of calories burn = 273 + 11m &#8211; (265 + 7m)<br \/>\n= 273 + 11m &#8211; 265 &#8211; 7m<br \/>\n= 8 + 4m<br \/>\nThe difference in the amounts of calories burned by you and your friend is 8 + 4m.<\/p>\n<p>Question 31.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou start a new job. After w weeks, you have (10w + 120) dollars in your savings account and (45w + 25) dollars in your checking account.<br \/>\na. What is the total amount of money in the accounts? Explain.<br \/>\nb. How much money did you have before you started your new job? How much money do you save each week?<br \/>\nc. You want to buy a new phone for $150, and still have $500 left in your accounts afterwards. Explain how to determine when you can buy the phone.<\/p>\n<p>Answer:<br \/>\na. The total amount of money in the accounts = (55w + 145) dollars<br \/>\nb. You started a new job with 120 dollars savings and you earned 10 dollars savings each week.<br \/>\nc. You can buy the phone after 9 weeks of starting new job.<\/p>\n<p>Explanation:<br \/>\nYou have (10w + 120) dollars in your savings account and (45w + 25) dollars in your checking account.<br \/>\na.<br \/>\nThe total amount of money in the accounts = 10w + 120 + 45w + 25<br \/>\n= 55w + 145<br \/>\nb.<br \/>\nIn the saving&#8217;s account the multiple of w is the amount earned during job and other constant is the amount you have before the new job.<br \/>\nSo, you started a new job with 120 dollars savings and you earned 10 dollars savings each week.<br \/>\nc.<br \/>\nThe total amount in accounts is (55w + 145) dollars<br \/>\nYou want to buy a new phone for $150, and still have $500 left in your accounts afterwards<br \/>\nDeduct $150 from total amount so that the remaining amount should be $500.<br \/>\n55w + 145 &#8211; 150 = 500<br \/>\n55w &#8211; 5 = 500<br \/>\n55w = 500 + 5<br \/>\n55w = 505<br \/>\nw = $505\/55<br \/>\nw = 9.1818<br \/>\nSo, you can buy the phone after 9 weeks of starting new job.<\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nWrite an expression in simplest form that represents the vertical distance between the two lines shown. What is the distance when x = 3? when x = -3?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-47.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 47\" width=\"214\" height=\"203\" \/><\/p>\n<p>Answer:<br \/>\nThe vertical distance between the two lines is 3 units.<\/p>\n<p>Explanation:<br \/>\nGiven equations are y = x &#8211; 1, y = 2x &#8211; 4<br \/>\nEquating those two<br \/>\nx &#8211; 1 = 2x &#8211; 4<br \/>\n-1 + 4 = 2x &#8211; x<br \/>\n3 = x<br \/>\nSo, the vertical distance between the two lines is 3 units.<\/p>\n<h3><a id=\"Lesson_3.3_The_Distributive_Property\"><\/a>Lesson 3.3 The Distributive Property<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Using Models to Write Expressions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Write an expression that represents the area of the shaded region in each \ufb01gure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-48.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 48\" width=\"392\" height=\"548\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-48.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-48-215x300.png 215w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-48.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 48.1\" width=\"160\" height=\"174\" \/><br \/>\nb. Compare your expressions in part(a) with other groups in your class. Did other groups write expressions that look different than yours? If so, determine whether the expressions are equivalent.<\/p>\n<p><strong>3.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n-1(x + 9)<\/p>\n<p>Answer:<br \/>\n-1(x + 9) = 9 &#8211; x<\/p>\n<p>Explanation:<br \/>\nGiven expression is -1(x + 9)<br \/>\n= -x + 9<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-49.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 49\" width=\"89\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n2\/3 (-3z &#8211; 6) = -2z &#8211; 4<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2\/3 (-3z &#8211; 6)<br \/>\n= 2\/3(-3z) &#8211; 2\/3(6)<br \/>\n= -2z &#8211; 2(2)<br \/>\n= -2z &#8211; 4<\/p>\n<p>Question 3.<br \/>\n-1.5(8m &#8211; n)<\/p>\n<p>Answer:<br \/>\n-1.5(8m &#8211; n) = -12m + 1.5n<\/p>\n<p>Explanation:<br \/>\nGiven expression is -1.5(8m &#8211; n)<br \/>\n= -1.5(8m) + 1.5(n)<br \/>\n= -12m + 1.5n<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n2(-3s + 1 &#8211; 5)<\/p>\n<p>Answer:<br \/>\n2(-3s + 1 &#8211; 5) = -6s &#8211; 8<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2(-3s + 1 &#8211; 5)<br \/>\n= 2(-3s) + 2(1) + 2(-5)<br \/>\n= -6s + 2 &#8211; 10<br \/>\n= -6s &#8211; 8<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-50.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 50\" width=\"116\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n-3\/2 (a &#8211; 4 &#8211; 2a) = 3a\/2 + 6<\/p>\n<p>Explanation:<br \/>\nGiven expression is -3\/2 (a &#8211; 4 &#8211; 2a)<br \/>\n= -3\/2 (a) + 3\/2(4) + 3\/2(2a)<br \/>\n= -3a\/2 + 3(2) + 3(a)<br \/>\n= -3a\/2 + 6 + 3a<br \/>\n= (-3a + 6a)\/2 + 6<br \/>\n= 3a\/2 + 6<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 6.<br \/>\n3.5m &#8211; 1.5(m &#8211; 10)<\/p>\n<p>Answer:<br \/>\n3.5m &#8211; 1.5(m &#8211; 10) = 2m + 15<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3.5m &#8211; 1.5(m &#8211; 10)<br \/>\n= 3.5m &#8211; 1.5(m) + 1.5(10)<br \/>\n= 3.5m &#8211; 1.5m + 15<br \/>\n= 2m + 15<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-51.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 51\" width=\"172\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n4\/5(10w &#8211; 5) &#8211; 2(w + 9) = 6w &#8211; 22<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4\/5(10w &#8211; 5) &#8211; 2(w + 9)<br \/>\n= 4\/5(10w) &#8211; 4\/5(5) &#8211; 2w &#8211; 18<br \/>\n= 4(2w) &#8211; 4 &#8211; 2w &#8211; 18<br \/>\n= 8w &#8211; 2w &#8211; 22<br \/>\n= 6w &#8211; 22<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use the Distributive Property when simplifying an expression.<\/p>\n<p>Answer:<br \/>\nDistributive property says that a(b+ c) = ab + ac and a(b &#8211; c) = ab &#8211; ac<br \/>\nSo, you need to expand the outer number with the sum or difference inside the braces<br \/>\nAnd perform the required arithmetical operations to get the simplified expression.<\/p>\n<p><strong>USING THE DISTRIBUTIVE PROPERTY<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-52.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 52\" width=\"92\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n5\/6 (-2y + 3) = -5y\/3 + 5\/2<\/p>\n<p>Explanation:<br \/>\nGiven expression is 5\/6 (-2y + 3)<br \/>\n= 5\/6(-2y) + 5\/6(3)<br \/>\n= -10y\/6 + 15\/6<br \/>\n= -5y\/3 + 5\/2<\/p>\n<p>Question 10.<br \/>\n6(3s &#8211; 2.5 &#8211; 5s)<\/p>\n<p>Answer:<br \/>\n6(3s &#8211; 2.5 &#8211; 5s) = -15 &#8211; 12s<\/p>\n<p>Explanation:<br \/>\nGiven expression is 6(3s &#8211; 2.5 &#8211; 5s)<br \/>\n= 6(-2.5 &#8211; 2s)<br \/>\n= 6(-2.5) &#8211; 6(2s)<br \/>\n= -15 &#8211; 12s<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-53.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 53\" width=\"135\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n3\/10(4m &#8211; 8) + 9m = (51m &#8211; 12)\/5<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3\/10(4m &#8211; 8) + 9m<br \/>\n= 3\/10(4m) &#8211; 3\/10(8) + 9m<br \/>\n= 3\/5(2m) &#8211; 3\/5(4) + 9m<br \/>\n= 6m\/5 &#8211; 12\/5 + 9m<br \/>\n= (6m + 45m)\/5 &#8211; 12\/5<br \/>\n= 51m\/5 &#8211; 12\/5<br \/>\n= (51m &#8211; 12)\/5<\/p>\n<p>Question 12.<br \/>\n2.25 &#8211; 2(7.5 &#8211; 4h)<\/p>\n<p>Answer:<br \/>\n2.25 &#8211; 2(7.5 &#8211; 4h) = 8h &#8211; 12.75<\/p>\n<p>Explanation:<br \/>\nGiven expression is 2.25 &#8211; 2(7.5 &#8211; 4h)<br \/>\n= 2.25 &#8211; 2(7.5) + 2(4h)<br \/>\n= 2.25 &#8211; 15 + 8h<br \/>\n= 8h &#8211; 12.75<\/p>\n<p>Question 13.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-54.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 54\" width=\"153\" height=\"133\" \/><br \/>\nUse the terms at the left to complete the expression below so that it is equivalent to 9x &#8211; 12. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-55.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 55\" width=\"193\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n3\/2 (4x &#8211; 8) + 3x<\/p>\n<p>Explanation:<br \/>\nThe expression can be<br \/>\n3\/2 (4x &#8211; 8) + 3x<br \/>\n= 3\/2(4(x &#8211; 2)) + 3x<br \/>\n= 3(2(x &#8211; 2)) + 3x<br \/>\n= 6(x &#8211; 2) + 3x<br \/>\n= 6x &#8211; 12 + 3x<br \/>\n= 9x &#8211; 12<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 14.<br \/>\nA rectangular room is 10 feet longer than it is wide. How many 1-foot square tiles does it take to tile along the inside walls of the room?<\/p>\n<p>Answer:<br \/>\nThe number of tiles required is 4w + 20.<\/p>\n<p>Explanation:<br \/>\nLet the width of the rectangular room is w<br \/>\nThe length of the rectangular room is w + 10<br \/>\nPerimeter of the rectangular room = 2(length + with)<br \/>\n= 2(w + 10 + w)<br \/>\n= 2(2w +10)<br \/>\n= 4w + 20<br \/>\nSo, the number of tiles required is 4w + 20.<\/p>\n<p>Question 15.<br \/>\nHow many 2-foot square tiles does it take to tile the border of the pool in Example 4? Explain.<\/p>\n<p>Answer:<br \/>\n(4s + 8) 2 foot square tiles are required.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-6.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 6\" width=\"560\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-6.jpg 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-6-300x113.jpg 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\nThe diagram shows that the tiled border can be divided into two sections that each requires s + 4 tiles and two sections that each requires s tiles. So, the number of tiles can be represented as 2(s + 4) + 2s<br \/>\n2(s + 4) + 2s = 2(s) + 2(4) + 2s<br \/>\n= 4s + 8<br \/>\nSo, (4s + 8) 2 foot square tiles are required.<\/p>\n<h3><a id=\"The_Distributive_Property_Homework_&amp;_Practice_3.3\"><\/a>The Distributive Property Homework &amp; Practice 3.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the sum or difference.<\/strong><\/p>\n<p>Question 1.<br \/>\n(5b &#8211; 9) + (b + 8)<\/p>\n<p>Answer:<br \/>\n(5b &#8211; 9) + (b + 8) = 6b &#8211; 1<\/p>\n<p>Explanation:<br \/>\nGiven expression is (5b &#8211; 9) + (b + 8)<br \/>\n= 5b &#8211; 9 + b + 8<br \/>\n= 6b &#8211; 1<\/p>\n<p>Question 2.<br \/>\n(3m + 5) &#8211; (6 &#8211; 5m)<\/p>\n<p>Answer:<br \/>\n(3m + 5) &#8211; (6 &#8211; 5m) = 8m &#8211; 1<\/p>\n<p>Explanation:<br \/>\nGiven expression is (3m + 5) &#8211; (6 &#8211; 5m)<br \/>\n= 3m + 5 &#8211; 6 + 5m<br \/>\n= 8m &#8211; 1<\/p>\n<p>Question 3.<br \/>\n(1 &#8211; 9z) + 3(z &#8211; 2)<\/p>\n<p>Answer:<br \/>\n(1 &#8211; 9z) + 3(z &#8211; 2) = -5 &#8211; 6z<\/p>\n<p>Explanation:<br \/>\nGiven expression is (1 &#8211; 9z) + 3(z &#8211; 2)<br \/>\n= 1 &#8211; 9z + 3(z) &#8211; 3(2)<br \/>\n= 1 &#8211; 9z + 3z &#8211; 6<br \/>\n= -5 &#8211; 6z<\/p>\n<p>Question 4.<br \/>\n(7g &#8211; 6) &#8211; (-3n &#8211; 4)<\/p>\n<p>Answer:<br \/>\n(7g &#8211; 6) &#8211; (-3n &#8211; 4) = 7g + 3n &#8211; 2<\/p>\n<p>Explanation:<br \/>\nGiven expression is (7g &#8211; 6) &#8211; (-3n &#8211; 4)<br \/>\n= 7g &#8211; 6 -(-3n) -(-4)<br \/>\n= 7g &#8211; 6 + 3n + 4<br \/>\n= 7g + 3n &#8211; 2<\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 5.<br \/>\n-6<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n-6\u00b2 = -36<\/p>\n<p>Explanation:<br \/>\nGiven expression is -6<sup>2<\/sup><br \/>\n-6 x 6 = -36<\/p>\n<p>Question 6.<br \/>\n-9<sup>2<\/sup> . 3<\/p>\n<p>Answer:<br \/>\n-9\u00b2 . 3 = -243<\/p>\n<p>Explanation:<br \/>\nGiven expression is -9\u00b2 . 3<br \/>\n= -9 . 9 . 3<br \/>\n= -9 . 27<br \/>\n= -243<\/p>\n<p>Question 7.<br \/>\n(-7) . (-2) . (-4)<\/p>\n<p>Answer:<br \/>\n(-7) . (-2) . (-4) = -56<\/p>\n<p>Explanation:<br \/>\nGiven expression is (-7) . (-2) . (-4)<br \/>\n= -7 . -2 . -4<br \/>\n= 14 . -4<br \/>\n= -56<\/p>\n<p>Copy and complete the statement using &lt;, &gt;, or =.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-56.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 56\" width=\"111\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n11 = | -11 |<\/p>\n<p>Explanation:<br \/>\n11 = | -11 |<br \/>\nmod of -11 is positive 11<br \/>\nSo, they are equal.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-57.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 57\" width=\"141\" height=\"39\" \/><\/p>\n<p>Answer:<br \/>\n| 3.5 | &lt;\u00a0 | -5.8 |<\/p>\n<p>Explanation:<br \/>\n| 3.5 | _\u00a0 | -5.8 |<br \/>\n3.5 &lt; 5.8<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-58.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 58\" width=\"137\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n| -3.5 | &lt;\u00a0 | 17\/5 |<\/p>\n<p>Explanation:<br \/>\n| -3.5 | _\u00a0 | 17\/5 |<br \/>\n3.5 &lt; 3.4<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING MODELS<\/strong><br \/>\n<strong>Write two different expressions that represent the area of the shaded region. Show that the expressions are equivalent.<\/strong> (See Exploration 1, p. 103.)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-59.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 59\" width=\"199\" height=\"150\" \/><\/p>\n<p>Answer:<br \/>\n6.5(2x + 2), 13x + 13<\/p>\n<p>Explanation:<br \/>\nThe length of the shaded region is 6.5<br \/>\nThe width of the shaded region is (3x + 4) &#8211; (x + 2) = 3x + 4 &#8211; x &#8211; 2<br \/>\n= 2x + 2<br \/>\nThe area of the shaded region = length . width<br \/>\n= 6.5 . (2x + 2)<br \/>\n= 6.5(2x + 2)<br \/>\n= 6.5(2x) + 6.5(2)<br \/>\n= 13x + 13<br \/>\nThe second way is as follows<br \/>\nThe length of bigger rectangle is 3x + 4<br \/>\nWidth of the bigger rectangle is 6.5<br \/>\nArea of the bigger rectangle = length . width<br \/>\n= 6.5(3x + 4)<br \/>\nThe length of unshaded region is x + 2<br \/>\nwidth of the unshaded region is 6.2<br \/>\nArea of the unshaded region = length . width<br \/>\n= 6.5(x + 2)<br \/>\nArea of the shaded region = Area of the bigger rectangle &#8211; area of the shaded region<br \/>\n= 6.5(3x + 4) &#8211; 6.5(x + 2)<br \/>\n= 6.5(3x + 4 -(x + 2))<br \/>\n= 6.5(3x + 4 &#8211; x &#8211; 2)<br \/>\n= 6.5(2x + 2)<br \/>\n= 6.5(2x) + 6.5(2)<br \/>\n= 13x + 13<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-60.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 60\" width=\"222\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\n2.5m\u00b2 &#8211; 2m, 1.5m\u00b2 + m(m &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nThe first way is here.<br \/>\nThe length of the bigger rectangle is 1.5m<br \/>\nThe width of the bigger rectangle is 2m<br \/>\nThe area of the bigger rectangle = length . width<br \/>\n= 1.5m x 2m = 3m\u00b2<br \/>\nLength of the unshaded region is 1.5m &#8211; (m &#8211; 2) = 1.5m &#8211; m + 2<br \/>\n= 0.5m + 2<br \/>\nWidth of the unshaded region = 2m &#8211; m = m<br \/>\nArea of the unshaded region = length . width<br \/>\n= (0.5m + 2) . m<br \/>\nArea of the shaded region = The area of the bigger rectangle &#8211; Area of the unshaded region<br \/>\n= 3m\u00b2 &#8211; m(0.5m + 2)<br \/>\n= 3m\u00b2 &#8211; 0.5m\u00b2 -2m<br \/>\n= 2.5m\u00b2 &#8211; 2m<br \/>\nThe second way is as follows<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-7.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 7\" width=\"290\" height=\"201\" \/><br \/>\nThe length of the first shaded rectangle = 1.5m<br \/>\nThe width of the first shaded rectangle = m<br \/>\nArea of the first shaded rectangle = length . width<br \/>\n= 1.5m x m<br \/>\n= 1.5m\u00b2<br \/>\nThe length of the second shaded rectangle = m &#8211; 2<br \/>\nThe width of the first shaded rectangle = 2m &#8211; m = m<br \/>\nArea of the second shaded rectangle = length . width<br \/>\n= m(m &#8211; 2)<br \/>\nTherefore, area of the shaded region = Area of the first shaded rectangle + Area of the second shaded rectangle<br \/>\n= 1.5m\u00b2 + m(m &#8211; 2)<br \/>\n= 1.5m\u00b2 + m\u00b2 &#8211; 2m<br \/>\n= 2.5m\u00b2 &#8211; 2m<br \/>\nTherefore, two expressions that represent the area of the shaded region is 2.5m\u00b2 &#8211; 2m, 1.5m\u00b2 + m(m &#8211; 2).<\/p>\n<p><strong>USING THE DISTRIBUTIVE PROPERTY<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 13.<br \/>\n3(a &#8211; 7)<\/p>\n<p>Answer:<br \/>\n3(a &#8211; 7) = 3a &#8211; 21<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3(a &#8211; 7)<br \/>\n= 3(a) &#8211; 3(7)<br \/>\n= 3a &#8211; 21<\/p>\n<p>Question 14.<br \/>\n-6(2 + x)<\/p>\n<p>Answer:<br \/>\n-6(2 + x) = -12 &#8211; 6x<\/p>\n<p>Explanation:<br \/>\nThe given expression is -6(2 + x)<br \/>\n= -6(2) +(-6)(x)<br \/>\n= -12 -6(x)<br \/>\n= -12 &#8211; 6x<\/p>\n<p>Question 15.<br \/>\n-5(3m &#8211; 4)<\/p>\n<p>Answer:<br \/>\n-5(3m &#8211; 4) = -15m + 20<\/p>\n<p>Explanation:<br \/>\nThe given expression is -5(3m &#8211; 4)<br \/>\n= -5(3m) &#8211; (-5) (4)<br \/>\n= -15m +5(4)<br \/>\n= -15m + 20<\/p>\n<p>Question 16.<br \/>\n-9(-5 &#8211; 4c)<\/p>\n<p>Answer:<br \/>\n-9(-5 &#8211; 4c) = 45 + 36c<\/p>\n<p>Explanation:<br \/>\nThe given expression is -9(-5 &#8211; 4c)<br \/>\n= -9(-5) &#8211; (-9) (4c)<br \/>\n= 45 + 9(4c)<br \/>\n= 45 + 36c<\/p>\n<p>Question 17.<br \/>\n4.5 (3s + 6)<\/p>\n<p>Answer:<br \/>\n4.5 (3s + 6) = 13.5s+ 27<\/p>\n<p>Explanation:<br \/>\nThe given expression is 4.5 (3s + 6)<br \/>\n= 4.5(3s) + 4.5(6)<br \/>\n= 13.5s+ 27<\/p>\n<p>Question 18.<br \/>\n-1.4 (-5 + 7g)<\/p>\n<p>Answer:<br \/>\n-1.4 (-5 + 7g) = 7 &#8211; 9.8g<\/p>\n<p>Explanation:<br \/>\nThe given expression is -1.4 (-5 + 7g)<br \/>\n= -1.4(-5) -1.4(7g)<br \/>\n= 7 &#8211; 9.8g<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-61.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 61\" width=\"80\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n2\/5(6 &#8211; 5p) = 12\/5 &#8211; 2p<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2\/5(6 &#8211; 5p)<br \/>\n= 2\/5(6) &#8211; 2\/5(5p)<br \/>\n= 12\/5 &#8211; 2p<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-3-Expressions-62.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 3 Expressions 62\" width=\"95\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n-4\/3 (3q &#8211; 10) = -4q + 40\/3<\/p>\n<p>Explanation:<br \/>\nThe given expression is -4\/3 (3q &#8211; 10)<br \/>\n= -4\/3 (3q) + 4\/3(10)<br \/>\n= -4q + 40\/3<\/p>\n<p>Question 21.<br \/>\n2(3 + 4y + 5)<\/p>\n<p>Answer:<br \/>\n2(3 + 4y + 5) = 16 + 8y<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2(3 + 4y + 5)<br \/>\n= 2(8 + 4y)<br \/>\n= 2(8) + 2(4y)<br \/>\n= 16 + 8y<\/p>\n<p>Question 22.<br \/>\n-9(8 + 6n &#8211; 4)<\/p>\n<p>Answer:<br \/>\n-9(8 + 6n &#8211; 4) = -36 &#8211; 54n<\/p>\n<p>Explanation:<br \/>\nThe given expression is -9(8 + 6n &#8211; 4)<br \/>\n= -9(4 + 6n)<br \/>\n= -9(4) &#8211; 9(6n)<br \/>\n= -36 &#8211; 54n<\/p>\n<p>Question 23.<br \/>\n-6(-4d &#8211; 8.3 + 3d)<\/p>\n<p>Answer:<br \/>\n-6(-4d &#8211; 8.3 + 3d) = 6d + 49.8<\/p>\n<p>Explanation:<br \/>\nThe given expression is -6(-4d &#8211; 8.3 + 3d)<br \/>\n= -6(-d &#8211; 8.3)<br \/>\n= -6(-d) + 6(8.3)<br \/>\n= 6d + 49.8<\/p>\n<p>Question 24.<br \/>\n2.3h(6 &#8211; k)<\/p>\n<p>Answer:<br \/>\n2.3h(6 &#8211; k) = 13.8h &#8211; 2.3hk<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2.3h(6 &#8211; k)<br \/>\n= 2.3h(6) &#8211; 2.3h(k)<br \/>\n= 13.8h &#8211; 2.3hk<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-63.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 63\" width=\"102\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n-3\/8 (-4y + z) = 3y\/2 &#8211; 3z\/8<\/p>\n<p>Explanation:<br \/>\nThe given expression is -3\/8 (-4y + z)<br \/>\n= -3\/8 (-4y) &#8211; 3\/8(z)<br \/>\n= 3y\/2 &#8211; 3z\/8<\/p>\n<p>Question 26.<br \/>\n2(-2w &#8211; 1.2 + 7x)<\/p>\n<p>Answer:<br \/>\n2(-2w &#8211; 1.2 + 7x) = -4w- 2.4 + 14x<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2(-2w &#8211; 1.2 + 7x)<br \/>\n= 2(-2w) + 2(-1.2) + 2(7x)<br \/>\n= -4w- 2.4 + 14x<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-64.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 64\" width=\"128\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n5\/3(4\/3 a + 9b + 2\/3 a) = 10a\/3 + 15b<\/p>\n<p>Explanation:<br \/>\nThe given expression is 5\/3(4\/3 a + 9b + 2\/3 a)<br \/>\n= 5\/3 ( 6a\/3 + 9b)<br \/>\n= 5\/3 (2a + 9b)<br \/>\n= 5\/3 (2a) + 5\/3 (9b)<br \/>\n= 10a\/3 + 5 (3b)<br \/>\n= 10a\/3 + 15b<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend simpli\ufb01es the expression. Is your friend correct? Explain your reasoning<\/strong><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-65.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 65\" width=\"244\" height=\"105\" \/><\/p>\n<p>Answer:<br \/>\nWrong.<\/p>\n<p>Explanation:<br \/>\n-2(h + 8k) = -2(h) -2(8k)<br \/>\n= -2h &#8211; 16k<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-66.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 66\" width=\"315\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-66.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-66-300x120.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\n-3(4 &#8211; 5b + 7) = -3(11 &#8211; 5b)<br \/>\n= -3(11) -3(-5b)<br \/>\n= -33 + 15b<\/p>\n<p><strong>SIMPLIFYING EXPRESSIONS<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 30.<br \/>\n-3(5g + 1) + 8g<\/p>\n<p>Answer:<br \/>\n-3(5g + 1) + 8g = -7g &#8211; 3<\/p>\n<p>Explanation:<br \/>\nThe given expression is -3(5g + 1) + 8g<br \/>\n= -3(5g) -3(1) + 8g<br \/>\n= -15g &#8211; 3 + 8g<br \/>\n= -7g &#8211; 3<\/p>\n<p>Question 31.<br \/>\n-6a + 7(-2a &#8211; 4)<\/p>\n<p>Answer:<br \/>\n-6a + 7(-2a &#8211; 4) = -20a &#8211; 28<\/p>\n<p>Explanation:<br \/>\nThe given expression is -6a + 7(-2a &#8211; 4)<br \/>\n= -6a + 7(-2a) +7(-4)<br \/>\n= -6a &#8211; 14a &#8211; 28<br \/>\n= -20a &#8211; 28<\/p>\n<p>Question 32.<br \/>\n9 &#8211; 3(5 &#8211; 4x)<\/p>\n<p>Answer:<br \/>\n9 &#8211; 3(5 &#8211; 4x) = -6 + 12x<\/p>\n<p>Explanation:<br \/>\nThe given expression is 9 &#8211; 3(5 &#8211; 4x)<br \/>\n= 9 &#8211; 3(5) -3(-4x)<br \/>\n= 9 &#8211; 15 + 12x<br \/>\n= -6 + 12x<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-67.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 67\" width=\"184\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n-3\/4(5p &#8211; 12) + 2(8 &#8211; 1\/4 p) = -17p\/4 + 25<\/p>\n<p>Explanation:<br \/>\nThe given expression is -3\/4(5p &#8211; 12) + 2(8 &#8211; 1\/4 p)<br \/>\n= -3\/4 (5p) -3\/4(-12) + 2(8) + 2(-1\/4p)<br \/>\n= -15p\/4 + 9 + 16 &#8211; p\/2<br \/>\n= (-15p -2p)\/4 + 25<br \/>\n= -17p\/4 + 25<\/p>\n<p>Question 34.<br \/>\nc(4 + 3c) &#8211; 0.75(c + 3)<\/p>\n<p>Answer:<br \/>\nc(4 + 3c) &#8211; 0.75(c + 3) = 4c + 3c\u00b2 &#8211; 0.75c &#8211; 2.25<\/p>\n<p>Explanation:<br \/>\nThe given expression is c(4 + 3c) &#8211; 0.75(c + 3)<br \/>\n= c(4) + c(3c) &#8211; 0.75(c) &#8211; 0.75(3)<br \/>\n= 4c + 3c\u00b2 &#8211; 0.75c &#8211; 2.25<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-68.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 68\" width=\"117\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n-1 &#8211; 2\/3(6\/7 &#8211; 3\/7 n) = -33\/21 + 6n\/21<\/p>\n<p>Explanation:<br \/>\nThe given expression is -1 &#8211; 2\/3(6\/7 &#8211; 3\/7 n)<br \/>\n= -1 -2\/3(6\/7) &#8211; 2\/3(-3\/7 n)<br \/>\n= -1 &#8211; 12\/21 + 6n\/21<br \/>\n= (-21 &#8211; 12)\/21 + 6n\/21<br \/>\n= -33\/21 + 6n\/21<\/p>\n<p>Question 36.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe cost (in dollars) of a custom-made sweatshirt is represented by 3.5n + 29.99, where n is the number of different colors in the design. Write and interpret a simpli\ufb01ed expression that represents the cost of 15 sweatshirts.<\/p>\n<p>Answer:<br \/>\nThe cost of 15 sweatshirts is 52.5n + 449.85<\/p>\n<p>Explanation:<br \/>\nThe cost (in dollars) of a custom-made sweatshirt is represented by 3.5n + 29.99<br \/>\nTo find the cost of 15 sweatshirts, we need to multiply the expression by 15<br \/>\n= 15(3.5n + 29.99)<br \/>\n= 15(3.5n) + 15(29.99)<br \/>\n= 52.5n + 449.85<br \/>\nTherefore, the cost of 15 sweatshirts is 52.5n + 449.85<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA ski resort makes snow using a snow fan that costs $1200. The fan has an average daily operation cost of $9.50. Write and interpret a simpli\ufb01ed expression that represents the cost to purchase and operate 6 snow fans.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-69.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 69\" width=\"225\" height=\"182\" \/><\/p>\n<p>Answer:<br \/>\nThe expression that represents the cost to purchase and operate 6 snow fans is 7200 + 57d.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA ski resort makes snow fan that costs $1200<br \/>\nThe fan has an average daily operation cost of $ 9.50<br \/>\nWe have to write a simplified expression that represents the cost to purchase and operate 6 snow fans.<br \/>\nAnd variable d represents the number of days that the resort operates the fans.<br \/>\nNow, cost of 6 snow fans = 6 x cost of each snow fan = 6 x 1200 = 7200<br \/>\nThe cost to operate 6 fans = 6 x number of days x cost to operate each fan<br \/>\n= 6 x d x 9.5 = 57d<br \/>\nSo, the expression for total cost will be cost of fans + cost to operate = 7200 + 57d.<\/p>\n<p>Question 38.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nPredict whether the instructions below will produce equivalent expressions. Then show whether your prediction is correct.<\/p>\n<ul>\n<li>Subtract 3 from n, add 3 to the result, and then triple that expression.<\/li>\n<li>Subtract 3 from n, triple the result, and then add 3 to that expression.<\/li>\n<\/ul>\n<p>Answer:<br \/>\nYour prediction is wrong.<\/p>\n<p>Explanation:<br \/>\na. Subtract 3 from n = n &#8211; 3<br \/>\nAdd 3 to the result = n &#8211; 3 + 3 = n<br \/>\nAnd then triple that expression = n x n x n = n\u00b3.<br \/>\nb. Subtract 3 from n = n &#8211; 3<br \/>\nTriple the result = (n &#8211; 3) . (n &#8211; 3) . (n &#8211; 3) = (n &#8211; 3)\u00b3<br \/>\nAnd then add 3 to that expression = (n &#8211; 3)\u00b3 + 3<br \/>\nTherefore, n\u00b3 is not equivalent to (n &#8211; 3)\u00b3 + 3<br \/>\nHence, the prection is wrong.<\/p>\n<p><strong>USING A MODEL<\/strong><br \/>\n<strong>Draw a diagram that shows how the expression can represent the area of a \ufb01gure. Then simplify the expression.<\/strong><\/p>\n<p>Question 39.<br \/>\n5(2 + x + 3)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-8.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 8\" width=\"421\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-8.jpg 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-8-300x147.jpg 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Explanation:<br \/>\nThe area of rectangle = length . width<br \/>\n= 5(2 + x + 3)<br \/>\n= 5(5 + x)<br \/>\n= 5(5) + 5(x)<br \/>\n= 25 + 5x<br \/>\nTherefore, area is (25 + 5x)<\/p>\n<p>Question 40.<br \/>\n(4 + 1)(x + 2x)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-9.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 9\" width=\"475\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-9.jpg 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-9-300x126.jpg 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Explanation:<br \/>\nLength = 4 + 1<br \/>\nwidth = x + 2x<br \/>\nThe area of rectangle = length . width<br \/>\n= (4 + 1) . (x + 2x)<br \/>\n= 5 . (3x)<br \/>\n= 15x<br \/>\nTherefore, area is 15x.<\/p>\n<p>Question 41.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA square \ufb01repit with a side length of s feet is bordered by 1-foot square stones as shown.<br \/>\na. How many stones does it take to border the \ufb01repit with two rows of stones? Use a diagram to justify your answer.<br \/>\nb. You border the \ufb01re pit with rows of stones. How many stones are in the nth row? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-70.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 70\" width=\"276\" height=\"204\" \/><\/p>\n<p>Answer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-39473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-11.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 11\" width=\"361\" height=\"266\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-11.jpg 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-3-expressions-11-300x221.jpg 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\nThe number of stones = (s + 2)\u00b2 + (s + 4)\u00b2<br \/>\nb. The area of the nth row square is (s + 2n)\u00b2 ft\u00b2.<\/p>\n<p>Explanation:<br \/>\na. The side length of the inner sqaure is s<br \/>\nThe area of the sqaure = side\u00b2<br \/>\n= s\u00b2<br \/>\nThe side length of the 1st row square is s + 1 + 1 = s + 2 ft<br \/>\nThe area of the 1st row square = side\u00b2<br \/>\n= (s + 2)\u00b2 ft\u00b2<br \/>\nThe side length of the 2nd row of the sqaure is s + 2 + 2 = s + 4 ft<br \/>\nThe area of the 2st row square = side\u00b2<br \/>\n= (s + 4)\u00b2 ft\u00b2<br \/>\nSo, the number of stones = (s + 2)\u00b2 + (s + 4)\u00b2<br \/>\nb.<br \/>\nThe side length of the nth row is s + 2n ft<br \/>\nThe area of the nth row square = side\u00b2<br \/>\n= (s + 2n)\u00b2 ft\u00b2<\/p>\n<p>Question 42.<br \/>\n<strong>PUZZLE<\/strong><br \/>\nYour friend asks you to perform the following steps.<\/p>\n<ol>\n<li>Pick any number except 0.<\/li>\n<li>Add 2 to your number.<\/li>\n<li>Multiply the result by 3.<\/li>\n<li>Subtract 6 from the result.<\/li>\n<li>Divide the result by your original number.<\/li>\n<\/ol>\n<p>Your friend says, \u201cThe \ufb01nal result is 3!\u201d Is your friend correct? If so, explain how your friend knew the \ufb01nal result. If not, explain why not.<\/p>\n<p>Answer:<br \/>\nYes, my friend is correct.<\/p>\n<p>Explanation:<\/p>\n<ol>\n<li>Pick any number except 0.<br \/>\nI have taken 2.<\/li>\n<li>Add 2 to your number.<br \/>\n2 + 2 = 4<\/li>\n<li>Multiply the result by 3.<br \/>\n4 x 3 = 12<\/li>\n<li>Subtract 6 from the result.<br \/>\n12 &#8211; 6 = 6<\/li>\n<li>Divide the result by your original number.<br \/>\n6\/2 = 3<\/li>\n<\/ol>\n<h3><a id=\"Lesson_3.4_Factoring_Expressions\"><\/a>Lesson 3.4 Factoring Expressions<\/h3>\n<p><strong>Factoring Expressions<\/strong><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Finding Dimensions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. The models show the areas (in square units) of parts of rectangles.<br \/>\nUse the models to \ufb01nd the missing values that complete the expressions. Explain your reasoning.?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-71.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 71\" width=\"656\" height=\"427\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-71.png 656w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-71-300x195.png 300w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><br \/>\nb. Are the expressions you wrote in part(a) equivalent to the original expressions? Explain your reasoning.<br \/>\nc. Explain how you can use the Distributive Property to \ufb01nd rational number factors of an expression.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 1.<br \/>\n15x + 25<\/p>\n<p>Answer:<br \/>\n15x + 25 = 5(3x + 5)<\/p>\n<p>Explanation:<br \/>\nFind the G.C.F of 15x and 25<br \/>\n15x = 3 . 5 . x<br \/>\n25 = 5. 5<br \/>\nThe common prime factor is 5.<br \/>\nSo, the GCF of 15x and 25 is 5<br \/>\nUse the GCF to factor the expression<br \/>\n15x + 25 = 5(3x) + 5(5)<br \/>\n= 5(3x + 5)<\/p>\n<p>Question 2.<br \/>\n4y &#8211; 20<\/p>\n<p>Answer:<br \/>\n4y &#8211; 20 = 4(y &#8211; 5)<\/p>\n<p>Explanation:<br \/>\nFind the G.C.F of 4y and 20<br \/>\n15x = 2 . 2 . y<br \/>\n20 = 2 . 2 . 5<br \/>\nThe common prime factors are 2 . 2 = 4<br \/>\nSo, the GCF of 4y and 20 is 4<br \/>\nUse the GCF to factor the expression<br \/>\n4y &#8211; 20 = 4(y) &#8211; 4(5)<br \/>\n= 4(y &#8211; 5)<\/p>\n<p>Question 3.<br \/>\n36c + 24d<\/p>\n<p>Answer:<br \/>\n36c + 24d = 12(3c + 2d)<\/p>\n<p>Explanation:<br \/>\nThe G.C.F of 36c, 24d is<br \/>\n36c = 2 . 2 . 3 . 3 . c<br \/>\n24d = 2 . 3 . 2 . 2 . d<br \/>\nThe common prime factors are 2 . 2 . 3 = 12<br \/>\nThe G.C.F of 36c, 24d is 12<br \/>\nUse the GCF to factor the expression<br \/>\n36c + 24d = 12(3c) + 12(2d)<br \/>\n= 12(3c + 2d)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Factor out the coefficient of the variable term.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-72.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 72\" width=\"69\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n\u00bdn &#8211; \u00bd = \u00bd(n &#8211; 1)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n\u00bdn &#8211; \u00bd<br \/>\n\u00bdn = \u00bd . n<br \/>\n\u00bd = \u00bd . 1<br \/>\nUse the distributive property to factor out \u00bd.<br \/>\n\u00bdn &#8211; \u00bd = \u00bd(n) &#8211; \u00bd(1)<br \/>\n= \u00bd(n &#8211; 1)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-73.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 73\" width=\"68\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n3\/4 p &#8211; 3\/2 = 3\/2(p\/2 &#8211; 1)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n3\/4 p &#8211; 3\/2<br \/>\n3\/2 = 3\/2 . 1<br \/>\n3\/4 p = 3\/2 . 1\/2 . p<br \/>\nUse the distributive property to factor out 3\/2<br \/>\n3\/4 p &#8211; 3\/2 = 3\/2(1\/2 p) &#8211; 3\/2(1)<br \/>\n= 3\/2(p\/2 &#8211; 1)<\/p>\n<p>Question 6.<br \/>\n5 + 2.5q<\/p>\n<p>Answer:<br \/>\n5 + 2.5q = 2.5(2 + q)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n5 + 2.5q<br \/>\n5 = 2.5 . 2<br \/>\n2.5 = 2.5 . 1<br \/>\nUse the distributive property to factor out 2.5<br \/>\n5 + 2.5q = 2.5(2) + 2.5(q)<br \/>\n= 2.5(2 + q)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 7.<br \/>\nFactor -5 out of -5d + 30.<\/p>\n<p>Answer:<br \/>\n-5d + 30 = -5(d &#8211; 6)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n-5d + 30.<br \/>\n-5d = -5 . d<br \/>\n30 = 5 . 6 = -5 . -6<br \/>\n-5d + 30 = -5(d) &#8211; 5(-6)<br \/>\n= -5(d &#8211; 6)<\/p>\n<p>Question 8.<br \/>\nFactor -4 out of -8k &#8211; 12.<\/p>\n<p>Answer:<br \/>\n-8k &#8211; 12 = -4(2k + 3)<\/p>\n<p>Explanation:<br \/>\ngiven that,<br \/>\n-8k &#8211; 12<br \/>\n-8k = -2 . 4 . k<br \/>\n-12 = -4 . 3<br \/>\nThe G.C.f of -8k, -12 is -4.<br \/>\n-8k &#8211; 12 = -4(2k) &#8211; 4(3)<br \/>\n= -4(2k + 3)<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>FACTORING OUT THE GCF<\/strong><br \/>\n<strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 9.<br \/>\n16n &#8211; 24<\/p>\n<p>Answer:<br \/>\n16n &#8211; 24 = 8(2n &#8211; 3)<\/p>\n<p>Explanation:<br \/>\nFind the G.C.F of 16n, 24<br \/>\n16n = 2 . 2 . 2 . 2 . n<br \/>\n24 = 2 . 2 . 2 . 3<br \/>\nThe G.C.F of 16n, 24 is 2 . 2 . 2 = 8<br \/>\nUse the GCF to factor the expression<br \/>\n16n &#8211; 24 = 8(2n)- 8(3)<br \/>\n= 8(2n &#8211; 3)<\/p>\n<p>Question 10.<br \/>\n42a + 14b<\/p>\n<p>Answer:<br \/>\n42a + 14b = 14(3a + b)<\/p>\n<p>Explanation:<br \/>\nFind the G.C.F of 42a, 14b<br \/>\n42a = 2 . 3 . 7 . a<br \/>\n14b = 2 . 7 . b<br \/>\nThe greatest common factor of 42a, 14b is 2 . 7 = 14<br \/>\nUse the GCF to factor the expression<br \/>\n42a + 14b = 14(3a) + 14(b)<br \/>\n= 14(3a + b)<\/p>\n<p><strong>FACTORING OUT A RATIONAL NUMBER<\/strong><br \/>\n<strong>Factor out the coefficient of the variable term.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-74.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 74\" width=\"84\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n1\/10 k &#8211; 7\/10 = 1\/10(k &#8211; 7)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n1\/10 k &#8211; 7\/10<br \/>\nThe factors of 1\/10, 7\/10 are<br \/>\n1\/10 = 1\/10 . 1<br \/>\n7\/10 = 7 . 1\/10<br \/>\nUse the distributive property to factor out 1\/10<br \/>\n1\/10 k &#8211; 7\/10 = 1\/10 (k) &#8211; 1\/10(7)<br \/>\n= 1\/10(k &#8211; 7)<\/p>\n<p>Question 12.<br \/>\n42 + 3.5h<\/p>\n<p>Answer:<br \/>\n42 + 3.5h = 3.5(12 + h)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 42, 3.5<br \/>\n42 = 4 . 3 . 3.5<br \/>\n3.5 = 3.5 . 1<br \/>\nUse the distributive property to factor out 3.5<br \/>\n42 + 3.5h = 3.5(12) + 3.5(h)<br \/>\n= 3.5(12 + h)<\/p>\n<p><strong>FACTORING OUT A NEGATIVE NUMBER<\/strong><br \/>\n<strong>Factor out the indicated number.<\/strong><\/p>\n<p>Question 13.<br \/>\nFactor -8 out of -3d + 56.<\/p>\n<p>Answer:<br \/>\n-3d + 56 = -8(3d\/8\u00a0 &#8211; 7)<\/p>\n<p>Explanation:<br \/>\nGet the factors of -3d, 56<br \/>\n-3d = 3d\/8 . -8<br \/>\n56 = -7 . -8<br \/>\nUse the distributive property to factor out -8<br \/>\n-3d + 56 = -8(3d\/8) &#8211; 8(-7)<br \/>\n= -8(3d\/8\u00a0 &#8211; 7)<\/p>\n<p>Question 14.<br \/>\nFactor -12 out of -24k + 120.<\/p>\n<p>Answer:<br \/>\n-24k + 120 = -12(2k &#8211; 10)<\/p>\n<p>Explanation:<br \/>\nGet the factors of -24k, 120<br \/>\n-24k = -12. 2. k<br \/>\n120 = -12. -10<br \/>\nUse the distributive property to factor out -12<br \/>\n-24k + 120 = -12(2k) -12(-10)<br \/>\n= -12(2k &#8211; 10)<\/p>\n<p>Question 15.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe the relationship between using the Distributive Property to simplify an expression and to factor an expression. Give an example to justify your answer.<\/p>\n<p>Answer:<br \/>\nThe distributive property tells that a(b &#8211; c) = ab &#8211; ac and a(b + c) = ab + ac. It means you can seperate the common term and represent it as the factor.<\/p>\n<p>Explanation:<br \/>\nThe relationship between using the Distributive Property to simplify an expression and to factor an expression is mentioned here.<br \/>\nThe distributive property tells that a(b &#8211; c) = ab &#8211; ac and a(b + c) = ab + ac. It means you can seperate the common term and represent it as the factor.<br \/>\nLet us take one example question 12x + 40y<br \/>\nThe factors of 12x = 3 . 4 . x, the factors of 40y = 5 . 2 . 4 . y<br \/>\nThe common factor is 4. So, take out the common factor and use the distribuyive property.<br \/>\n12x + 4y = 4(3x) + 4(10y)<br \/>\n= 4(3x + 10y)<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 16.<br \/>\nAn organization drills 3 wells to provide access to clean drinking water. The cost (in dollars) to drill and maintain the wells for n years is represented by 34,500 + 540n. Write and interpret an expression that represents the cost to drill and maintain one well for n years.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-75.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 75\" width=\"186\" height=\"259\" \/><\/p>\n<p>Answer:<br \/>\nThe cost to drill and maintain one well for n years is 10(1150 + 18n).<\/p>\n<p>Explanation:<br \/>\nThe cost to drill and maintain 3 wells for n years is 34,500 + 540n<br \/>\nTo get the drill and maintainance cost for 1 well, you need to find the factors<br \/>\n34500 = 10 . 10 . 3 . 5 . 23<br \/>\n540n = 3. 9 . 2 . 10 . n<br \/>\nThe G.C.F of 34500 and 540n is 10 . 3 = 30<br \/>\n34,500 + 540n = 30(1150) + 30(18n)<br \/>\n= 30(1150 + 18n)<br \/>\nDivide the expression by 3 to get the drill and maintainance cost for 1 well<br \/>\n= 30(1150 + 18n)\/ 3 = 10(1150 + 18n)<br \/>\nSo, the cost to drill and maintain one well for n years is 10(1150 + 18n)<\/p>\n<p>Question 17.<br \/>\nA photograph is 16 inches long and has an area of (16x + 96) square inches. A custom-made frame is 2 inches wide and costs $0.50 per square inch. Write an expression that represents the cost of the frame.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-76.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 76\" width=\"150\" height=\"209\" \/><\/p>\n<p>Answer:<br \/>\nThe cost of frame is $0.50(4x + 104)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nLength of photograph = 16 inches<br \/>\nArea of photograph = (16x + 96) sq inches<br \/>\nFactor out 16 from the expression<br \/>\n= 16(x) + 16(6) = 16(x + 6)<br \/>\nSo, the width of the photograph is x + 6 inches<br \/>\nA custom-made frame is 2 inches wide and costs $0.50 per square inch.<br \/>\nThe length of frame and photograph is 16 + 2 + 2 = 20 inches<br \/>\nThe bredth of the frame &amp; photograph is (x + 6 + 4) = x + 10 inches<br \/>\nArea of the photograph and frame = length . width<br \/>\n= 20(x + 10)<br \/>\nThe area of frame = The area of photograph and frame &#8211; Area of photograph<br \/>\n= 20(x + 10) &#8211; (16x + 96)<br \/>\n= 20x + 200 &#8211; 16x &#8211; 96<br \/>\n= 4x + 104 sq inches<br \/>\nThe cost of frame is $0.50 per square inch<br \/>\nSo, the cost of the frame is 0.50(4x + 104).<\/p>\n<h3><a id=\"Factoring_Expressions_Homework_&amp;_Practice_3.4\"><\/a>Factoring Expressions Homework &amp; Practice 3.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n8(k &#8211; 5)<\/p>\n<p>Answer:<br \/>\n8(k &#8211; 5) = 8k &#8211; 40<\/p>\n<p>Explanation:<br \/>\nThe given expression is 8(k &#8211; 5)<br \/>\n= 8(k) &#8211; 8(5)<br \/>\n= 8k &#8211; 40<\/p>\n<p>Question 2.<br \/>\n-4.5(-6 + 2d)<\/p>\n<p>Answer:<br \/>\n-4.5(-6 + 2d) = 27 &#8211; 9d<\/p>\n<p>Explanation:<br \/>\nThe given expression is -4.5(-6 + 2d)<br \/>\n= -4.5(-6) &#8211; 4.5(2d)<br \/>\n= 27 &#8211; 9d<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-77.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 77\" width=\"121\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\n-1\/4 (3g &#8211; 6 &#8211; 5g) = 3\/2 + g\/2<\/p>\n<p>Explanation:<br \/>\nThe given expression is -1\/4 (3g &#8211; 6 &#8211; 5g)<br \/>\n= -1\/4(-6 &#8211; 2g)<br \/>\n= -1\/4(-6) &#8211; 1\/4(-2g)<br \/>\n= 3\/2 + 1\/2 g<\/p>\n<p><strong>Find the difference. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-78.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 78\" width=\"88\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n2\/3 &#8211; (-5\/3) = 7\/3<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n2\/3 &#8211; (-5\/3) = 2\/3 + 5\/3<br \/>\n= (2 + 5)\/3 = 7\/3<\/p>\n<p>Question 5.<br \/>\n-4.7 &#8211; 5.6<\/p>\n<p>Answer:<br \/>\n-4.7 &#8211; 5.6 = -10.3<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n-4.7 &#8211; 5.6 = -10.3<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-79.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 79\" width=\"115\" height=\"63\" \/><\/p>\n<p>Answer:<br \/>\n-4(3\/8) &#8211; (-2(1\/4) = -17\/8<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n-4(3\/8) &#8211; (-2(1\/4) = -35\/8 &#8211; (-9\/4)<br \/>\n= -35\/8 + 9\/4 = (-35 + 18)\/8<br \/>\n= -17\/8<\/p>\n<p><strong>Evaluate the expression when x = 4, y = -6, and z = -3.<\/strong><\/p>\n<p>Question 7.<br \/>\ny \u00f7 z<\/p>\n<p>Answer:<br \/>\ny \u00f7 z = 2<\/p>\n<p>Explanation:<br \/>\nGiven expression is y \u00f7 z<br \/>\nPut y = -6, and z = -3<br \/>\ny \u00f7 z = -6 \u00f7 -3<br \/>\n= 6 \u00f7 3 = 2<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{4 y}{2 x}\\)<\/p>\n<p>Answer:<br \/>\n4y\/2x = -3<\/p>\n<p>Explanation:<br \/>\nGiven expression is 4y\/2x<br \/>\nPut x = 4, y = -6<br \/>\n4y\/2x =(4 x -6)\/ (2 x 4)<br \/>\n= -24\/8 = -3<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-80.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 80\" width=\"68\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n(3x &#8211; 2y)\/z = -8<\/p>\n<p>Explanation:<br \/>\nGiven expression is (3x &#8211; 2y)\/z<br \/>\nPut x = 4, y = -6, and z = -3<br \/>\n= (3 x 4 &#8211; 2(-6))\/-3<br \/>\n= (12 + 12)\/-3<br \/>\n= 24\/-3<br \/>\n= -24\/3<br \/>\n= -8<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>FINDING DIMENSIONS<\/strong><br \/>\n<strong>The model shows the area (in square units) of each part of a rectangle. Use the model to \ufb01nd the missing values that complete the expression. Explain your reasoning.<\/strong> (See Exploration 1, p. 109.)<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-81.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 81\" width=\"229\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\n2.25x + 3 = 1.5(1.5x + 2)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 2.25x, 3<br \/>\n2.25x = 1.5 . 1.5 . x<br \/>\n3 = 1.5 . 2<br \/>\nSo, 2.25x + 3 = 1.5(1.5x) +1.5(2)<br \/>\n= 1.5(1.5x + 2)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-82.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 82\" width=\"237\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\n5\/6 m + 2\/3 n = 1\/3(5m\/2 + 2n)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 5m\/6, 2n\/3<br \/>\n5m\/6 = 1\/3 . 5\/2 . m<br \/>\n2n\/3 = 1\/3 . 2 . n<br \/>\nSo, 5\/6 m + 2\/3 n = 1\/3(5m\/2) + 1\/3(2n)<br \/>\n= 1\/3(5m\/2 + 2n)<\/p>\n<p><strong>FACTORING OUT THE GCF<\/strong><br \/>\n<strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 12.<br \/>\n9b + 21<\/p>\n<p>Answer:<br \/>\n9b + 21 = 3(3b + 7)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 9b + 21<br \/>\nFind the factors of 9b, 21<br \/>\n9b = 3 . 3 . b<br \/>\n21= 7 . 3<br \/>\nG.C.F of 9b, 21 is 3<br \/>\nUse the GCF to factor the expression<br \/>\n9b + 21 = 3(3b) + 3(7)<br \/>\n= 3(3b + 7)<\/p>\n<p>Question 13.<br \/>\n32z &#8211; 48<\/p>\n<p>Answer:<br \/>\n32z &#8211; 48 = 16(2z &#8211; 3)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 32z &#8211; 48<br \/>\nFind the factors of 32z, -48<br \/>\n32z = 2 . 2 . 2 . 2 . 2 . z<br \/>\n48 = 2 . 2 . 2 . 2 . 3<br \/>\nG.C.F of 32z, -48 is 2 . 2 . 2 . 2 = 16<br \/>\nUse the GCF to factor the expression<br \/>\n32z &#8211; 48 = 16(2z) &#8211; 16(3)<br \/>\n= 16(2z &#8211; 3)<\/p>\n<p>Question 14.<br \/>\n8x + 2<\/p>\n<p>Answer:<br \/>\n8x + 2 = 2(4x + 1)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 8x + 2<br \/>\nfind the factors of 8x, 2<br \/>\n8x = 2 . 2 . 2 . x<br \/>\n2 = 2. 1<br \/>\nG.C.F of 8x, 2 is 2<br \/>\nUse the GCF to factor the expression<br \/>\n8x + 2 = 2(4x) + 2(1)<br \/>\n= 2(4x + 1)<\/p>\n<p>Question 15.<br \/>\n3y &#8211; 24<\/p>\n<p>Answer:<br \/>\n3y &#8211; 24 = 3(y &#8211; 4)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3y &#8211; 24<br \/>\nFind the factors of 3y, 24<br \/>\n3y = 3 . y<br \/>\n24 = 4 . 3<br \/>\nG.C.F of 3y, 24 is 3<br \/>\nUse the GCF to factor the expression<br \/>\n3y &#8211; 24 = 3(y) &#8211; 3(4)<br \/>\n= 3(y &#8211; 4)<\/p>\n<p>Question 16.<br \/>\n14p &#8211; 28<\/p>\n<p>Answer:<br \/>\n14p &#8211; 28 = 14(p &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 14p &#8211; 28<br \/>\nFind the factors of 14p, 28<br \/>\n14p = 7 . 2 . p<br \/>\n28 = 7 . 2 . 2<br \/>\nG.C.F of 14p, 28 is 14<br \/>\nUse the GCF to factor the expression<br \/>\n14p &#8211; 28 = 14(p) &#8211; 14(2)<br \/>\n= 14(p &#8211; 2)<\/p>\n<p>Question 17.<br \/>\n6 + 16k<\/p>\n<p>Answer:<br \/>\n6 + 16k = 2(3 + 8k)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 6 + 16k<br \/>\nFind the factors of 6, 16k<br \/>\n6 = 2 . 3<br \/>\n16k = 2 . 2 . 2 . 2 . k<br \/>\nG.C.F of 6, 16k is 2<br \/>\nUse the GCF to factor the expression<br \/>\n6 + 16k = 2(3) + 2(8k)<br \/>\n= 2(3 + 8k)<\/p>\n<p>Question 18.<br \/>\n21 &#8211; 14d<\/p>\n<p>Answer:<br \/>\n21 &#8211; 14d = 7(3 &#8211; 2d)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 21 &#8211; 14d<br \/>\nGet the factors of 21, 14d<br \/>\n21 = 7 . 3<br \/>\n14d = 7 . 2 . d<br \/>\nG.C.F of 21, 14d is 7<br \/>\nUse the GCF to factor the expression<br \/>\n21 &#8211; 14d = 7(3) &#8211; 7(2d)<br \/>\n= 7(3 &#8211; 2d)<\/p>\n<p>Question 19.<br \/>\n20z &#8211; 8<\/p>\n<p>Answer:<br \/>\n20z &#8211; 8 = 4(5z &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 20z &#8211; 8<br \/>\nGet the factors of 20z, 8<br \/>\n20z = 5 . 2 . 2 . z<br \/>\n8 = 2 . 2 . 2<br \/>\nG.C.F of 20z, 8 is 4<br \/>\nUse the GCF to factor the expression<br \/>\n20z &#8211; 8 = 4(5z) &#8211; 4(2)<br \/>\n= 4(5z &#8211; 2)<\/p>\n<p>Question 20.<br \/>\n15w + 65<\/p>\n<p>Answer:<br \/>\n15w + 65 = 5(3w + 13)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 15w + 65<br \/>\nGet the factors of 15w, 65<br \/>\n15w = 5 . 3 . w<br \/>\n65 = 5 . 13<br \/>\nG.C.F of 15w, 65 is 5<br \/>\nUse the GCF to factor the expression<br \/>\n15w + 65 = 5(3w) + 5(13)<br \/>\n= 5(3w + 13)<\/p>\n<p>Question 21.<br \/>\n36a + 16b<\/p>\n<p>Answer:<br \/>\n36a + 16b = 4(9a + 4b)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 36a + 16b<br \/>\nGet the factors of 36a, 16b<br \/>\n36a = 3 . 2 . 3 . 2 . a<br \/>\n16b = 2 . 2 . 2 . 2 . b<br \/>\nG.C.F of 36a, 16b is 4<br \/>\nUse the GCF to factor the expression<br \/>\n36a + 16b = 4(9a) + 4(4b)<br \/>\n= 4(9a + 4b)<\/p>\n<p>Question 22.<br \/>\n21m &#8211; 49n<\/p>\n<p>Answer:<br \/>\n21m &#8211; 49n = 7(3m + 7n)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 21m &#8211; 49n<br \/>\nGet the factors of 21m, 49n<br \/>\n21m = 7 . 3 . m<br \/>\n49n = 7 . 7 . n<br \/>\nG.C.F of 21m, 49n<br \/>\nUse the GCF to factor the expression<br \/>\n21m &#8211; 49n = 7(3m) + 7(7n)<br \/>\n= 7(3m + 7n)<\/p>\n<p>Question 23.<br \/>\n12 + 9g &#8211; 30h<\/p>\n<p>Answer:<br \/>\n12 + 9g &#8211; 30h = 3(4 + 3g &#8211; 10h)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 12 + 9g &#8211; 30h<br \/>\nGet the factors of 12, 9g, 30h<br \/>\n12 = 3 . 2 . 2<br \/>\n9g = 3 . 3 . g<br \/>\n30h = 3 . 5 . 2 . h<br \/>\nG.C.F of 12, 9g, 30h is 3<br \/>\nUse the GCF to factor the expression<br \/>\n12 + 9g &#8211; 30h = 3(4) + 3(3g) &#8211; 3(10h)<br \/>\n= 3(4 + 3g &#8211; 10h)<\/p>\n<p><strong>FACTORING OUT A RATIONAL NUMBER<\/strong><br \/>\n<strong>Factor out the coefficient of the variable term.<\/strong><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-83.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 83\" width=\"63\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n1\/7 a + 1\/7 = 1\/7 (a + 1)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/7 a + 1\/7<br \/>\n1\/7a = 1\/7 . a<br \/>\n1\/7 = 1\/7 . 1<br \/>\nUse the distributive property to factor out 1\/7<br \/>\n1\/7 a + 1\/7 = 1\/7(a) + 1\/7(1)<br \/>\n= 1\/7 (a + 1)<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-84.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 84\" width=\"62\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n1\/3 b &#8211; 1\/3 = 1\/3(b &#8211; 1)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/3 b &#8211; 1\/3<br \/>\n1\/3b = 1\/3 . b<br \/>\n1\/3 = 1\/3 . 1<br \/>\nUse the distributive property to factor out 1\/3<br \/>\n1\/3 b &#8211; 1\/3 = 1\/3(b) &#8211; 1\/3(1)<br \/>\n= 1\/3(b &#8211; 1)<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-85.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 85\" width=\"63\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\n3\/8 d + 3\/4 = 3\/4(d\/2 + 1)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3\/8 d + 3\/4<br \/>\n3\/8 d = 3\/4 . 1\/2 . d<br \/>\n3\/4 = 3\/4 . 1<br \/>\nUse the distributive property to factor out 3\/4<br \/>\n3\/8 d + 3\/4 = 3\/4 (d\/2) + 3\/4(1)<br \/>\n= 3\/4(d\/2 + 1)<\/p>\n<p>Question 27.<br \/>\n2.2x + 4.4<\/p>\n<p>Answer:<br \/>\n2.2x + 4.4 = 2.2(x +2)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2.2x + 4.4<br \/>\n2.2x = 1.1 . 2 . x<br \/>\n4.4 = 1.1 . 2 . 2<br \/>\nUse the distributive property to factor out 2.2<br \/>\n2.2x + 4.4 = 2.2(x) + 2.2(2)<br \/>\n= 2.2(x +2)<\/p>\n<p>Question 28.<br \/>\n1.5y &#8211; 6 = 1.5(y &#8211; 4)<\/p>\n<p>Answer:<br \/>\n1.5y &#8211; 6<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1.5y &#8211; 6<br \/>\n1.5y = 1.5 . y<br \/>\n6 = 1.5 . 2 . 2<br \/>\nUse the distributive property to factor out 1.5<br \/>\n1.5y &#8211; 6 = 1.5(y) &#8211; 1.5(4)<br \/>\n= 1.5(y &#8211; 4)<\/p>\n<p>Question 29.<br \/>\n0.8w + 3.6<\/p>\n<p>Answer:<br \/>\n0.8w + 3.6 = 0.8(w + 4.5)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 0.8w + 3.6<br \/>\n0.8w = 0.8 . w<br \/>\n3.6 = 0.8 . 4.5<br \/>\nUse the distributive property to factor out 0.8<br \/>\n0.8w + 3.6 = 0.8(w) + 0.8(4.5)<br \/>\n= 0.8(w + 4.5)<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-86.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 86\" width=\"66\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n15\/4 + 3\/8 x = 3\/4(5 + x\/2)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 15\/4 + 3\/8 x<br \/>\n15\/4 = 3\/4 . 5<br \/>\n3\/8x = 3\/4 . 1\/2 . x<br \/>\nUse the distributive property to factor out 3\/4<br \/>\n15\/4 + 3\/8 x = 3\/4(5) + 3\/4(x\/2)<br \/>\n= 3\/4(5 + x\/2)<\/p>\n<p>Question 31.<br \/>\n4h &#8211; 3<\/p>\n<p>Answer:<br \/>\n4h &#8211; 3 = 2(2h &#8211; 1.5)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 4h &#8211; 3<br \/>\n4h = 2 . 2 h<br \/>\n3 = 2 . 1.5<br \/>\nUse the distributive property to factor out 2<br \/>\n4h &#8211; 3 = 2(2h) &#8211; 2(1.5)<br \/>\n= 2(2h &#8211; 1.5)<\/p>\n<p>Question 32.<br \/>\n0.15c &#8211; 0.072<\/p>\n<p>Answer:<br \/>\n0.15c &#8211; 0.072 = 0.03(5c &#8211; 2.4)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 0.15c &#8211; 0.072<br \/>\n0.15c = 0.03 . 5 . c<br \/>\n0.072 = 0.03 . 2.4<br \/>\nUse the distributive property to factor out 0.03<br \/>\n0.15c &#8211; 0.072 = 0.03(5c) &#8211; 0.03(2.4)<br \/>\n= 0.03(5c &#8211; 2.4)<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-87.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 87\" width=\"66\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n3\/8 z + 1 = 1\/8(3z + 8)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3\/8 z + 1<br \/>\n3\/8 z = 1\/8 . 3 . z<br \/>\n1 = 1\/8 . 8<br \/>\nUse the distributive property to factor out 1\/8<br \/>\n3\/8 z + 1 = 1\/8(3z) + 1\/8(8)<br \/>\n= 1\/8(3z + 8)<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-88.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 88\" width=\"61\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n6s &#8211; 3\/4 = 3(2s &#8211; 1\/4)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 6s &#8211; 3\/4<br \/>\n6s = 3 . 2 . s<br \/>\n3\/4 = 3 . 1\/4<br \/>\nUse the distributive property to factor out 3<br \/>\n6s &#8211; 3\/4 = 3(2s) &#8211; 3(1\/4)<br \/>\n= 3(2s &#8211; 1\/4)<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-89.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 89\" width=\"71\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n5\/2 k &#8211; 2 = 1\/2(5k &#8211; 4)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 5\/2 k &#8211; 2<br \/>\n5\/2k = 1\/2 . 5 . k<br \/>\n2 = 1\/2 . 4<br \/>\nUse the distributive property to factor out 1\/2<br \/>\n5\/2 k &#8211; 2 = 1\/2 (5k) &#8211; 1\/2(4)<br \/>\n= 1\/2(5k &#8211; 4)<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend factors the expression. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-90.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 90\" width=\"249\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nFactors of 16p, 28<br \/>\n16p = 4 . 4 . p<br \/>\n28 = 4 . 7<br \/>\nUse the distributive property to factor out 4<br \/>\n16p &#8211; 28 = 4(4p) &#8211; 4(7)<br \/>\n= 4(4p &#8211; 7)<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-91.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 91\" width=\"216\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nCorrect.<\/p>\n<p>Explanation:<br \/>\nFind the factors of 2\/3y, 14\/3<br \/>\n2\/3y = 2 . 1\/3 . y<br \/>\n14\/3 = 2 . 7 . 1\/3<br \/>\nUse the distributive property to factor out 2\/3<br \/>\n2\/3y &#8211; 14\/3 = 2\/3(y) &#8211; 2\/3(7)<br \/>\n= 2\/3(y &#8211; 7)<\/p>\n<p><strong>FACTORING OUT A NEGATIVE NUMBER<\/strong><br \/>\n<strong>Factor out the indicated number.<\/strong><\/p>\n<p>Question 38.<br \/>\nFactor -4 out of -8d + 20.<\/p>\n<p>Answer:<br \/>\n-4(2d &#8211; 5)<\/p>\n<p>Explanation:<br \/>\nGiven expression is -8d + 20<br \/>\nFind factors of 8d, 20<br \/>\n-8d = -4 . 2 . d<br \/>\n20 = -4. -5<br \/>\nUse the distributive property to factor out -4<br \/>\n-8d + 20 = -4(2d) &#8211; 4(-5)<br \/>\n= -4(2d &#8211; 5)<\/p>\n<p>Question 39.<br \/>\nFactor -6 out of 18z &#8211; 15.<\/p>\n<p>Answer:<br \/>\n18z &#8211; 15 = -6(-3z + 5\/2)<\/p>\n<p>Explanation:<br \/>\nGiven expression is 18z &#8211; 15<br \/>\nFind factors of 18z, -15<br \/>\n18z = -6 . -3 . z<br \/>\n-15 = -3 . 5\/2 . 2<br \/>\nUse the distributive property to factor out -6<br \/>\n18z &#8211; 15 = -6(-3z) &#8211; 6(5\/2)<br \/>\n= -6(-3z + 5\/2)<\/p>\n<p>Question 40.<br \/>\nFactor -0.25 out of 7g+ 3.5.<\/p>\n<p>Answer:<br \/>\n7g+ 3.5 = -0.25(-28g &#8211; 14)<\/p>\n<p>Explanation:<br \/>\nGiven expression is 7g+ 3.5<br \/>\nFind factors of 7g, 3.5<br \/>\n7g = -0.25 x -28 x g<br \/>\n3.5 = -0.25 x -14<br \/>\nUse the distributive property to factor out -0.25<br \/>\n7g+ 3.5 = -0.25(-28g) -0.25(-14)<br \/>\n= -0.25(-28g &#8211; 14)<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-92.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 92\" width=\"185\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n-1\/2 x + 6 = -1\/2(x &#8211; 12)<\/p>\n<p>Explanation:<br \/>\nGiven expression is -1\/2 x + 6<br \/>\nFind factors of -1\/2 x, 6<br \/>\n-1\/2x = -1\/2 . x<br \/>\n6 = -1\/2 . -4 . 3<br \/>\nUse the distributive property to factor out -1\/2<br \/>\n-1\/2 x + 6 = -1\/2(x) &#8211; 1\/2(-12)<br \/>\n= -1\/2(x &#8211; 12)<\/p>\n<p>Question 42.<br \/>\nFactor -1.75 out of -14m &#8211; 5.25n.<\/p>\n<p>Answer:<br \/>\n-14m &#8211; 5.25n = -1.75(8m + 3n)<\/p>\n<p>Explanation:<br \/>\nGiven expression is -14m &#8211; 5.25n<br \/>\nFind factors of -14m, -5.25n<br \/>\n-14m = -1.75 . 8 . m<br \/>\n-5.25n = -1.75 . 3 . n<br \/>\nUse the distributive property to factor out -1.75<br \/>\n-14m &#8211; 5.25n = -1.75(8m) -1.75(3n)<br \/>\n= -1.75(8m + 3n)<\/p>\n<p>Question 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-92.1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 92.1\" width=\"196\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n-1\/2 x &#8211; 5\/4 y = -1\/4(2x + 5y)<\/p>\n<p>Explanation:<br \/>\nGiven expression is -1\/2 x &#8211; 5\/4 y<br \/>\nFind factors of -1\/2 x, &#8211; 5\/4 y<br \/>\n-1\/2x = -1\/4 . 2. x<br \/>\n-5\/4y = -1\/4 . 5 . y<br \/>\nUse the distributive property to factor out -1\/4<br \/>\n-1\/2 x &#8211; 5\/4 y = -1\/4(2x) -1\/4(5y)<br \/>\n= -1\/4(2x + 5y)<\/p>\n<p>Question 44.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nA rectangle has an area of (4x + 12) square units. Write three multiplication expressions that can represent the product of the length and the width of the rectangle.<\/p>\n<p>Answer:<br \/>\nThree multiplication expressions that can represent the product of the length and the width of the rectangle are1\/2(4x + 24), 2(2x + 6), 4(x + 3).<\/p>\n<p>Explanation:<br \/>\nRectangle area is (4x + 12) square units<br \/>\nFind the factors of 4x, 12<br \/>\n4x = 2 . 2 . x<br \/>\n12 = 2 . 2 . 3<br \/>\nUse the distributive property to factor out 2<br \/>\n(4x + 12) = 2(2x) + 2(6)<br \/>\n= 2(2x + 6)<br \/>\nArea of rectangle = length . width<br \/>\n= 2(2x + 6)<br \/>\nUse the distributive property to factor out 4 of (4x + 12)<br \/>\n(4x + 12) = 4(x) + 4(3)<br \/>\n= 4(x + 3)<br \/>\n4x = 1\/2 . 4x<br \/>\n12 = 1\/2 . 6 . 4<br \/>\nUse the distributive property to factor out 1\/2<br \/>\n(4x + 12) = 1\/2(4x) + 1\/2(24)<br \/>\n= 1\/2(4x + 24)<br \/>\nSo, three multiplication expressions that can represent the product of the length and the width of the rectangle are1\/2(4x + 24), 2(2x + 6), 4(x + 3).<\/p>\n<p>Question 45.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA square wrestling mat has a perimeter of (12x &#8211; 32) feet. Explain how to use the expression to \ufb01nd the length (in feet) of the mat. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-93.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 93\" width=\"229\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nThe expression that represents the length of the side of the mat is 3x &#8211; 8 feet.<\/p>\n<p>Explanation:<br \/>\nThe wrestling mat is a sqauare<br \/>\nLet a is the length of the side of a square<br \/>\nThe perimeter of mat = 4 x side = 4 . a<br \/>\n12x &#8211; 32 = 4a<br \/>\nIn order to find the length of the side of te mat we have to solve the equation above for a<br \/>\n4a = 12x &#8211; 32<br \/>\na = (12x &#8211; 32)\/4<br \/>\na = 3x &#8211; 8 feet<br \/>\nThe expression that represents the length of the side of the mat is 3x &#8211; 8 feet.<\/p>\n<p>Question 46.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical leaves table. The extended table is rectangular with an area of (18 + 6x) square feet. Write and interpret an expression that represents the length (in feet) of the extended table.<\/p>\n<p>Answer:<br \/>\nThe length of the extended table is 6 + 2x<\/p>\n<p>Explanation:<br \/>\nA table is 6 feet long and 3 feet wide.<br \/>\nTable area = length. width<br \/>\n= 6 . 3 = 18 sq feet<br \/>\nThe extended table is rectangular with an area of (18 + 6x) square feet.<br \/>\nFind factors of 18, 6x<br \/>\n18 = 3 . 6<br \/>\n6x = 3 . 2 . x<br \/>\n(18 + 6x) = 3(6) + 3(2x)<br \/>\n= 3(6 + 2x)<br \/>\nSo, the length of the extended table is 6 + 2x<\/p>\n<p>Question 47.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and packages of plastic. An art club purchases 6 identical kits for (180 + 58.5p) dollars. Write and interpret an expression that represents the cost of one kit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-94.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 94\" width=\"227\" height=\"208\" \/><\/p>\n<p>Answer:<br \/>\nThe cost of one kit is (30 + 9.75) dollars.<\/p>\n<p>Explanation:<br \/>\nArt club purchases 6 identical kits for (180 + 58.5p) dollars<br \/>\nDivide (180 + 58.5p) by 6 to get the cost of one kit<br \/>\n= (180 + 58.5p) \/ 6<br \/>\n= 180\/6 + 58.5p\/6<br \/>\n= 30 + 9.75<br \/>\nHence, the cost of one kit is (30 + 9.75) dollars.<\/p>\n<p>Question 48.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe area of the trapezoid is <img loading=\"lazy\" class=\"alignnone size-full wp-image-29353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-3-Expressions-95.1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 3 Expressions 95.1\" width=\"64\" height=\"45\" \/> square centimeters. Write two different pairs of expressions that represent the possible base lengths (in centimeters). Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-3-Expressions-95.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 3 Expressions 95\" width=\"182\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\n(3x &#8211; 1)\/2<\/p>\n<p>Explanation:<br \/>\nArea of the trapezoid = height * (sum of parallel lengths)\/2<br \/>\n= (3x\/4 &#8211; 1\/4)<br \/>\n= (3x &#8211; 1)\/4<br \/>\nHere height is 1\/2<br \/>\nSo, base length is (3x &#8211; 1)\/2<\/p>\n<h3><a id=\"Expressions_Connecting_Concepts\"><\/a>Expressions Connecting Concepts<\/h3>\n<p><strong>3 Connecting Concepts<\/strong><\/p>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nThe runway shown has an area of (0.05x + 0.125) square miles. Write an expression that represents the perimeter (in feet) of the runway.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-96.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 96\" width=\"546\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-96.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-96-300x48.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\n<strong>Understand the problem<\/strong><br \/>\nYou know the area of the rectangular runway in square miles and the width of the runway in miles. You want to know the perimeter of the runway in feet.<br \/>\n<strong>Make a plan.<\/strong><br \/>\nFactor the width of 0.05 mile out of the expression that represents the area to \ufb01nd an expression that represents the length of the runway. Then write an expression that represents the perimeter (in miles) of the runway. Finally, use a measurement conversion to write the expression in terms of feet.<br \/>\n<strong>Solve and check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nThe perimeter of the runway is 2(x + 2.55) miles.<\/p>\n<p>Explanation:<br \/>\nThe runway shown has an area of (0.05x + 0.125)<br \/>\n= 0.05(x) + 0.05(2.5)<br \/>\n= 0.05(x + 2.5)<br \/>\nThe length of the run way is (x + 2.5) miles<br \/>\nWidth = 0.05<br \/>\nPerimeter of the runway = 2(length + width)<br \/>\n= 2(x + 2.5 + 0.05)<br \/>\n= 2(x + 2.55)<\/p>\n<p>Question 2.<br \/>\nThe populations of two towns after t years can be modeled by -300t + 7000 and -200t + 5500. What is the combined population of the two towns after years? The combined population of the towns in Year 10 is what percent of the combined population in Year 0?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-97.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 97\" width=\"218\" height=\"155\" \/><\/p>\n<p>Answer:<br \/>\nThe combined population of two towns after t years is -500t + 12500.<br \/>\nThe combined population of the towns in 10 Years is 60% of the combined population in Year 0.<\/p>\n<p>Explanation:<br \/>\nThe populations of two towns after t years can be modeled by -300t + 7000 and -200t + 5500<br \/>\nThe combined population of two towns after t years = -300t + 7000 + (-200t + 5500)<br \/>\n= -300t + 7000 &#8211; 200t + 5500<br \/>\n= -500t + 12500<br \/>\nThe combined population of the towns in 10 Years = -500(10) + 12500<br \/>\n= -5000 + 12500 = 7500<br \/>\nThe combined population in Year 0 = -500(0) + 12500<br \/>\n= 12500<br \/>\nThe combined population of the towns in 10 Years is what percent of the combined population in Year 0 is 7500\/12500 x 100<br \/>\n= 7500\/125 = 60<br \/>\nSo, The combined population of the towns in 10 Years is 60% of the combined population in Year 0.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Chlorophyll in Plants<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM Video called \u201cTropic Status.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-98.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 98\" width=\"280\" height=\"199\" \/><\/p>\n<h3><a id=\"Expressions_Chapter_Review\"><\/a>Expressions Chapter Review<\/h3>\n<p><strong>3 Chapter Review<\/strong><\/p>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-99.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 99\" width=\"593\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-99.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-99-300x31.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use an Example and Non-Example Chart to list examples and non-examples of a concept. Here is an Example and Non-Example Chart for like terms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-100.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 100\" width=\"423\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-100.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-100-300x160.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p><strong>Choose and complete a graphic organizer to help you study the concept.<\/strong><\/p>\n<ol>\n<li>simplest form<\/li>\n<li>equivalent expressions<\/li>\n<li>linear expression<\/li>\n<li>Distributive Property<\/li>\n<li>factoring an expression<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-29359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-101.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 101\" width=\"261\" height=\"370\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-101.png 261w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-101-212x300.png 212w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-102.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 102\" width=\"646\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-102.png 646w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-102-300x40.png 300w\" sizes=\"(max-width: 646px) 100vw, 646px\" \/><\/p>\n<p><strong>3.1 Algebraic Expressions<\/strong> (pp. 91\u201396)<\/p>\n<p><strong>Identify the terms and like terms in the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\nz + 8 &#8211; 4z<\/p>\n<p>Answer:<br \/>\nLike terms are z, -4z<br \/>\nTerms are z, 8, -4z<\/p>\n<p>Explanation:<br \/>\nLike terms are z, -4z<br \/>\nTerms are z, 8, -4z<\/p>\n<p>Question 2.<br \/>\n3n + 7 &#8211; n &#8211; 3<\/p>\n<p>Answer:<br \/>\nLike terms are 3n, -n<br \/>\nTerms are 3n, 7, -n, -3<\/p>\n<p>Explanation:<br \/>\nLike terms are 3n, -n<br \/>\nTerms are 3n, 7, -n, -3<\/p>\n<p>Question 3.<br \/>\n10x<sup>2<\/sup> &#8211; y + 12 &#8211; 2x<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\nLike terms are10x\u00b2, -2x\u00b2<br \/>\nTerms are 10x\u00b2, -y, 12, -2x\u00b2<\/p>\n<p>Explanation:<br \/>\nLike terms are10x\u00b2, -2x\u00b2<br \/>\nTerms are 10x\u00b2, -y, 12, -2x\u00b2<\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n4h &#8211; 8h<\/p>\n<p>Answer:<br \/>\n4h &#8211; 8h = -4h<\/p>\n<p>Explanation:<br \/>\nThe given expression is 4h &#8211; 8h<br \/>\n= -4h<\/p>\n<p>Question 5.<br \/>\n6.4r &#8211; 7 &#8211; 2.9r<\/p>\n<p>Answer:<br \/>\n6.4r &#8211; 7 &#8211; 2.9r = 3.5r &#8211; 7<\/p>\n<p>Explanation:<br \/>\nThe given expression is 6.4r &#8211; 7 &#8211; 2.9r<br \/>\n= 3.5r &#8211; 7<\/p>\n<p>Question 6.<br \/>\n2m &#8211; m &#8211; 7m<\/p>\n<p>Answer:<br \/>\n2m &#8211; m &#8211; 7m = -6m<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2m &#8211; m &#8211; 7m<br \/>\n= 2m &#8211; 8m = -6m<\/p>\n<p>Question 7.<br \/>\n6y + 9 + 3y &#8211; 7<\/p>\n<p>Answer:<br \/>\n6y + 9 + 3y &#8211; 7 = 9y + 2<\/p>\n<p>Explanation:<br \/>\nThe given expression is 6y + 9 + 3y &#8211; 7<br \/>\n= 9y + 2<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-103.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 103\" width=\"138\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n3\/5 x + 19 &#8211; 3\/20 x &#8211; 7 = 9x\/20 + 12<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3\/5 x + 19 &#8211; 3\/20 x &#8211; 7<br \/>\n= 3x\/5 + 19 &#8211; 3x\/20 &#8211; 7<br \/>\n= (12x &#8211; 3x)\/20 + 19 &#8211; 7<br \/>\n= 9x\/20 + 12<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-104.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 104\" width=\"132\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\n2\/3 y + 14 &#8211; 1\/6 y &#8211; 8 = y\/2 + 6<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2\/3 y + 14 &#8211; 1\/6 y &#8211; 8<br \/>\n= (4y &#8211; y)\/6 + 14 &#8211; 8<br \/>\n= 3y\/6 + 6<br \/>\n= y\/2 + 6<\/p>\n<p>Question 10.<br \/>\nWrite an expression with 4 different terms that is equivalent to 5x<sup>2<\/sup> &#8211; 8. Justify your answer.<\/p>\n<p>Answer:<br \/>\n5x\u00b2 &#8211; 8 = 3x\u00b2 + 2x\u00b2 &#8211; 6 &#8211; 2<\/p>\n<p>Explanation:<br \/>\nGiven expression is 5x\u00b2 &#8211; 8<br \/>\n= 3x\u00b2 + 2x\u00b2 &#8211; 6 &#8211; 2<\/p>\n<p>Question 11.<br \/>\nFind the earnings for selling the same number of each type of sandwich. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-105.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 105\" width=\"331\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-105.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-105-300x84.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><\/p>\n<p>Answer:<br \/>\nThe earnings in turkey is 2.25x + 1.15y<br \/>\nThe earnings in Ham is 1.55x + 1.30y<\/p>\n<p>Explanation:<br \/>\nLet us take the earnings for selling pretzel roll sandwich is x, begel sandwich is y<br \/>\nSo, The earnings in turkey is 2.25x + 1.15y<br \/>\nThe earnings in Ham is 1.55x + 1.30y<\/p>\n<p>Question 12.<br \/>\nYou buy the same number of brushes, rollers, and paint cans.<br \/>\na. Write and interpret an expression in simplest form that represents the total amount of money you spend on painting supplies.<br \/>\nb. How much do you spend when you buy one set of supplies for each of 3 painters?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-106.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 106\" width=\"340\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-106.png 340w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-106-300x171.png 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/p>\n<p>Answer:<br \/>\na. The total amount of money you spend on painting supplies is 32.67x<br \/>\nb. The cost of one set of supplies for each of 3 painters is $98.01.<\/p>\n<p>Explanation:<br \/>\na.<br \/>\nlet us take you buy the x number of brushes, rollers, and paint cans.<br \/>\nSo, the amount sped to buy those is 3.99x + 21.79x + 6.89x<br \/>\n= x(3.99 + 21.79 + 6.89)<br \/>\n= x(32.67)<br \/>\nb. The cost for 1 set of painting supplies = (3.99 + 21.79 + 6.89)<br \/>\n= 32.67<br \/>\nThe cost for 3 sets of painting supplies = 3(32.67)<br \/>\n= 98.01<\/p>\n<p><strong>3.2 Adding and Subtracting Linear Expressions<\/strong> (pp. 97\u2013102)<\/p>\n<p><strong>Find the sum.<\/strong><\/p>\n<p>Question 13.<br \/>\n(c &#8211; 4) + (3c + 9)<\/p>\n<p>Answer:<br \/>\n(c &#8211; 4) + (3c + 9) = 4c + 5<\/p>\n<p>Explanation:<br \/>\nThe given expression is (c &#8211; 4) + (3c + 9)<br \/>\n= c &#8211; 4 + 3c + 9<br \/>\n= 4c + 5<\/p>\n<p>Question 14.<br \/>\n(5z + 4) + (3z &#8211; 6)<\/p>\n<p>Answer:<br \/>\n(5z + 4) + (3z &#8211; 6) = 8z- 2<\/p>\n<p>Explanation:<br \/>\nThe given expression is (5z + 4) + (3z &#8211; 6)<br \/>\n= 5z + 4 + 3z &#8211; 6<br \/>\n= 8z- 2<\/p>\n<p>Question 15.<br \/>\n(-2.1m &#8211; 5) + (3m &#8211; 7)<\/p>\n<p>Answer:<br \/>\n(-2.1m &#8211; 5) + (3m &#8211; 7) = 0.9m &#8211; 12<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-2.1m &#8211; 5) + (3m &#8211; 7)<br \/>\n= -2.1m &#8211; 5 + 3m &#8211; 7<br \/>\n= 0.9m &#8211; 12<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-107.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 107\" width=\"234\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n(5\/4 q + 1) + (q &#8211; 4) + (-1\/4 q + 2) = 2q &#8211; 1<\/p>\n<p>Explanation:<br \/>\nThe given expression is (5\/4 q + 1) + (q &#8211; 4) + (-1\/4 q + 2)<br \/>\n= 5\/4 q + 1 + q &#8211; 4 -1\/4 q + 2<br \/>\n= (5q &#8211; q)\/4 + q + 3 &#8211; 4<br \/>\n= 4q\/4 + q &#8211; 1<br \/>\n= q + q &#8211; 1<br \/>\n= 2q &#8211; 1<\/p>\n<p><strong>Find the difference.<\/strong><\/p>\n<p>Question 17.<br \/>\n(x &#8211; 1) &#8211; (3x + 2)<\/p>\n<p>Answer:<br \/>\n(x &#8211; 1) &#8211; (3x + 2) = -2x &#8211; 3<\/p>\n<p>Explanation:<br \/>\nThe given expression is (x &#8211; 1) &#8211; (3x + 2)<br \/>\n= x &#8211; 1 &#8211; 3x &#8211; 2<br \/>\n= -2x &#8211; 3<\/p>\n<p>Question 18.<br \/>\n(4y + 3) &#8211; (2y &#8211; 9)<\/p>\n<p>Answer:<br \/>\n(4y + 3) &#8211; (2y &#8211; 9) = 2y + 12<\/p>\n<p>Explanation:<br \/>\nThe given expression is (4y + 3) &#8211; (2y &#8211; 9)<br \/>\n= 4y + 3 &#8211; 2y + 9<br \/>\n= 2y + 12<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-108.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 108\" width=\"160\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\n(1\/2 h + 7) &#8211; (3\/2 h + 9) = -h &#8211; 2<\/p>\n<p>Explanation:<br \/>\nThe given expression is\u00a0 (1\/2 h + 7) &#8211; (3\/2 h + 9)<br \/>\n= 1\/2 h + 7 &#8211; 3\/2 h &#8211; 9<br \/>\n= (1 &#8211; 3)\/2 h &#8211; 2<br \/>\n= -2h\/2 &#8211; 2<br \/>\n= -h &#8211; 2<\/p>\n<p>Question 20.<br \/>\n(4 &#8211; 3.7b) &#8211; (-5.4b &#8211; 4) &#8211; (1.2b + 1)<\/p>\n<p>Answer:<br \/>\n(4 &#8211; 3.7b) &#8211; (-5.4b &#8211; 4) &#8211; (1.2b + 1) = 7 &#8211; 0.5b<\/p>\n<p>Explanation:<br \/>\nThe given expression is (4 &#8211; 3.7b) &#8211; (-5.4b &#8211; 4) &#8211; (1.2b + 1)<br \/>\n= 4 &#8211; 3.7b + 5.4b + 4 &#8211; 1.2b &#8211; 1<br \/>\n= 7 &#8211; 4.9b + 5.4b<br \/>\n= 7 &#8211; 0.5b<\/p>\n<p>Question 21.<br \/>\nA basket holds apples. You pick (2n &#8211; 3) apples, and your friend picks (n + 4) apples. How many apples do you and your friend pick together? How many baskets do you need to carry all the apples? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe number of apples you and your friend picked is 3n + 1.<\/p>\n<p>Explanation:<br \/>\nThe number of apples you picked = 2n &#8211; 3<br \/>\nThe number of apples your friend picked = n + 4<br \/>\nThe number of apples you and your friend picked = (2n &#8211; 3) + (n + 4)<br \/>\n= 3n + 1<br \/>\nThe number of apples you and your friend picked is 3n + 1<\/p>\n<p>Question 22.<br \/>\nGreenland has a population of x people. Barbados has a population of about 4500 more than 5 times the population of Greenland. Find and interpret the difference in the populations of these two countries.<\/p>\n<p>Answer:<br \/>\nThe difference in the populations of these two countries is 4500 + 4x.<\/p>\n<p>Explanation:<br \/>\nGreenland population = x<br \/>\nBarbados population = 4500 + 5x<br \/>\nThe difference in the populations of these two countries = 4500 + 5x &#8211; x<br \/>\n= 4500 + 4x<\/p>\n<p><strong>3.3 The Distributive Property<\/strong> (pp. 103\u2013108)<\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 23.<br \/>\n2(a &#8211; 3)<\/p>\n<p>Answer:<br \/>\n2(a &#8211; 3) = 2a &#8211; 6<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2(a &#8211; 3)<br \/>\n= 2(a) &#8211; 2(3)<br \/>\n= 2a &#8211; 6<\/p>\n<p>Question 24.<br \/>\n-3(4x &#8211; 10)<\/p>\n<p>Answer:<br \/>\n-3(4x &#8211; 10) = -12x + 30<\/p>\n<p>Explanation:<br \/>\nThe given expression is -3(4x &#8211; 10)<br \/>\n= -3(4x) + 3(10)<br \/>\n= -12x + 30<\/p>\n<p>Question 25.<br \/>\n-2.5(8 &#8211; b)<\/p>\n<p>Answer:<br \/>\n-2.5(8 &#8211; b) = -20 + 2.5b<\/p>\n<p>Explanation:<br \/>\nThe given expression is -2.5(8 &#8211; b)<br \/>\n= -2.5(8) + 2.5(b)<br \/>\n= -20 + 2.5b<\/p>\n<p>Question 26.<br \/>\n-7(1 &#8211; 3d &#8211; 5)<\/p>\n<p>Answer:<br \/>\n-7(1 &#8211; 3d &#8211; 5) = 21d + 28<\/p>\n<p>Explanation:<br \/>\nThe given expression is -7(1 &#8211; 3d &#8211; 5)<br \/>\n= -7(-3d &#8211; 4)<br \/>\n= -7(-3d) &#8211; 7(-4)<br \/>\n= 21d + 28<\/p>\n<p>Question 27.<br \/>\n9(-3w &#8211; 6.2 + 2w)<\/p>\n<p>Answer:<br \/>\n9(-3w &#8211; 6.2 + 2w) = -9w &#8211; 55.8<\/p>\n<p>Explanation:<br \/>\nThe given expression is 9(-3w &#8211; 6.2 + 2w)<br \/>\n= 9(-w &#8211; 6.2)<br \/>\n= 9(-w) &#8211; 9(6.2)<br \/>\n= -9w &#8211; 55.8<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-109.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 109\" width=\"118\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n3\/4 (8g &#8211; 1\/4 &#8211; 2\/3 g) = 11g\/2 &#8211; 3\/8<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3\/4 (8g &#8211; 1\/4 &#8211; 2\/3 g)<\/p>\n<p>= 3\/4((24g &#8211; 2g)\/3 &#8211; 1\/4)<br \/>\n= 3\/4(22g\/3 &#8211; 1\/4)<br \/>\n= 3\/4(22g\/3) &#8211; 3\/4(1\/4)<br \/>\n= 11g\/2 &#8211; 3\/8<\/p>\n<p>Question 29.<br \/>\nMars has m moons. The number of moons of Pluto is one more than twice the number of moons of Mars. The number of moons of Neptune is one less than 3 times the number of moons of Pluto. Write and interpret a simpli\ufb01ed expression that represents the number of moons of Neptune.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-109.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 109.1\" width=\"156\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe number of moons of Neptune is 6m + 2.<\/p>\n<p>Explanation:<br \/>\nNumber of moons of marks = m<br \/>\nThe number of moons of pluto = 1 + 2m<br \/>\nThe number of moons of Neptune = 3(1 + 2m) &#8211; 1<br \/>\n= 3 + 6m &#8211; 1 = 6m + 2<\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 30.<br \/>\n3( 2 + q) + 15<\/p>\n<p>Answer:<br \/>\n3( 2 + q) + 15 = 21 + 3q<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3( 2 + q) + 15<br \/>\n= 3(2) + 3(q) + 15<br \/>\n= 6 + 3q + 15<br \/>\n= 21 + 3q<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-110.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 110\" width=\"124\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n1\/8 (16m &#8211; 8) &#8211; 17 = 2m &#8211; 18<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/8 (16m &#8211; 8) &#8211; 17<br \/>\n= 1\/8(16m) + 1\/8(-8) &#8211; 17<br \/>\n= 2m &#8211; 1 &#8211; 17<br \/>\n= 2m &#8211; 18<\/p>\n<p>Question 32.<br \/>\n-1.5(4 &#8211; n) + 2.8<\/p>\n<p>Answer:<br \/>\n-1.5(4 &#8211; n) + 2.8 = -3.2 + 1.5n<\/p>\n<p>Explanation:<br \/>\nThe given expression is -1.5(4 &#8211; n) + 2.8<br \/>\n= -1.5(4)- 1.5(-n) + 2.8<br \/>\n= -6 + 1.5n + 2.8<br \/>\n= -3.2 + 1.5n<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-111.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 111\" width=\"153\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-111.png 153w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-111-150x52.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><\/p>\n<p>Answer:<br \/>\n2\/5 (d &#8211; 10) &#8211; 2\/3 (d + 6) = -4d\/15 &#8211; 8<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2\/5 (d &#8211; 10) &#8211; 2\/3 (d + 6)<br \/>\n= 2\/5(d) + 2\/5(-10) &#8211; 2\/3(d) &#8211; 2\/3(6)<br \/>\n= 2d\/5 &#8211; 4 &#8211; 2d\/3 &#8211; 4<br \/>\n= (6d &#8211; 10d)\/15 &#8211; 8<br \/>\n= -4d\/15 &#8211; 8<\/p>\n<p>Question 34.<br \/>\nThe expression for degrees Fahrenheit is <img loading=\"lazy\" class=\"alignnone size-full wp-image-29372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-112.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 112\" width=\"61\" height=\"37\" \/> where C represents degrees Celsius. The temperature today is 5 degrees Celsius more than yesterday. Write and simplify an expression for the difference in degrees Fahrenheit for these two days.<\/p>\n<p>Answer:<br \/>\nThe difference in degrees Fahrenheit for these two days 9 degrees celsius.<\/p>\n<p>Explanation:<br \/>\nThe expression for degrees Fahrenheit is 9\/5 C + 32<br \/>\nThe temperature today is 5 degrees Celsius more than yesterday.<br \/>\nToday temperature = 9\/5 (x + 5) + 32<br \/>\nYesterday Temperature = 9\/5 x + 32<br \/>\nThe difference in degrees Fahrenheit for these two days = 9\/5 (x + 5) + 32 &#8211; ( 9\/5 x + 32)<br \/>\n= 9\/5(x) + 9\/5(5) + 32 &#8211; 9\/5 x &#8211; 32<br \/>\n= 9x\/5 + 9 + 32 &#8211; 9x\/5 &#8211; 32<br \/>\n= 9<\/p>\n<p><strong>3.4 Factoring Expressions<\/strong> (pp. 109\u2013114)<\/p>\n<p><strong>Factor the expression using GCF.<\/strong><\/p>\n<p>Question 35.<br \/>\n18a &#8211; 12<\/p>\n<p>Answer:<br \/>\n18a &#8211; 12 = 6(3a &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nThe G.C.F of 18a, 12 is<br \/>\n18a = 2 . 3 . 3 . a<br \/>\n12 = 3 . 2 . 2<br \/>\nThe common prime factors are 2 . 3 = 6<br \/>\nThe G.C.F of 18a, 12 is 6<br \/>\nUse the GCF to factor the expression<br \/>\n18a &#8211; 12 = 6(3a) &#8211; 6(2)<br \/>\n= 6(3a &#8211; 2)<\/p>\n<p>Question 36.<br \/>\n2b + 8<\/p>\n<p>Answer:<br \/>\n2b + 8 = 2(b + 3)<\/p>\n<p>Explanation:<br \/>\nThe G.C.F of 2b, 8 is<br \/>\n2b = 2 . b<br \/>\n8 = 2 . 2 . 2<br \/>\nThe common prime factors are 2<br \/>\nThe G.C.F of 2b, 8 is 2<br \/>\nUse the GCF to factor the expression<br \/>\n2b + 8 = 2(b) + 2(3)<br \/>\n= 2(b + 3)<\/p>\n<p>Question 37.<br \/>\n9 &#8211; 15x<\/p>\n<p>Answer:<br \/>\n9 &#8211; 15x = 3(3 &#8211; 5x)<\/p>\n<p>Explanation:<br \/>\nThe G.C.F of 9, 15x is<br \/>\n9 = 3 . 3<br \/>\n15x = 3 . 5 . x<br \/>\nThe common prime factor is 3<br \/>\nThe G.C.F of 9, 15x is 3<br \/>\nUse the GCF to factor the expression<br \/>\n9 &#8211; 15x = 3(3) &#8211; 3(5x)<br \/>\n= 3(3 &#8211; 5x)<\/p>\n<p><strong>Factor out the coefficient of the variable term.<\/strong><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-112.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 112.1\" width=\"69\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n1\/4 y + 3\/8 = 1\/4(y + 3\/2)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 1\/4 y, 3\/8<br \/>\n1\/4y = 1\/4 . y<br \/>\n3\/8 = 1\/4 . 1\/2 . 3<br \/>\nUse the distributive property to factor out 1\/4<br \/>\n1\/4 y + 3\/8 = 1\/4(y) + 1\/4(3\/2)<br \/>\n= 1\/4(y + 3\/2)<\/p>\n<p>Question 39.<br \/>\n1.7j &#8211; 3.4<\/p>\n<p>Answer:<br \/>\n1.7j &#8211; 3.4 = 1.7(j &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 1.7j, 3.4<br \/>\n1.7j = 1.7 . j<br \/>\n3.4 = 1.7 . 2<br \/>\nUse the distributive property to factor out 1.7<br \/>\n1.7j &#8211; 3.4 = 1.7(j) &#8211; 1.7(2)<br \/>\n= 1.7(j &#8211; 2)<\/p>\n<p>Question 40.<br \/>\n-5p + 20<\/p>\n<p>Answer:<br \/>\n-5p + 20 = 5(-p + 4)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 5p, 20<br \/>\n5p = 5 . p<br \/>\n20 = 5 . 4<br \/>\nUse the distributive property to factor out 5<br \/>\n-5p + 20 = 5(-p) + 5(4)<br \/>\n= 5(-p + 4)<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-113.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 113\" width=\"185\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n3\/2 x &#8211; 9\/4y = -3\/4(-2 + 3y)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 3\/2 x , -9\/4 y<br \/>\n3\/2x = -3\/4 . -2<br \/>\n-9\/4 y = -3\/4 . 3 . y<br \/>\nUse the distributive property to factor out -3\/4<br \/>\n3\/2 x &#8211; 9\/4y = -3\/4(-2) &#8211; 3\/4(3y)<br \/>\n= -3\/4(-2 + 3y)<\/p>\n<p>Question 42.<br \/>\nYou and 4 friends are buying tickets for a concert. The cost to buy one ticket is c dollars. If you buy all the tickets together, there is a discount and the cost is (5c &#8211; 12.5) dollars. How much do you save per ticket when you buy the tickets together?<\/p>\n<p>Answer:<br \/>\nThe amount saved by buying all tickets is 12.5 dollars.<\/p>\n<p>Explanation:<br \/>\nThe cost per 1 ticket is c<br \/>\nThe cost to buy 5 tickets = 5c dollars<br \/>\nIf you buy all the tickets together, there is a discount and the cost is (5c &#8211; 12.5) dollars<br \/>\nThe amount saved by buying all tickets = 5c &#8211; (5c &#8211; 12.5) dollars<br \/>\n= 5c &#8211; 5c + 12.5<br \/>\n= 12.5 dollars<\/p>\n<p>Question 43.<br \/>\nThe rectangular pupil of an octopus is estimated to be 20 millimeters long with an area of (20x &#8211; 200) square millimeters. Write an expression that represents the perimeter (in millimeters) of the octopus pupil.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-114.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 114\" width=\"282\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter the octopus pupil is 2x milli meters.<\/p>\n<p>Explanation:<br \/>\nThe length of an octopus pupil = 20 millimeters<br \/>\nArea of an octopus = (20x &#8211; 200) sq milli meters<br \/>\nFactor 20 out of (20x &#8211; 200)<br \/>\n= 20(x) &#8211; 20(10)<br \/>\n= 20(x &#8211; 20)<br \/>\nSo, the width of the octopus pupil = x &#8211; 20 milli meters<br \/>\nThe perimeter of octopus pupil = 2(length + width)<br \/>\n= 2(20 + (x &#8211; 20))<br \/>\n= 2(20 + x &#8211; 20)<br \/>\n= 2x milli meters<br \/>\nPerimeter the octopus pupil is 2x milli meters.<\/p>\n<p>Question 44.<br \/>\nA building block has a square base that has a perimeter of (12x &#8211; 9) inches. Explain how to use the expression to \ufb01nd the length (in inches) of the wall shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-114.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 114.1\" width=\"213\" height=\"150\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the wall is 7(3x &#8211; 9\/4)\u00a0inches<\/p>\n<p>Explanation:<br \/>\nThe perimeter of the square base = (12x &#8211; 9) inches<br \/>\n4 x length of the base = (12x &#8211; 9)<br \/>\nlength of the base = (12x\/4 &#8211; 9\/4)<br \/>\n= (3x &#8211; 9\/4) inches<br \/>\nThe length of wall = 7(3x &#8211; 9\/4)<\/p>\n<h3><a id=\"Expressions_Practice_Test\"><\/a>Expressions Practice Test<\/h3>\n<p><strong>3 Practice Test<\/strong><\/p>\n<p>Question 1.<br \/>\nIdentify the terms and like terms in 4x + 9x<sup>2<\/sup> &#8211; 2x + 2.<\/p>\n<p>Answer:<br \/>\nThe terms are 4x, 9x\u00b2, -2x, 2<br \/>\nThe like terms are 4x -2x<\/p>\n<p>Explanation:<br \/>\nThe given expression is 4x + 9x\u00b2 &#8211; 2x + 2<br \/>\nThe terms are 4x, 9x\u00b2, -2x, 2<br \/>\nThe like terms are 4x -2x<\/p>\n<p>Simplify the expression.<\/p>\n<p>Question 2.<br \/>\n8x &#8211; 5 + 2x<\/p>\n<p>Answer:<br \/>\n8x &#8211; 5 + 2x = 10x &#8211; 5<\/p>\n<p>Explanation:<br \/>\nThe given expression is 8x &#8211; 5 + 2x<br \/>\n= 10x &#8211; 5<\/p>\n<p>Question 3.<br \/>\n2.5w &#8211; 3y + 4w<\/p>\n<p>Answer:<br \/>\n2.5w &#8211; 3y + 4w = 6.5w &#8211; 3y<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2.5w &#8211; 3y + 4w<br \/>\n= 6.5w &#8211; 3y<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-115.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 115\" width=\"141\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\n5\/7 x + 15 &#8211; 9\/14 x &#8211; 9 = x\/14 + 6<\/p>\n<p>Explanation:<br \/>\nThe given expression is 5\/7 x + 15 &#8211; 9\/14 x &#8211; 9<br \/>\n= (10x &#8211; 9x)\/14 + 15 &#8211; 9<br \/>\n= x\/14 + 6<\/p>\n<p>Question 5.<br \/>\n(3j + 11) + (8j &#8211; 7)<\/p>\n<p>Answer:<br \/>\n(3j + 11) + (8j &#8211; 7) = 11j + 4<\/p>\n<p>Explanation:<br \/>\nThe given expression is (3j + 11) + (8j &#8211; 7)<br \/>\n= 3j + 11 + 8j &#8211; 7<br \/>\n= 11j + 4<\/p>\n<p>Question 6.<br \/>\n(2r &#8211; 13) &#8211; (-6r + 4)<\/p>\n<p>Answer:<br \/>\n(2r &#8211; 13) &#8211; (-6r + 4) = 8r &#8211; 17<\/p>\n<p>Explanation:<br \/>\nThe given expression is (2r &#8211; 13) &#8211; (-6r + 4)<br \/>\n= 2r &#8211; 13 + 6r &#8211; 4<br \/>\n= 8r &#8211; 17<\/p>\n<p>Question 7.<br \/>\n-2(4 &#8211; 3n)<\/p>\n<p>Answer:<br \/>\n-2(4 &#8211; 3n) = -8 + 6n<\/p>\n<p>Explanation:<br \/>\nThe given expression is -2(4 &#8211; 3n)<br \/>\n= -2(4) &#8211; 2(-3n)<br \/>\n= -8 + 6n<\/p>\n<p>Question 8.<br \/>\n3(5 &#8211; 2n) + 9n<\/p>\n<p>Answer:<br \/>\n3(5 &#8211; 2n) + 9n = 15 + 3n<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3(5 &#8211; 2n) + 9n<br \/>\n= 3(5) &#8211; 3(2n) + 9n<br \/>\n= 15 &#8211; 6n + 9n<br \/>\n= 15 + 3n<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-116.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 116\" width=\"103\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\n1\/3 (6x + 9) &#8211; 2 = 2x + 1<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/3 (6x + 9) &#8211; 2<br \/>\n= 1\/3 (6x) + 1\/3(9) &#8211; 2<br \/>\n= 2x + 3 &#8211; 2<br \/>\n= 2x + 1<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-117.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 117\" width=\"180\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n3\/4 (8p + 12) + 3\/8 (16p &#8211; 8) = 12p + 6<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3\/4 (8p + 12) + 3\/8 (16p &#8211; 8)<br \/>\n= 3\/4(8p) + 3\/4(12) + 3\/8(16p) + 3\/8(-8)<br \/>\n= 3(2p) + 3(3) + 3(2p) + 3(-1)<br \/>\n= 6p + 9 + 6p &#8211; 3<br \/>\n= 12p + 6<\/p>\n<p>Question 11.<br \/>\n-2.5(2s &#8211; 5) &#8211; 3(4.5s &#8211; 5.2)<\/p>\n<p>Answer:<br \/>\n-2.5(2s &#8211; 5) &#8211; 3(4.5s &#8211; 5.2) = -18.5s + 28.1<\/p>\n<p>Explanation:<br \/>\nThe given expression is -2.5(2s &#8211; 5) &#8211; 3(4.5s &#8211; 5.2)<br \/>\n= -2.5(2s) &#8211; 2.5(-5) &#8211; 3(4.5s) &#8211; 3(-5.2)<br \/>\n= -5s + 12.5 &#8211; 13.5s + 15.6<br \/>\n= -18.5s + 28.1<\/p>\n<p><strong>Factor out the coefficient of the variable term.<\/strong><\/p>\n<p>Question 12.<br \/>\n6n &#8211; 24<\/p>\n<p>Answer:<br \/>\n6n &#8211; 24 = 6(n &#8211; 4)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 6n, 24<br \/>\n6n = 6 . n<br \/>\n24 = 6 . 4<br \/>\nUse the distributive property to factor out 6<br \/>\n6n &#8211; 24 = 6(n) &#8211; 6(4)<br \/>\n= 6(n &#8211; 4)<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-118.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 118\" width=\"68\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n1\/2 q + 5\/2 = 1\/2(q + 5)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 1\/2 q, 5\/2<br \/>\n1\/2q = 1\/2 . q<br \/>\n5\/2 = 5 . 1\/2<br \/>\nUse the distributive property to factor out 1\/2<br \/>\n1\/2 q + 5\/2 = 1\/2(q) + 1\/2(5)<br \/>\n= 1\/2(q + 5)<\/p>\n<p>Question 14.<br \/>\n-4x + 36<\/p>\n<p>Answer:<br \/>\n-4x + 36 = 4(-x + 9)<\/p>\n<p>Explanation:<br \/>\nFind the factors of 4x, 36<br \/>\n4x = 4 . x<br \/>\n36 = 4 . 9<br \/>\nUse the distributive property to factor out 4<br \/>\n-4x + 36 = 4(-x) + 4(9)<br \/>\n= 4(-x + 9)<\/p>\n<p>Question 15.<br \/>\nFind the earnings for giving a haircut and a shampoo to m men and w women. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-119.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 119\" width=\"258\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe earnings for giving a haircut and a shampoo to women is 45w + 12w<br \/>\nThe earnings for giving a haircut and a shampoo to men is 15m + 7m<\/p>\n<p>Explanation:<br \/>\nThe earning for giving haircut to women is 45w<br \/>\nThe earning for giving shampoo to women is 12w<br \/>\nThe earning for giving haircut to men is 15m<br \/>\nThe earning for giving shampoo to men is 7m<br \/>\nThe earnings for giving a haircut and a shampoo to women is 45w + 12w<br \/>\nThe earnings for giving a haircut and a shampoo to men is 15m + 7m<\/p>\n<p>Question 16.<br \/>\nThe expression 15x + 11 represents the perimeter of the trapezoid. What is the length of the fourth side? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-120.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 120\" width=\"234\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the fourth side of trapezoid is 6x + 5.<\/p>\n<p>Explanation:<br \/>\nPerimeter of the trapezoid = 15x + 11<br \/>\n2x + 3 + 3x + 4 + 4x &#8211; 1 + fourth side length = 15x + 11<br \/>\n9x + 7 &#8211; 1 + fourth side length = 15x + 11<br \/>\n9x + 6 + fourth side length = 15x + 11<br \/>\nfourth side length = (15x + 11) &#8211; (9x + 6)<br \/>\n= 15x + 11 &#8211; 9x &#8211; 6<br \/>\n= 6x + 5<\/p>\n<p>Question 17.<br \/>\nThe maximum number of charms that will \ufb01t on a bracelet is <img loading=\"lazy\" class=\"alignnone size-full wp-image-29383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-121.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 121\" width=\"77\" height=\"52\" \/>, where d is the diameter(in centimeters) of the bracelet.<br \/>\na. Write and interpret a simpli\ufb01ed expression that represents the maximum number of charms on a bracelet.<br \/>\nb. What is the maximum number of charms that \ufb01t on a bracelet that has a diameter of 6 centimeters?<\/p>\n<p>Answer:<br \/>\na. The maximum number of charms that will \ufb01t on a bracelet = 3d &#8211; 2<br \/>\nb. The maximum number of charms that \ufb01t on a bracelet that has a diameter of 6 centimeters is 16.<\/p>\n<p>Explanation:<br \/>\na. The maximum number of charms that will \ufb01t on a bracelet = 3(d &#8211; 2\/3)<br \/>\n= 3(d) &#8211; 3(2\/3)<br \/>\n= 3d &#8211; 2<br \/>\nb. The maximum number of charms that \ufb01t on a bracelet that has a diameter of 6 centimeters is 3(6) &#8211; 2<br \/>\n= 18 &#8211; 2 = 16<\/p>\n<p>Question 18.<br \/>\nYou expand a rectangular garden so the perimeter is now twice the perimeter of the old garden. The expression 12w + 16 represents the perimeter of the new garden, where w represents the width of the old garden.<br \/>\na. Write an expression that represents the perimeter of the old garden. Justify your answer.<br \/>\nb. Write an expression that represents the area of the old garden.<\/p>\n<p>Answer:<br \/>\na. Perimeter of old rectangular garden is 6w + 8<br \/>\nb. The area of the old garden is 12w.<\/p>\n<p>Explanation:<br \/>\na. New garden perimeter = 2 * perimeter of old garden<br \/>\n(12w + 16) = 2 * perimeter of old garden<br \/>\n(12w\/2 + 16\/2) = Perimeter of old garden<br \/>\n6w + 8 = Perimeter of old garden<br \/>\nb. Perimeter of old rectangular garden is 6w + 8<br \/>\nFind the factors of 6w, 8<br \/>\n6w = 2 . 3 . w<br \/>\n8 = 2 . 2 . 2<br \/>\nUse the distributive property to factor out 2<br \/>\n6w + 8 = 2(3w) + 2(4)<br \/>\n= 2(3w + 4)<br \/>\nPerimeter of old garden = 2(length + width) = 2(3w + 4)<br \/>\nSo, length of the garden is 3w, width of the garden is 4<br \/>\nThe area of old garden = length . width<br \/>\n= 3w . 4 = 12w<\/p>\n<h3><a id=\"Expressions_Cumulative_Practice\"><\/a>Expressions Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhat is the simpli\ufb01ed form of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-121.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 121.1\" width=\"127\" height=\"44\" \/><br \/>\nA. -3.6x<br \/>\nB. 6x &#8211; 5<br \/>\nC. 1.4x &#8211; 5<br \/>\nD. 3.7x &#8211; 7.3<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-29384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-122.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 122\" width=\"347\" height=\"417\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-122.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-122-250x300.png 250w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Answer:<br \/>\nC. 1.4x &#8211; 5<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3.7x &#8211; 5 &#8211; 2.3x<br \/>\n= 1.4x &#8211; 5<\/p>\n<p>Question 2.<br \/>\nWhat is the value of the expression when c = 0 and d = -6?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-123.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 123\" width=\"79\" height=\"69\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-124.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 124\" width=\"73\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n-9.<\/p>\n<p>Explanation:<br \/>\nThe give expression is (cd &#8211; d\u00b2)\/4<br \/>\nPut c = 0, d= -6 in above expression<br \/>\n= (0 . -6 &#8211; (-6)\u00b2)\/4<br \/>\n= -(36)\/4<br \/>\n= -9<\/p>\n<p>Question 3.<br \/>\nWhat is the value of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-125.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 125\" width=\"111\" height=\"40\" \/><br \/>\nF. -52<br \/>\nG. -24<br \/>\nH. 24<br \/>\nI. 52<\/p>\n<p>Answer:<br \/>\nG. -24<\/p>\n<p>Explanation:<br \/>\nThe given expression is -38 &#8211; (-14)<br \/>\n= -38 + 14 = -24<\/p>\n<p>Question 4.<br \/>\nThe daily low temperatures for a week are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-126.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 126\" width=\"585\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-126.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-126-300x84.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\nWhat is the mean low temperature of the week?<br \/>\nA. \u22122\u00b0F<br \/>\nB. 6\u00b0F<br \/>\nC. 8\u00b0F<br \/>\nD. 10\u00b0F<\/p>\n<p>Answer:<br \/>\nThe mean low temperature of the week is 6\u00b0F.<\/p>\n<p>Explanation:<br \/>\nThe list of low temperatures are -2\u00b0F, -3\u00b0F, -1\u00b0F, 8\u00b0F, 10\u00b0F, 12\u00b0F, 18\u00b0F<br \/>\nThe mean temperature of the week = sum of the observations\/ number of observations<br \/>\n= (-2 &#8211; 3 &#8211; 1 + 8 + 10 + 12 + 18)\/7<br \/>\n= (-6 + 48)\/7<br \/>\n= 42\/7<br \/>\n= 6\u00b0F<br \/>\nThe mean low temperature of the week is 6\u00b0F.<\/p>\n<p>Question 5.<br \/>\nYou and a friend collect seashells on a beach. After h minutes, you have collected (11 + 2h) seashells and your friend has collected (5h &#8211; 2) seashells. How many total seashells have you and your friend collected?<br \/>\nF. 7h + 9<br \/>\nG. 3h &#8211; 13<br \/>\nH. 16h<br \/>\nI. 7h + 13<\/p>\n<p>Answer:<br \/>\nF. 7h + 9<\/p>\n<p>Explanation:<br \/>\nThe number of seashells collected by you = (11 + 2h)<br \/>\nThe number of seashells collected by your friend = (5h &#8211; 2)<br \/>\nThe total seashells have you and your friend collected = The number of seashells collected by you + The number of seashells collected by your friend<br \/>\n= 11 + 2h + 5h &#8211; 2<br \/>\n= 9 + 7h<\/p>\n<p>Question 6.<br \/>\nWhat is the value of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-127.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 127\" width=\"269\" height=\"68\" \/><\/p>\n<p>Answer:<br \/>\n-0.28 \u00f7 (-0.07) = 4<\/p>\n<p>Explanation:<br \/>\nThe value of the expression is -0.28 \u00f7 (-0.07)<br \/>\n= 0.28 \u00f7 0.07 = 4<\/p>\n<p>Question 7.<br \/>\nWhich list is ordered from least to greatest?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-128.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 128\" width=\"554\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-128.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-128-300x75.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Answer:<br \/>\nD.<\/p>\n<p>Explanation:<br \/>\nA. -3\/4, -1\/2, 3\/8, -1\/4, 7\/8 is not in the order<br \/>\nB. -1\/2, -1\/4, 3\/8, -3\/4, 7\/8 is not in the order<br \/>\nC. 7\/8, 3\/8, -1\/4, -1\/2, -3\/4 is not in the order<br \/>\nD. -3\/4, -1\/2, -1\/4, 3\/8, 7\/8 is in the order from least to greatest.<\/p>\n<p>Question 8.<br \/>\nWhich number is equivalent to the expression shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-129.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 129\" width=\"426\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-129.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-129-300x132.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p>Answer:<br \/>\nH. 6(1\/8)<\/p>\n<p>Explanation:<br \/>\n-2(1\/4) &#8211; (-8(3\/8)) = -9\/4 + 67\/8<br \/>\n= (-18 + 67)\/8 = 49\/8<br \/>\n= 6(1\/8)<\/p>\n<p>Question 9.<br \/>\nWhat is the simpli\ufb01ed form of the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-130.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 130\" width=\"130\" height=\"42\" \/><br \/>\nA. 15x + 30<br \/>\nB. x &#8211; 12<br \/>\nC. 13x + 12<br \/>\nD. -11x<\/p>\n<p>Answer:<br \/>\nB. x &#8211; 12<\/p>\n<p>Explanation:<br \/>\nThe given expression is 7x &#8211; 2(3x + 6)<br \/>\n= 7x &#8211; 2(3x) &#8211; 2(6)<br \/>\n= 7x &#8211; 6x &#8211; 12<br \/>\n= x &#8211; 12<\/p>\n<p>Question 10.<br \/>\nWhich expression is not equivalent to the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-131.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 131\" width=\"97\" height=\"38\" \/><br \/>\nF. 6(12m &#8211; 10)<br \/>\nG. 4(18m &#8211; 15)<br \/>\nH. 12m<br \/>\nI. 12(6m &#8211; 5)<\/p>\n<p>Answer:<br \/>\nI. 12(6m &#8211; 5)<\/p>\n<p>Explanation:<br \/>\nThe given expression is 72m &#8211; 60<br \/>\nFind the factors of 72m, 60<br \/>\n72m = 2 . 2 . 3 . 3 . 2 . m<br \/>\n60 = 2 . 2 . 3 . 5<br \/>\nThe G.C.F of 72m, 60 is 2 . 2 . 3 = 12<br \/>\n72m &#8211; 60 = 12(6m) &#8211; 12(5)<br \/>\n= 12(6m &#8211; 5)<\/p>\n<p>Question 11.<br \/>\nYou want to buy a bicycle with your friend. You have $43.50 saved and plan to save an additional $7.25 every week. Your friend has $24.50 saved and plans to save an additional $8.75 every week.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-132.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 132\" width=\"85\" height=\"90\" \/><br \/>\n<strong>Part A<\/strong><br \/>\nSimplify and interpret an expression that represents the amount of money you and your friend save after weeks.<br \/>\n<strong>Part B<\/strong><br \/>\nAfter 10 weeks, you and your friend use all of the money and buy the bike. How much does the bike cost? Who pays more towards the cost of the bike? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nA. The total amount of money you and your friend saved after x weeks is 68 + 16x<br \/>\nB. The cost of the bike is 228 dollars<br \/>\nYou will pay more money towards the bike.<\/p>\n<p>Explanation:<br \/>\nA. Let the number of weeks we need to save be x<br \/>\nThe amount you saved 43.50 + 7.25x<br \/>\nThe amount your friend saved = 24.50 + 8.75x<br \/>\nThe total amount of money you and your friend saved after x weeks is 43.50 + 7.25x + 24.50 + 8.75x<br \/>\n= 68 + 16x<br \/>\nB. The amount saved after 10 weeks is<br \/>\nThe amount you saved = 43.50 + 7.25(10) = 43.50 + 72.5 = 116<br \/>\nThe amount your friend saved = 24.50 + 8.75(10) = 24.50 + 87.5 = 112<br \/>\nThe cost of bike = The amount you saved + The amount your friend saved<br \/>\n= 116 + 112 = 228 dollars<br \/>\nYou will pay more money towards the bike.<\/p>\n<p>Question 12.<br \/>\nYour friend evaluated 3 + x<sup>2<\/sup> \u00f7 y when x = 2 and y = 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-3-Expressions-133.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 3 Expressions 133\" width=\"273\" height=\"162\" \/><br \/>\nWhat should your friend do to correct his error?<br \/>\nA. Divide 3 by 4 before subtracting.<br \/>\nB. Square -2, then divide.<br \/>\nC. Divide -2 by 4, then square.<br \/>\nD. Subtract 4 from 3 before dividing.<\/p>\n<p>Answer:<br \/>\nB. Square -2, then divide.<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3 + x<sup>2<\/sup> \u00f7 y<br \/>\nPut x = 2 and y = 4<br \/>\n= 3 + 2\u00b2 \u00f7 4<br \/>\n= 3 + 4 \u00f7\u00a0 4<br \/>\n= 3 + 1<br \/>\n= 4<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>To help all the candidates, we have provided Chapter 3 Expressions in this article. Just click on the respective direct link and download the pdf and start your preparation and learn all the fundamentals which are included in it. Bookmark our website of Big Ideas Math Answers and get the solutions to Grade 7 chapters. If you bookmark our page, you will get instant updates of all 7th Grade chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math 7th Grade Chapter 3 Expressions Answer Key: Download free step-by-step problem and solution pdf of Big Ideas Math Grade 7 Chapter 3 Expressions from here. 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