{"id":6586,"date":"2022-03-25T19:14:56","date_gmt":"2022-03-25T13:44:56","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6586"},"modified":"2022-04-07T12:47:41","modified_gmt":"2022-04-07T07:17:41","slug":"go-math-grade-8-answer-key-chapter-7-solving-linear-equations","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-7-solving-linear-equations\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations"},"content":{"rendered":"<p>Are you searching for Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations? If your answer is yes, then you are on the right page. Students of 8th standard can get the Download link of HMH Go Math Grade 8 Solution Key Chapter 7 Solving Linear Equations for free. Get the best maths tactics and ways of solving the problems for all the questions with the help of the Go Math Grade 8 Chapter 7 Solving Linear Equations Answer Key. You can practice all the questions to have a perfect grip on the Grade 8 maths subject. <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> is the best resource to improve math skills.<\/p>\n<h2>Go Math Grade 8 Chapter 7 Solving Linear Equations Answer Key<\/h2>\n<p>Improve your performance in exams with the help of Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations. You can find the review questions at the end of the chapter to test your knowledge. The topics covered in this Solving Linear Equations chapter are equations with the variable on both sides, equations with rational numbers, equations with the distributive property, equations with many solutions or no solution, etc. Just go through the online pdf and start practicing now. By looking into the questions and answers available on Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations.<\/p>\n<p><strong>Lesson 1: Equations with the Variable on Both Sides<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Equations_with_the_Variable_on_Both_Sides_\u2013_Page_No._200\">\u00b7 Equations with the Variable on Both Sides \u2013 Page No. 200<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_the_Variable_on_Both_Sides_\u2013_Page_No._201\">\u00b7 Equations with the Variable on Both Sides \u2013 Page No. 201<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_the_Variable_on_Both_Sides_Lesson_Check_\u2013_Page_No._202\">\u00b7 Equations with the Variable on Both Sides Lesson Check \u2013 Page No. 202<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Equations with Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Equations_with_Rational_Numbers_\u2013_Page_No._206\">\u00b7 Equations with Rational Numbers \u2013 Page No. 206<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_Rational_Numbers_\u2013_Page_No._207\">\u00b7 Equations with Rational Numbers \u2013 Page No. 207<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_Rational_Numbers_Lesson_Check_\u2013_Page_No._208\">\u00b7 Equations with Rational Numbers Lesson Check \u2013 Page No. 208<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Equations with the Distributive Property<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Equations_with_the_Distributive_Property_\u2013_Page_No._212\">\u00b7 Equations with the Distributive Property \u2013 Page No. 212<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_the_Distributive_Property_\u2013_Page_No._213\">\u00b7 Equations with the Distributive Property \u2013 Page No. 213<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_the_Distributive_Property_Lesson_Check_\u2013_Page_No._214\">\u00b7 Equations with the Distributive Property Lesson Check \u2013 Page No. 214<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Equations with Many Solutions or No Solution<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Equations_with_Many_Solutions_or_No_Solution_\u2013_Page_No._218\">\u00b7 Equations with Many Solutions or No Solution \u2013 Page No. 218<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_Many_Solutions_or_No_Solution_\u2013_Page_No._219\">\u00b7 Equations with Many Solutions or No Solution \u2013 Page No. 219<\/a><\/li>\n<li><a href=\"#\u00b7_Equations_with_Many_Solutions_or_No_Solution_Lesson_Check_\u2013_Page_No._220\">\u00b7 Equations with Many Solutions or No Solution Lesson Check \u2013 Page No. 220<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5: Equations with the Variable on Both Sides<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Equations_with_the_Variable_on_Both_Sides_\u2013_Model_Quiz_\u2013_Page_No._221\">\u00b7 Equations with the Variable on Both Sides \u2013 Model Quiz \u2013 Page No. 221<\/a><\/li>\n<\/ul>\n<p><strong>Reviews<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Mixed_Review_\u2013_Page_No._222\">Mixed Review \u2013 Page No. 222<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><a id=\"\u00b7_Equations_with_the_Variable_on_Both_Sides_\u2013_Page_No._200\"><\/a>Guided Practice &#8211; Equations with the Variable on Both Sides &#8211; Page No. 200<\/h3>\n<p><strong>Use algebra tiles to model and solve each equation.<\/strong><\/p>\n<p>Question 1.<br \/>\nx + 4 = -x &#8211; 4<br \/>\nx = ________<\/p>\n<p>Answer:<br \/>\nx = -4<\/p>\n<p>Explanation:<br \/>\nModel x + 4 on the left side of the mat and -x -4 on the right side.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-1-300x109.png\" alt=\"grade 8 chapter 7 image 1\" width=\"300\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-1-300x109.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-1.png 563w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAdd one c-tile to both sides. This represents adding x to both sides of the equation. Remove zero pairs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-2-300x134.png\" alt=\"grade 8 chapter 7 image 2\" width=\"300\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-2-300x134.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-2.png 563w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nPlace four -1-tiles on both sides. This represents subtracting -4 from both sides of the equation. Remove zero pairs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-3-300x144.png\" alt=\"grade 8 chapter 7 image 3\" width=\"300\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-3-300x144.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-3.png 563w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSeparate each side into 2 equal groups. One x-tile is equivalent to four -1-tiles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-4-300x125.png\" alt=\"grade 8 chapter 7 image 4\" width=\"300\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-4-300x125.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-4.png 563w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nx = -4<\/p>\n<p>Question 2.<br \/>\n2 &#8211; 3x = -x &#8211; 8<br \/>\nx = ________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nGiven 2 &#8211; 3x = -x &#8211; 8<br \/>\nModel 2-3x on the left side of the mat and -x-8 on the right side.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-5-300x181.png\" alt=\"grade 8 chapter 7 image 5\" width=\"300\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-5-300x181.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-5.png 618w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nPlace one x tile to both sides. This represents subtracting from both sides of the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-6-300x181.png\" alt=\"grade 8 chapter 7 image 6\" width=\"300\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-6-300x181.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-6.png 617w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRemove 2 1 tiles from sides. This represents subtracting from both sides of the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-7-300x185.png\" alt=\"grade 8 chapter 7 image 7\" width=\"300\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-7-300x185.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-7.png 613w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSeparate each side into 2 equal groups. One -x tile is equivalent to 5 &#8211; 1 tile.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-8-300x181.png\" alt=\"grade 8 chapter 7 image 8\" width=\"300\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-8-300x181.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-8.png 617w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe solution is -x = -5 or x = 5<\/p>\n<p>Question 3.<br \/>\nAt Silver Gym, membership is $25 per month, and personal training sessions are $30 each. At Fit Factor, membership is $65 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?<br \/>\n________ sessions<\/p>\n<p>Answer:<br \/>\n4 sessions<\/p>\n<p>Explanation:<br \/>\nAt Silver Gym, membership is $25 per month, and personal training sessions are $30 each.<br \/>\nMembership + Personal training session = 25 + 30x<br \/>\nAt Fit Factor, membership is $65 per month, and personal training sessions are $20 each.<br \/>\nMembership + Personal training session = 65 + 20x<br \/>\nMembership at Silver Gym = Membership at Fit Factor<br \/>\n25 + 30x = 65 + 20x<br \/>\n30x &#8211; 20x = 65 &#8211; 25<br \/>\n10x = 40<br \/>\nx = 4<br \/>\nSarah would have to buy 4 sessions for the total cost at the two gyms to be equal.<\/p>\n<p>Question 4.<br \/>\nWrite a real-world situation that could be modeled by the equation 120 + 25x = 45x.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n120 + 25x = 45x<br \/>\nSarah offers a plan to tutor a student at $25 per her plus a one-time registration fee of $ 120.<br \/>\nSurah offers an alternative plan to tutor a student at $45 per hour and no registration fee.<br \/>\n120 + 25x = 45x<\/p>\n<p>Question 5.<br \/>\nWrite a real-world situation that could be modeled by the equation 100 &#8211; 6x = 160 &#8211; 10x.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n100 &#8211; 6x = 160 &#8211; 10x<br \/>\nThe initial water in Tank A is 100 gallons and leaks at 6 gallons per week.<br \/>\nThe initial water in Tank B is 160 gallon and leaks at 10 gallons per week<br \/>\n100 &#8211; 6x = 160 &#8211; 10x<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nHow can you solve an equation with the variable on both sides?<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nIsolate the variable on one side. Add\/subtract the variable with a lower coefficient from both sides. Add\/subtract the constant (with the variable) from both sides. Divide both sides by coefficient of isolated variable.<\/p>\n<h3><a id=\"\u00b7_Equations_with_the_Variable_on_Both_Sides_\u2013_Page_No._201\"><\/a>Independent Practice &#8211; Equations with the Variable on Both Sides &#8211; Page No. 201<\/h3>\n<p>Question 7.<br \/>\nDerrick&#8217;s Dog Sitting and Darlene&#8217;s Dog Sitting are competing for new business. The companies ran the ads shown.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 1: Equations with the Variable on Both Sides img 1\" width=\"174\" height=\"355\" \/><br \/>\na. Write and solve an equation to find the number of hours for which the total cost will be the same for the two services.<br \/>\n________ hours<\/p>\n<p>Answer:<br \/>\n3 hours<\/p>\n<p>Explanation:<br \/>\nHourly rate + One time fee = 5x + 12<br \/>\nHourly rate + One time fee = 3x + 18<br \/>\n5x + 12 = 3x + 18<br \/>\n5x &#8211; 3x = 18 &#8211; 12<br \/>\n2x = 6<br \/>\nx = 3<br \/>\nthe cost of the two dog sitting would be same for 3 hrs.<\/p>\n<p>Question 7.<br \/>\nb. Analyze Relationships<br \/>\nWhich dog sitting service is more economical to use if you need 5 hours of service? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nDarlene&#8217;s Dog Sitting would be cheaper<\/p>\n<p>Explanation:<br \/>\nLet y be the cost of dog sitting after x hours for both companies<br \/>\ny = 5x +12<br \/>\ny = 3x +18<br \/>\nSubstitute x = 5<br \/>\ny = 5(5) + 12 = 37<br \/>\ny = 3 (5) + 18 = 33<br \/>\ncompare the cost for both companies for x = 5hr.<br \/>\n$37 &gt; $33<br \/>\nDarlene&#8217;s Dog Sitting would be cheaper<\/p>\n<p>Question 8.<br \/>\nCountry Carpets charges $22 per square yard for carpeting, and an additional installation fee of $100. City Carpets charges $25 per square yard for the same carpeting, and an additional installation fee of $70.<br \/>\na. Write and solve an equation to find the number of square yards of carpeting for which the total cost charged by the two companies will be the same.<br \/>\n_______ square yards<\/p>\n<p>Answer:<br \/>\n10 square yards<\/p>\n<p>Explanation:<br \/>\nUnit square rate + One time installation fee = 22x + 100<br \/>\nUnit square rate + One time installation fee = 25x + 70<br \/>\n22x + 100 = 25x + 70<br \/>\n25x &#8211; 22x = 100 &#8211; 70<br \/>\n3x = 30<br \/>\nx = 10<br \/>\nthe total cost charged by the two companies will be the same for 10 square yards of carpeting.<\/p>\n<p>Question 8.<br \/>\nb. Justify Reasoning<br \/>\nMr. Shu wants to hire one of the two carpet companies to install carpeting in his basement. Is he more likely to hire Country Carpets or City Carpets? Explain your reasoning.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nCity Carpets are cheaper when x &lt; 10<br \/>\ny = 25(9) + 70 = 295<br \/>\ny = 22(9) + 100 = 298<br \/>\nCountry Carpets are cheaper when x &gt; 10<br \/>\ny = 25(11) + 70 = 345<br \/>\ny = 25(11) + 100 = 342<br \/>\nIf Mr.Shu needs the carpenting done for less than 10square yards, he will hire City Carpets and if he needs carpenting for more than 10 square yard, he will hire Country Carpets.<\/p>\n<p><strong>Write an equation to represent each relationship. Then solve the equation.<\/strong><\/p>\n<p>Question 9.<br \/>\nTwo less than 3 times a number is the same as the number plus 10.<br \/>\n________<\/p>\n<p>Answer:<br \/>\n3x &#8211; 2 = x + 10<br \/>\nx = 6<\/p>\n<p>Explanation:<br \/>\nTwo less than 3 times a number is the same as the number plus 10.<br \/>\nTwo less than 3 times x is the same as the x plus 10.<br \/>\nTwo less than 3x is the same as the x + 10<br \/>\n3x &#8211; 2 is the same as x + 10<br \/>\n3x &#8211; 2 = x + 10<br \/>\n3x &#8211; x = 10 + 2<br \/>\n2x = 12<br \/>\nx = 6<\/p>\n<p>Question 10.<br \/>\nA number increased by 4 is the same as 19 minus 2 times the number.<br \/>\n______<\/p>\n<p>Answer:<br \/>\nx + 4 = 19 &#8211; 2x<br \/>\nx = 5<\/p>\n<p>Explanation:<br \/>\nA number increased by 4 is the same as 19 minus 2 times the number.<br \/>\nx increased by 4 is the same as 19 minus 2x.<br \/>\nx + 4 is the same as 19 &#8211; 2x<br \/>\nx + 4 = 19 &#8211; 2x<br \/>\nx + 2x = 19 &#8211; 4<br \/>\n3x = 15<br \/>\nx = 15\/3<br \/>\nx = 5<\/p>\n<p>Question 11.<br \/>\nTwenty less than 8 times a number is the same as 15 more than the number.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n8x &#8211; 20 = x + 15<br \/>\nx = 5<\/p>\n<p>Explanation:<br \/>\nTwenty less than 8 times a number is the same as 15 more than the number.<br \/>\nTwenty less than 8 times x is the same as 15 more than the x.<br \/>\nTwenty less than 8x is the same as 15 more than the x<br \/>\n8x &#8211; 20 is the same as x + 15<br \/>\n8x &#8211; 20 = x + 15<br \/>\n8x &#8211; x = 15 + 20<br \/>\n7x = 35<br \/>\nx = 35\/7 = 5<br \/>\nx = 5<\/p>\n<h3><a id=\"\u00b7_Equations_with_the_Variable_on_Both_Sides_Lesson_Check_\u2013_Page_No._202\"><\/a>Equations with the Variable on Both Sides &#8211; Page No. 202<\/h3>\n<p>Question 12.<br \/>\nThe charges for an international call made using the calling card for two phone companies are shown in the table.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 1: Equations with the Variable on Both Sides img 2\" width=\"314\" height=\"100\" \/><br \/>\na. What is the length of a phone call that would cost the same no matter which company is used?<br \/>\n_______ minutes<\/p>\n<p>Answer:<br \/>\n10 minutes<\/p>\n<p>Explanation:<br \/>\nCost of minutes + One time fee = 3x + 35<br \/>\nCost of minutes + One time fee = 2x + 45<br \/>\n3x + 35 = 2x + 45<br \/>\n3x &#8211; 2x = 45 &#8211; 35<br \/>\nx = 10<br \/>\nThe cost would be same for 10 minutes.<\/p>\n<p>Question 12.<br \/>\nb. Analyze Relationships<br \/>\nWhen is it better to use the card from Company B?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 3x + 35<br \/>\ny = 3(11) + 35 = $68<br \/>\ny = 2x + 45<br \/>\ny = 2(11) + 45 = $67<br \/>\nSince when x &gt; 10, Company B is cheaper so it should be better to use when the length of the call is greater than 10 minutes.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 13.<br \/>\nDraw Conclusions<br \/>\nLiam is setting up folding chairs for a meeting. If he arranges the chairs in 9 rows of the same length, he has 3 chairs left over. If he arranges the chairs in 7 rows of that same length, he has 19 left over. How many chairs does Liam have?<br \/>\n______ chairs<\/p>\n<p>Answer:<br \/>\n75 chairs<\/p>\n<p>Explanation:<br \/>\nNumber of chairs in 9 row + left over chairs = 9x + 3<br \/>\nNumber of chairs in 7 row + left over chairs = 7x + 19<br \/>\n9x + 3 = 7x + 19<br \/>\n9x &#8211; 7x = 19 &#8211; 3<br \/>\n2x = 16<br \/>\nx = 16\/2<br \/>\nx = 8<br \/>\nTotal number of chairs = 9(8) + 3 = 75<\/p>\n<p>Question 14.<br \/>\nExplain the Error<br \/>\nRent-A-Tent rents party tents for a flat fee of $365 plus $125 a day. Capital Rentals rents party tents for a flat fee of $250 plus $175 a day. Delia wrote the following equation to find the number of days for which the total cost charged by the two companies would be the same:<br \/>\n365x + 125 = 250x + 175<br \/>\nFind and explain the error in Delia&#8217;s work. Then write the correct equation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nDelia&#8217;s equation<br \/>\n365x + 125 = 250x + 175<br \/>\nThe error is that she attached the variable with the flat fee (which is constant) and put the daily rent as a constant (which is variable).<br \/>\nCorrect equation<br \/>\n125x + 365 = 175x + 250<\/p>\n<p>Question 15.<br \/>\nPersevere in Problem Solving<br \/>\nLilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 3 laps on a running trail and then runs 6 more miles.On Tuesday and Sunday, she runs 5 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How many laps does Lilliana run on Saturday?<br \/>\n________ laps<\/p>\n<p>Answer:<br \/>\n2 laps<\/p>\n<p>Explanation:<br \/>\nMiles covered by lap + Addition number of miles = 3x + 6<br \/>\nMiles covered by lap + Addition number of miles = 5x + 2<br \/>\n3x + 6 = 5x + 2<br \/>\n5x &#8211; 3x = 6 &#8211; 2<br \/>\n2x = 4<br \/>\nx = 4\/2<br \/>\nx = 2<\/p>\n<h3><a id=\"\u00b7_Equations_with_Rational_Numbers_\u2013_Page_No._206\"><\/a>Guided Practice &#8211; Equations with Rational Numbers &#8211; Page No. 206<\/h3>\n<p>Question 1.<br \/>\nSandy is upgrading her Internet service. Fast Internet charges $60 for installation and $50.45 per month. Quick Internet has free installation but charges $57.95 per month.<br \/>\na. Write an equation that can be used to find the number of months at which the Internet service would cost the same.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n50.45x + 60 = 57.95x<\/p>\n<p>Explanation:<br \/>\nWrite an equation for Fast Internet, where x is the number of months.<br \/>\nCharge per Month \u00d7 Number of Month + Installation Fee<br \/>\n50.45x + 60<br \/>\nWrite an equation for Quick Internet, where x is the number of months.<br \/>\nCharge per Month \u00d7 Number of Month + Installation Fee<br \/>\n57.95x<br \/>\n50.45x + 60 = 57.95x<\/p>\n<p>Question 1.<br \/>\nb. Solve the equation.<br \/>\n_______ hours<\/p>\n<p>Answer:<br \/>\n8<\/p>\n<p>Explanation:<br \/>\n50.45x + 60 = 57.95x<br \/>\n57.95x &#8211; 50.45x = 60<br \/>\n7.5x = 60<br \/>\nx = 60\/7.5<br \/>\nx = 8<br \/>\nThe total cost will be the same for 8 months.<\/p>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{4}\\) n &#8211; 18 = \\(\\frac{1}{4}\\) n &#8211; 4<br \/>\n______<\/p>\n<p>Answer:<br \/>\nn = 28<\/p>\n<p>Explanation:<br \/>\n3\/4 . n &#8211; 18 = 1\/4 . n &#8211; 4<br \/>\nDetermine the least common multiple of the denominators<br \/>\nLCM is 4<br \/>\nMultiply both sides of the equation by the LCM<br \/>\n4(3\/4 . n &#8211; 18) = 4(1\/4 . n &#8211; 4)<br \/>\n3n &#8211; 72 = n &#8211; 16<br \/>\n3n &#8211; n = -16 + 72<br \/>\n2n = 56<br \/>\nn = 56\/2<br \/>\nn = 28<\/p>\n<p>Question 3.<br \/>\n6 + \\(\\frac{4}{5}\\) b = \\(\\frac{9}{10}\\) b<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nb = 60<\/p>\n<p>Explanation:<br \/>\n6 + \\(\\frac{4}{5}\\) b = \\(\\frac{9}{10}\\) b<br \/>\nLCM is 10<br \/>\n10(6 + \\(\\frac{4}{5}\\) b) = 10(\\(\\frac{9}{10}\\) b)<br \/>\n60 + 8b = 9b<br \/>\n9b &#8211; 8b = 60<br \/>\nb = 60<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{11}\\) m + 16 = 4 + \\(\\frac{6}{11}\\) m<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nm = 33<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{11}\\) m + 16 = 4 + \\(\\frac{6}{11}\\) m<br \/>\nThe LCM is 11<br \/>\n11(\\(\\frac{2}{11}\\) m + 16) = 11(4 + \\(\\frac{6}{11}\\) m)<br \/>\n2m + 176 = 44 + 6m<br \/>\n6m &#8211; 2m = 176 &#8211; 44<br \/>\n4m = 132<br \/>\nm = 132\/4<br \/>\nm = 33<\/p>\n<p>Question 5.<br \/>\n2.25t + 5 = 13.5t + 14<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nt = -0.8<\/p>\n<p>Explanation:<br \/>\n2.25t + 5 = 13.5t + 14<br \/>\n13.5t &#8211; 2.25t = 5 &#8211; 14<br \/>\n11.25t = -9<br \/>\nt = -9\/11.25<br \/>\nt = -0.8<\/p>\n<p>Question 6.<br \/>\n3.6w = 1.6w + 24<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nw = 12<\/p>\n<p>Explanation:<br \/>\n3.6w = 1.6w + 24<br \/>\n3.6w &#8211; 1.6w = 24<br \/>\n2w = 24<br \/>\nw = 24\/2<br \/>\nw = 12<\/p>\n<p>Question 7.<br \/>\n-0.75p &#8211; 2 = 0.25p<br \/>\n_______<\/p>\n<p>Answer:<br \/>\np = -2<\/p>\n<p>Explanation:<br \/>\n-0.75p &#8211; 2 = 0.25p<br \/>\n-2 = 0.25p + 0.75p<br \/>\n-2 = p<br \/>\np = -2<\/p>\n<p>Question 8.<br \/>\nWrite a real-world problem that can be modeled by the equation 1.25x = 0.75x + 50.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n1.25x = 0.75x + 50.<br \/>\nCell offer Plan A for no base fee and $1.25 per minute.<br \/>\nCell offer Plan B for a $50 base fee and $0.75 per minute.<br \/>\nThe equation shows when the total cost of the plan would be equal.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 9.<br \/>\nHow does the method for solving equations with fractional or decimal coefficients and constants compare with the method for solving equations with integer coefficients and constants?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nWhen solving equations with fractional or decimal coefficients, the equations need to be multiplied by the multiple of denominator such that the equations have integer coefficients and constants.<\/p>\n<h3><a id=\"\u00b7_Equations_with_Rational_Numbers_\u2013_Page_No._207\"><\/a>Independent Practice &#8211; Equations with Rational Numbers &#8211; Page No. 207<\/h3>\n<p>Question 10.<br \/>\nMembers of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat. Nonmembers must pay $14.75 each time they rent a boat. How many times would a member and a non-member have to rent a boat in order to pay the same amount?<br \/>\n_______ times<\/p>\n<p>Answer:<br \/>\n20 times<\/p>\n<p>Explanation:<br \/>\nMembers of the Wide Waters Club pay $105 per summer season, plus $9.50 each time they rent a boat.<br \/>\n9.5x + $105<br \/>\nNonmembers must pay $14.75 each time they rent a boat.<br \/>\n9.5x + $105 = 14.75x<br \/>\n9.5x &#8211; 14.75x = $105<br \/>\n5.25x = 105<br \/>\nx = 105\/5.25<br \/>\nx = 20<br \/>\nThe cost for members and non-members will be the same for 8 visits.<\/p>\n<p>Question 11.<br \/>\nMargo can purchase tile at a store for $0.79 per tile and rent a tile saw for $24. At another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile. How many tiles must she buy for the cost to be the same at both stores?<br \/>\n_______ tiles<\/p>\n<p>Answer:<br \/>\n60 tiles<\/p>\n<p>Explanation:<br \/>\nMargo can purchase tile at a store for $0.79 per tile and rent a tile saw for $24.<br \/>\n0.79x + 24<br \/>\nAt another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile.<br \/>\n1.19x<br \/>\n0.79x + 24 = 1.19x<br \/>\n1.19x &#8211; 0.79x = 24<br \/>\n0.4x = 24<br \/>\nx = 24\/0.4<br \/>\nx = 60<br \/>\nMargo should buy 60 tiles for the cost to be the same at both stores.<\/p>\n<p>Question 12.<br \/>\nThe charges for two shuttle services are shown in the table. Find the number of miles for which the cost of both shuttles is the same.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 2: Equations with Rational Numbers img 3\" width=\"327\" height=\"116\" \/><br \/>\n_______ miles<\/p>\n<p>Answer:<br \/>\n40 miles<\/p>\n<p>Explanation:<br \/>\n0.1x + 10<br \/>\n0.35x<br \/>\n0.1x + 10 = 0.35x<br \/>\n0.35x &#8211; 0.1x = 10<br \/>\n0.25x = 10<br \/>\nx = 10\/0.25<br \/>\nx = 40<br \/>\nThe cost of shuttles would be the same for 40 miles.<\/p>\n<p>Question 13.<br \/>\nMultistep<br \/>\nRapid Rental Car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $45 for rental and gas and $0.35 per mile.<br \/>\na. For how many miles is the rental cost at both companies the same?<br \/>\n_______ miles<\/p>\n<p>Answer:<br \/>\n100 miles<\/p>\n<p>Explanation:<br \/>\n0.25x + 40 + 15 = 0.35x + 45<br \/>\n0.35x &#8211; 0.25x = 55 &#8211; 45<br \/>\n0.1x = 10<br \/>\nx = 10\/0.1<br \/>\nx = 100<br \/>\nThe cost of car rentals would be the same for 100 miles.<\/p>\n<p>Question 13.<br \/>\nb. What is that cost?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\n$80<\/p>\n<p>Explanation:<br \/>\nLet y be the total cost. Substitute 100 miles in any one of the two equations<br \/>\ny = 0.35x + 45<br \/>\ny = 0.35(100) + 45 = $80<br \/>\nTotal cost would be $80.<\/p>\n<p>Question 14.<br \/>\nWrite an equation with the solution x = 20. The equation should have the variable on both sides, a fractional coefficient on the left side, and a fraction anywhere on the right side.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4\/3x + 10 = 50\/3 + x<\/p>\n<p>Explanation:<br \/>\nWrite an equation with the solution x = 20. The equation should have the variable on both sides, a fractional coefficient on the left side, and a fraction anywhere on the right side.<br \/>\n1\/3 . x = 1\/3 . 20<br \/>\n1\/3 . x + x = 1\/3 . 20 + x<br \/>\n4\/3x = 20\/3 + x<br \/>\n4\/3x + 10 = 20\/3 + x + 10<br \/>\n4\/3x + 10 = 50\/3 + x<\/p>\n<p>Question 15.<br \/>\nWrite an equation with the solution x = 25. The equation should have the variable on both sides, a decimal coefficient on the left side, and a decimal anywhere on the right side. One of the decimals should be written in tenths, the other in hundredths.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nx=25<br \/>\ndivide both sides by 25<br \/>\nx\/25 = 1<br \/>\nconvert 1\/25 to decimal form 0.04<br \/>\n0.04x = 1<br \/>\nadd x on both sides<br \/>\n1.04x = 1 + x<br \/>\nadd 0.1 on both sides<br \/>\n1.04x + 0.1 = x + 1.1<\/p>\n<p>Question 16.<br \/>\nGeometry<br \/>\nThe perimeters of the rectangles shown are equal. What is the perimeter of each rectangle?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 2: Equations with Rational Numbers img 4\" width=\"255\" height=\"159\" \/><br \/>\nPerimeter = _______<\/p>\n<p>Answer:<br \/>\nPerimeter = 3.2<\/p>\n<p>Explanation:<br \/>\nPerimeter of the first rectangle<br \/>\nP = 2(n + n + 0.6) = 2(2n + 0.6) = 4n + 1.2<br \/>\nPerimeter of the second rectangle<br \/>\nP = 2(n + 0.1 + 2n) = 2(3n + 0.1) = 6n + 0.2<br \/>\nthe perimeter is equal<br \/>\n4n + 1.2 = 6n + 0.2<br \/>\n6n &#8211; 4n = 1.2 &#8211; 0.2<br \/>\n2n = 1<br \/>\nn = 1\/2<br \/>\nn = 0.5<br \/>\nP = 4n + 1.2 = 4(0.5) + 1.2 = 3.2<\/p>\n<p>Question 17.<br \/>\nAnalyze Relationships<br \/>\nThe formula F = 1.8C + 32 gives the temperature in degrees Fahrenheit (F) for a given temperature in degrees Celsius (C). There is one temperature for which the number of degrees Fahrenheit is equal to the number of degrees Celsius. Write an equation you can solve to find that temperature and then use it to find the temperature<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nx = 1.8x + 32<\/p>\n<p>Explanation:<br \/>\nF = 1.8C +32<br \/>\nlet x be the temperature such that it is same in both celsius and in fahrenheit<br \/>\nThen the required equation is<br \/>\nx = 1.8x + 32<br \/>\nsubtract 1.8x from both sides<br \/>\n-0.8x = 32<br \/>\ndivide by -0.8 on both sides<br \/>\nx = -40<br \/>\nSo -40 degree celsius<\/p>\n<h3><a id=\"\u00b7_Equations_with_Rational_Numbers_Lesson_Check_\u2013_Page_No._208\"><\/a>Equations with Rational Numbers &#8211; Page No. 208<\/h3>\n<p>Question 18.<br \/>\nExplain the Error<br \/>\nAgustin solved an equation as shown. What error did Agustin make? What is the correct answer?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 2: Equations with Rational Numbers img 5\" width=\"227\" height=\"196\" \/><br \/>\nx = _______<\/p>\n<p>Answer:<br \/>\nx = -12<\/p>\n<p>Explanation:<br \/>\nAgustin did not multiply by 12 on both sides in step 2. He only partially multiplied the variable and left the constants as such, which doesn&#8217;t make any sense.<br \/>\nThe correct solution is<br \/>\n12(x\/3 &#8211; 4) = 12(3x\/4 + 1)<br \/>\n4x &#8211; 48 = 9x + 12<br \/>\nsubtract 12 on both sides<br \/>\n4x &#8211; 60 = 9x<br \/>\nsubtract 4x on both sides<br \/>\n-60 = 5x<br \/>\nx = -12<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 19.<br \/>\nDraw Conclusions<br \/>\nSolve the equation \\(\\frac{1}{2} x-5+\\frac{2}{3} x=\\frac{7}{6} x+4\\). Explain your results.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2} x-5+\\frac{2}{3} x=\\frac{7}{6} x+4\\)<br \/>\nThe least common multiple of the denominators: LCM(2, 3, 6) = 6<br \/>\n6(\\(\\frac{1}{2} x-5+\\frac{2}{3} x=\\frac{7}{6} x+4\\))<br \/>\n6.1\/2x &#8211; 6.5 + 6.2\/3x = 6.7\/6x +6.4<br \/>\n3x &#8211; 30 + 4x = 7x + 24<br \/>\n7x &#8211; 30 = 7x + 24<br \/>\n-30 = 24<br \/>\nThis is not true. The equation has no solution.<\/p>\n<p>Question 20.<br \/>\nLook for a Pattern<br \/>\nDescribe the pattern in the equation. Then solve the equation.<br \/>\n0.3x + 0.03x + 0.003x + 0.0003x + .. = 3<br \/>\nx = ______<\/p>\n<p>Answer:<br \/>\nx = 9<\/p>\n<p>Explanation:<br \/>\n0.3x + 0.03x + 0.003x + 0.0003x + .. = 3<br \/>\n0.3x = 3<br \/>\n0.9x = 9<br \/>\nx = 9<\/p>\n<p>Question 21.<br \/>\nCritique Reasoning<br \/>\nJared wanted to find three consecutive even integers whose sum was 4 times the first of those integers. He let k represent the first integer, then wrote and solved this equation : k + (k + 1) + (k + 2) = 4k. Did he get the correct answer? Explain.<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nNo, it is wrong on two accounts.<br \/>\nFirst, he has not specified if k is even or not. An easy way of doing so would assume x to be any integer and k=2a<br \/>\nThis ensures that k is an even integer.<br \/>\nNest the question asks for 3 consecutive even integers, Jared just took 3 consecutive integers, and thus at least 1 of them is odd.<br \/>\nSo correct representation would be<br \/>\nk + (k+2) + (k + 4) = 4k<br \/>\nwhich upon solving yields k=6<\/p>\n<h3><a id=\"\u00b7_Equations_with_the_Distributive_Property_\u2013_Page_No._212\"><\/a>Guided Practice &#8211; Equations with the Distributive Property &#8211; Page No. 212<\/h3>\n<p><strong>Solve each equation.<\/strong><\/p>\n<p>Question 1.<br \/>\n4(x + 8) &#8211; 4 = 34 &#8211; 2x<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 1<\/p>\n<p>Explanation:<br \/>\n4(x + 8) &#8211; 4 = 34 &#8211; 2x<br \/>\n4x + 32 &#8211; 4 = 34 &#8211; 2x<br \/>\n4x + 2x = 34 &#8211; 28<br \/>\n6x = 6<br \/>\nx = 6\/6<br \/>\nx = 1<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{3}\\)(9 + x) = -5(4 &#8211; x)<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 6<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{3}\\)(9 + x) = -5(4 &#8211; x)<br \/>\n2\/3(9 + x) = -5(4 &#8211; x)<br \/>\n3 (2\/3(9 + x)) = 3(-5(4 &#8211; x))<br \/>\n2(9 + x ) = -15 (4 &#8211; x)<br \/>\n18 + 2x = -60 + 15x<br \/>\n15x &#8211; 2x = 18 + 60<br \/>\n13x = 78<br \/>\nx = 78\/13<br \/>\nx = 6<\/p>\n<p>Question 3.<br \/>\n-3(x + 4) + 15 = 6 &#8211; 4x<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 3<\/p>\n<p>Explanation:<br \/>\n-3(x + 4) + 15 = 6 &#8211; 4x<br \/>\n-3x &#8211; 12 + 15 = 6 &#8211; 4x<br \/>\n-3x + 3 = 6 &#8211; 4x<br \/>\n-3x + 4x = 6 &#8211; 3<br \/>\nx = 3<\/p>\n<p>Question 4.<br \/>\n10 + 4x = 5(x &#8211; 6) + 33<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 7<\/p>\n<p>Explanation:<br \/>\n10 + 4x = 5(x &#8211; 6) + 33<br \/>\n10 + 4x = 5x &#8211; 30 + 33<br \/>\n10 + 4x = 5x + 3<br \/>\n5x &#8211; 4x = 10 &#8211; 3<br \/>\nx = 7<\/p>\n<p>Question 5.<br \/>\nx &#8211; 9 = 8(2x + 3) &#8211; 18<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = -1<\/p>\n<p>Explanation:<br \/>\nx &#8211; 9 = 8(2x + 3) &#8211; 18<br \/>\nx &#8211; 9 = 16x + 24 &#8211; 18<br \/>\nx &#8211; 9 = 16x + 6<br \/>\n16x &#8211; x = -9 &#8211; 6<br \/>\n15x = &#8211; 15<br \/>\nx = -15\/15<br \/>\nx = -1<\/p>\n<p>Question 6.<br \/>\n-6(x &#8211; 1) &#8211; 7 = -7x + 2<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 3<\/p>\n<p>Explanation:<br \/>\n-6(x &#8211; 1) &#8211; 7 = -7x + 2<br \/>\n-6x + 6 &#8211; 7 = -7x + 2<br \/>\n-6x &#8211; 1 = -7x + 2<br \/>\n-7x + 6x = -1 -2<br \/>\n-x = -3<br \/>\nx = 3<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{10}\\)(x + 11) = -2(8 &#8211; x)<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 9<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{10}\\)(x + 11) = -2(8 &#8211; x)<br \/>\n10(\\(\\frac{1}{10}\\)(x + 11)) = 10 (-2(8 &#8211; x))<br \/>\nx + 11 = -20(8 &#8211; x)<br \/>\nx + 11 = -160 + 20x<br \/>\n20x &#8211; x = 11 + 160<br \/>\n19x = 171<br \/>\nx = 171\/19 = 9<\/p>\n<p>Question 8.<br \/>\n-(4 &#8211; x) = \\(\\frac{3}{4}\\)(x &#8211; 6)<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\n-(4 &#8211; x) = \\(\\frac{3}{4}\\)(x &#8211; 6)<br \/>\n4(-(4 &#8211; x)) = 4 (3\/4(x &#8211; 6))<br \/>\n-16 + 4x = 3x &#8211; 18<br \/>\n4x &#8211; 3x = -18 + 16<br \/>\nx = -2<\/p>\n<p>Question 9.<br \/>\n-8(8 &#8211; x) = \\(\\frac{4}{5}\\)(x + 10)<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 10<\/p>\n<p>Explanation:<br \/>\n-8(8 &#8211; x) = \\(\\frac{4}{5}\\)(x + 10)<br \/>\n5(-8(8 &#8211; x)) = 5(\\(\\frac{4}{5}\\)(x + 10))<br \/>\n-40(8 &#8211; x) = 4(x + 10)<br \/>\n-320 + 40x = 4x + 40<br \/>\n40x &#8211; 4x = 40 + 320<br \/>\n36x = 360<br \/>\nx = 360\/36<br \/>\nx = 10<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{1}{2}\\)(16 &#8211; x) = -12(x + 7)<br \/>\n________<\/p>\n<p>Answer:<br \/>\nx = 8<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\)(16 &#8211; x) = -12(x + 7)<br \/>\n2 (\\(\\frac{1}{2}\\)(16 &#8211; x)) = 2 (-12(x + 7))<br \/>\n16 &#8211; x = -24 (x + 7)<br \/>\n16 &#8211; x = -24x &#8211; 168<br \/>\n24x &#8211; x = -168 &#8211; 16<br \/>\n23x = 184<br \/>\nx = 184\/23<br \/>\nx = 8<\/p>\n<p>Question 11.<br \/>\nSandra saves 12% of her salary for retirement. This year her salary was $3,000 more than in the previous year, and she saved $4,200.What was her salary in the previous year?<br \/>\nWrite an equation _____<br \/>\nSandra&#8217;s salary in the previous year was _____<br \/>\nSalary = $ _____<\/p>\n<p>Answer:<br \/>\nWrite an equation 0.12x + 360 = 4200<br \/>\nSandra&#8217;s salary in the previous year was $32000<br \/>\nSalary = $3000<\/p>\n<p>Explanation:<br \/>\n0.12(x + 3000) = 4200<br \/>\n0.12x + 360 = 4200<br \/>\n0.12x = 4200 &#8211; 360<br \/>\n0.12x = 3840<br \/>\nx = 3840\/0.12<br \/>\nx = 32000<br \/>\nSandra&#8217;s salary in the previous year was $32000<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 12.<br \/>\nWhen solving an equation using the Distributive Property, if the numbers being distributed are fractions, what is your first step? Why?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nMultiply both sides by the denominator of the fraction<\/p>\n<h3><a id=\"\u00b7_Equations_with_the_Distributive_Property_\u2013_Page_No._213\"><\/a>Independent Practice &#8211; Equations with the Distributive Property &#8211; Page No. 213<\/h3>\n<p>Question 13.<br \/>\nMultistep<br \/>\nMartina is currently 14 years older than her cousin Joey. In 5 years she will be 3 times as old as Joey. Use this information to answer the following questions.<br \/>\na. If you let x represent Joey&#8217;s current age, what expression can you use to represent Martina&#8217;s current age?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\ny = x + 14<\/p>\n<p>Explanation:<br \/>\ny = x + 14<br \/>\nwhere x is Joey&#8217;s current age and t is Martna&#8217;s current age.<\/p>\n<p>Question 13.<br \/>\nb. Based on your answer to part a, what expression represents Joey&#8217;s age in 5 years? What expression represents Martina&#8217;s age in 5 years?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nAges in 5 years<br \/>\nJoey&#8217;s age = x + 5<br \/>\nMartina&#8217;s age = x + 14 + 5 = x + 19<\/p>\n<p>Question 13.<br \/>\nc. What equation can you write based on the information given?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n3(x + 5) = x + 19<\/p>\n<p>Explanation:<br \/>\nIn 5 years, Martina will be three times as old as Joey<br \/>\n3(x + 5) = x + 19<\/p>\n<p>Question 13.<br \/>\nd. What is Joey&#8217;s current age? What is Martina&#8217;s current age?<br \/>\nJoey&#8217;s current age ___________<br \/>\nMartina&#8217;s current age ___________<\/p>\n<p>Answer:<br \/>\nJoey&#8217;s current age 2<br \/>\nMartina&#8217;s current age 16<\/p>\n<p>Explanation:<br \/>\n3(x + 5) = x + 19<br \/>\n3x + 15 = x + 19<br \/>\n3x &#8211; x = 19 &#8211; 15<br \/>\n2x = 4<br \/>\nx = 2<\/p>\n<p>Question 14.<br \/>\nAs part of a school contest, Sarah and Luis are playing a math game. Sarah must pick a number between 1 and 50 and give Luis clues so he can write an equation to find her number. Sarah says, &#8220;If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35.&#8221; What equation can Luis write based on Sarah&#8217;s clues and what is Sarah&#8217;s number?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nx = 12<\/p>\n<p>Explanation:<br \/>\nAs part of a school contest, Sarah and Luis are playing a math game. Sarah must pick a number between 1 and 50 and give Luis clues so he can write an equation to find her number. Sarah says, &#8220;If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35.&#8221;<br \/>\n4 (x &#8211; 5) + 7 = 35<br \/>\n4x &#8211; 20 + 7 = 35<br \/>\n4x &#8211; 13 = 35<br \/>\n4x = 35 + 13<br \/>\n4x = 48<br \/>\nx = 48\/4<br \/>\nx = 12<\/p>\n<p>Question 15.<br \/>\nCritical Thinking<br \/>\nWhen solving an equation using the Distributive Property that involves distributing fractions, usually the first step is to multiply by the LCD to eliminate the fractions in order to simplify computation. Is it necessary to do this to solve \\(\\frac{1}{2}\\)(4x + 6) = 13(9x &#8211; 24)? Why or why not?<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nIt is not necessary. In this case, distributing the fractions directly results in whole-number coefficients and constants, however, if the results are not in whole-number coefficients and constants it is harder to solve fractions.<\/p>\n<p>Question 16.<br \/>\nSolve the equation given in Exercise 15 with and without using the LCD of the fractions. Are your answers the same?<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nx = 11<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\)(4x + 6) = 13(9x &#8211; 24)<br \/>\n6(\\(\\frac{1}{2}\\)(4x + 6)) = 6(13(9x &#8211; 24))<br \/>\n3(4x + 6) = 2(9x &#8211; 24)<br \/>\n12x + 18 = 18x &#8211; 48<br \/>\n18x &#8211; 12x = 18 + 48<br \/>\n6x = 66<br \/>\nx = 66\/6<br \/>\nx = 11<\/p>\n<h3><a id=\"\u00b7_Equations_with_the_Distributive_Property_Lesson_Check_\u2013_Page_No._214\"><\/a>Equations with the Distributive Property &#8211; Page No. 214<\/h3>\n<p>Question 17.<br \/>\nRepresent Real-World Problems<br \/>\nA chemist mixed x milliliters of 25% acid solution with some 15% acid solution to produce 100 milliliters of a 19% acid solution. Use this information to fill in the missing information in the table and answer the questions that follow.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 3: Equations with the Distributive Property img 6\" width=\"613\" height=\"172\" \/><br \/>\na. What is the relationship between the milliliters of acid in the 25% solution, the milliliters of acid in the 15% solution, and the milliliters of acid in the mixture?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe milliliters of acid in the 25% solution plus the milliliters of acid in the 15% solution equals the milliliters of acid in the mixture<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-9-300x42.png\" alt=\"grade 8 chapter 7 image 9\" width=\"300\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-9-300x42.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-9-768x109.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-7-image-9.png 890w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 17.<br \/>\nb. What equation can you use to solve for x based on your answer to part a?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n0.25x + 0.15(100 &#8211; x) = 19<\/p>\n<p>Question 17.<br \/>\nc. How many milliliters of the 25% solution and the 15% solution did the chemist use in the mixture?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 3: Equations with the Distributive Property img 7\" width=\"233\" height=\"152\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n0.25x + 0.15(100 &#8211; x) = 19<br \/>\n0.25x + 15 &#8211; 0.15x = 19<br \/>\n0.1x + 15 = 19<br \/>\n0.1x = 4<br \/>\nx = 4\/0.1<br \/>\nx = 40<br \/>\nThe chemist used 40ml of the 25% solution and 100 &#8211; 40 = 60ml of the 15% solution.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 18.<br \/>\nExplain the Error<br \/>\nAnne solved 5(2x) &#8211; 3 = 20x + 15 for x by first distributing 5 on the left side of the equation. She got the answer x = -3. However, when she substituted -3 into the original equation for x, she saw that her answer was wrong. What did Anne do wrong, and what is the correct answer?<br \/>\nx = ________<\/p>\n<p>Answer:<br \/>\nx = -1.8<\/p>\n<p>Explanation:<br \/>\nDado que 5 solo se multiplica por 2x, no tiene sentido usar la distribuci\u00f3n aqu\u00ed. B\u00e1sicamente, distribuir 5 fue el problema<br \/>\nSoluci\u00f3n correcta:<br \/>\n5 (2x) &#8211; 3 = 20x + 15<br \/>\n10x -3 = 20x + 15<br \/>\nrestar 15 en ambos lados<br \/>\n10x &#8211; 18 = 20x<br \/>\nrestar 10x de ambos lados<br \/>\n-18 = 10x<br \/>\nx = -1.8<\/p>\n<p>Question 19.<br \/>\nCommunicate Mathematical Ideas<br \/>\nExplain a procedure that can be used to solve 5[3(x + 4) &#8211; 2(1 &#8211; x)] &#8211; x &#8211; 15 = 14x + 45. Then solve the equation.<br \/>\nx = ________<\/p>\n<p>Answer:<br \/>\nx = 1<\/p>\n<p>Explanation:<br \/>\n5[3(x + 4) &#8211; 2(1 &#8211; x)] &#8211; x &#8211; 15 = 14x + 45<br \/>\n5[3x + 12 &#8211; 2 + 2x] &#8211; x &#8211; 15 = 14x + 45<br \/>\n5[5x + 10] &#8211; x &#8211; 15 = 14x + 45<br \/>\n25x + 50 &#8211; x &#8211; 15 = 14x + 45<br \/>\n24x + 35 = 14x + 45<br \/>\n24x &#8211; 14x = 45 &#8211; 35<br \/>\n10x = 10<br \/>\nx = 1<\/p>\n<h3><a id=\"\u00b7_Equations_with_Many_Solutions_or_No_Solution_\u2013_Page_No._218\"><\/a>Guided Practice &#8211; Equations with Many Solutions or No Solution &#8211; Page No. 218<\/h3>\n<p><strong>Use the properties of equality to simplify each equation. Tell whether the final equation is a true statement.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 4: Equations with Many Solutions or No Solution img 8\" width=\"230\" height=\"442\" \/><br \/>\nThe statement is: _______<\/p>\n<p>Answer:<br \/>\nThe statement is: true<\/p>\n<p>Explanation:<br \/>\n3x &#8211; 2 = 25 &#8211; 6x<br \/>\n3x + 6x -2 = 25 -6x + 6x<br \/>\n9x &#8211; 2 = 25<br \/>\n9x -2 + 2 = 25 + 2<br \/>\n9x = 27<br \/>\nx = 27\/9<br \/>\nx = 3<br \/>\nThe statement is true.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 4: Equations with Many Solutions or No Solution img 9\" width=\"234\" height=\"295\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe statement is false.<\/p>\n<p>Explanation:<br \/>\n2x &#8211; 4 = 2(x &#8211; 1) + 3<br \/>\n2x &#8211; 4 = 2x &#8211; 2 + 3<br \/>\n2x &#8211; 4 = 2x + 1<br \/>\n2x &#8211; 4 &#8211; 2x = 2x + 1 &#8211; 2x<br \/>\n-4 not equal to 1<br \/>\nThe statement is false.<\/p>\n<p>Question 3.<br \/>\nHow many solutions are there to the equation in Exercise 2?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThere is no solution to exercise 2.<\/p>\n<p>Question 4.<br \/>\nAfter simplifying an equation, Juana gets 6 = 6. Explain what this means.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nWhen 6 = 6, there are infinite solutions.<\/p>\n<p><strong>Write a linear equation in one variable that has infinitely many solutions.<\/strong><\/p>\n<p>Question 5.<br \/>\nStart with a _____ statement.<br \/>\nAdd the _____ to both sides.<br \/>\nAdd the _____ to both sides.<br \/>\nCombine _____ terms.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 4: Equations with Many Solutions or No Solution img 10\" width=\"252\" height=\"203\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nStart with a &#8220;true&#8221; statement<br \/>\nAdd the &#8220;same variable&#8221; to both sides<br \/>\nAdd the &#8220;same constant&#8221; to both sides<br \/>\nCombine &#8220;like&#8221; terms<\/p>\n<p>Explanation:<br \/>\nStart with a &#8220;true&#8221; statement<br \/>\n10 = 10<br \/>\nAdd the &#8220;same variable&#8221; to both sides<br \/>\n10 + x = 10 + x<br \/>\nAdd the &#8220;same constant&#8221; to both sides<br \/>\n10 + x + 5 = 10 + x + 5<br \/>\nCombine &#8220;like&#8221; terms<br \/>\n15 + x = 15 + x<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nGive an example of an equation with an infinite number of solutions. Then make one change to the equation so that it has no solution.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAn equation with infinitely many solutions<br \/>\nx &#8211; 2x + 3 = 3 &#8211; x<br \/>\n-x + 3 = 3 &#8211; x<br \/>\n+x\/3 = +x\/3<br \/>\nAn equation for no solution<br \/>\nx &#8211; 2x + 3 = 3 &#8211; x + 4<br \/>\n-x + 3 = 7 &#8211; x<br \/>\n-x\/3 = -x\/7<\/p>\n<h3><a id=\"\u00b7_Equations_with_Many_Solutions_or_No_Solution_\u2013_Page_No._219\"><\/a>Independent Practice &#8211; Equations with Many Solutions or No Solution &#8211; Page No. 219<\/h3>\n<p><strong>Tell whether each equation has one, zero, or infinitely many solutions.<\/strong><\/p>\n<p>Question 7.<br \/>\n-(2x + 2) &#8211; 1 = -x &#8211; (x + 3)<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe statement is true<\/p>\n<p>Explanation:<br \/>\n-(2x + 2) &#8211; 1 = -x &#8211; (x + 3)<br \/>\n-2x &#8211; 2 &#8211; 1 = -x &#8211; x + 3<br \/>\n-2x &#8211; 3 = -2x + 3<br \/>\n-3 = -3<br \/>\nThe statement is true<\/p>\n<p>Question 8.<br \/>\n-2(z + 3) &#8211; z = -z &#8211; 4(z + 2)<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe statement is false.<\/p>\n<p>Explanation:<br \/>\n-2(z + 3) &#8211; z = -z &#8211; 4(z + 2)<br \/>\n-3z &#8211; 6 = -3z -8<br \/>\n-3z -6 + 3z = -3z &#8211; 8 + 3z<br \/>\n-6 not equal to -8<br \/>\nThe statement is false.<\/p>\n<p><strong>Create an equation with the indicated number of solutions.<\/strong><\/p>\n<p>Question 9.<br \/>\nNo solution:<br \/>\n3(x &#8211; \\(\\frac{4}{3}\\)) = 3x + _____<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n3(x &#8211; \\(\\frac{4}{3}\\)) = 3x + ?<br \/>\n3x &#8211; 4 = 3x + ?<br \/>\n3x &#8211; 4 = 3x + 2<br \/>\nWhen there is no solution, the statement should be false. Any number except -4 would make the equation have no solutions.<\/p>\n<p>Question 10.<br \/>\nInfinitely many solutions:<br \/>\n2(x &#8211; 1) + 6x = 4( _____ &#8211; 1) + 2<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2(x &#8211; 1) + 6x = 4( _____ &#8211; 1) + 2<br \/>\n2(x &#8211; 1) + 6x = 4( ? &#8211; 1) + 2<br \/>\n2x &#8211; 2 + 6x = 4(? &#8211; 1) + 2<br \/>\n8x &#8211; 2 = 4(? &#8211; 1) + 2<br \/>\n8x &#8211; 2 = 4(2x &#8211; 1) + 2<br \/>\n8x &#8211; 2 = 8x &#8211; 4 + 2<br \/>\n8x &#8211; 2 = 8x &#8211; 2<br \/>\nWhen there are infinitely many solutions, the statement should be true<\/p>\n<p>Question 11.<br \/>\nOne solution of x = -1:<br \/>\n5x &#8211; (x &#8211; 2) = 2x &#8211; ( _____ )<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPut x = -1 in the equation<br \/>\n-5 &#8211; (-1 &#8211; 2) = -2 &#8211; blank<br \/>\nsimplifying<br \/>\n-2 = -2 &#8211; blank<br \/>\nadd 2 on both sides<br \/>\n0 = blank<\/p>\n<p>Question 12.<br \/>\nInfinitely many solutions:<br \/>\n-(x &#8211; 8) + 4x = 2( _____ ) + x<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n-(x &#8211; 8) + 4x = 2( ?) + x<br \/>\n-x + 8 + 4x = 2(?) + x<br \/>\n3x + 8 = 2(?) + x<br \/>\n3x + 8 = 2 (x + 4) + x<br \/>\n3x + 8 = 2x + 8x + x<br \/>\n3x + 8 = 3x + 8<br \/>\nWhen there are infinitely many solutions, the statement should be true.<\/p>\n<p>Question 13.<br \/>\nPersevere in Problem Solving<br \/>\nThe Dig It Project is designing two gardens that have the same perimeter. One garden is a trapezoid whose nonparallel sides are equal. The other is a quadrilateral. Two possible designs are shown at the right.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 4: Equations with Many Solutions or No Solution img 11\" width=\"290\" height=\"361\" \/><br \/>\na. Based on these designs, is there more than one value for x? Explain how you know this.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThere are more than one value of x<\/p>\n<p>Explanation:<br \/>\nPerimeter of the trapezoid<br \/>\nP = 2x &#8211; 2 + x + 1 + x + x + 1 = 5x<br \/>\nPerimeter of the quadrilateral<br \/>\nP = 2x &#8211; 9 + x + x + 8 + x + 1 = 5x<br \/>\n5x = 5x<br \/>\nThere are more than one value of x<\/p>\n<p>Question 13.<br \/>\nb. Why does your answer to part a make sense in this context?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe condition was that the two perimeters are to be equal. However, a specific number was not given, so there are an infinite number of possible perimeters<\/p>\n<p>Explanation:<br \/>\nInterpretation of part a in this context<br \/>\nThe condition was that the two perimeters are to be equal. However, a specific number was not given, so there are an infinite number of possible perimeters<\/p>\n<p>Question 13.<br \/>\nc. Suppose the Dig It Project wants the perimeter of each garden to be 60 meters. What is the value of x in this case? How did you find this?<br \/>\n______ meters<\/p>\n<p>Answer:<br \/>\n12 meters<\/p>\n<p>Explanation:<br \/>\n2x &#8211; 2 + x + 1 + x + x + 1 = 60<br \/>\n5x = 60<br \/>\nx = 60\/5<br \/>\nx = 12<\/p>\n<h3><a id=\"\u00b7_Equations_with_Many_Solutions_or_No_Solution_Lesson_Check_\u2013_Page_No._220\"><\/a>Equations with Many Solutions or No Solution &#8211; Page No. 220<\/h3>\n<p>Question 14.<br \/>\nCritique Reasoning<br \/>\nLisa says that the indicated angles cannot have the same measure. Marita disagrees and says she can prove that they can have the same measure. Who do you agree with? Justify your answer.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Lesson 4: Equations with Many Solutions or No Solution img 12\" width=\"314\" height=\"144\" \/><br \/>\nI agree with: ______________<\/p>\n<p>Answer:<br \/>\nI agree with: Marita<\/p>\n<p>Explanation:<br \/>\n9x &#8211; 25 + x = x + 50 + 2x &#8211; 12<br \/>\n10x &#8211; 25 = 3x + 38<br \/>\n10x &#8211; 3x = 38 + 25<br \/>\n7x = 63<br \/>\nx = 63\/7<br \/>\nx = 9<br \/>\nWhen x = 9 the angles will be same and for any other value of x, the angles will not be the same.<\/p>\n<p>Question 15.<br \/>\nRepresent Real-World Problems<br \/>\nAdele opens an account with $100 and deposits $35 a month. Kent opens an account with $50 and also deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many months and how much will be in each account? Explain.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nAdele&#8217;s amount after x months<br \/>\nA = 100 + 35x<br \/>\nKent&#8217;s amount after x months<br \/>\nA = 50 + 35x<br \/>\n100 + 35x = 50 + 35x<br \/>\n100 is not equal to 50<br \/>\nThe statement is false, the amounts in two accounts would never be equal.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 16.<br \/>\nCommunicate Mathematical Ideas<br \/>\nFrank solved an equation and got the result x = x. Sarah solved the same equation and got 12 = 12. Frank says that one of them is incorrect because you cannot get different results for the same equation. What would you say to Frank? If both results are indeed correct, explain how this happened.<br \/>\nFrank is: ____________<\/p>\n<p>Answer:<br \/>\nBoth of them can be correct as both equations give the same result i.e. there are infinitely many solutions. Frank eliminated the constant from both sides while Sarah eliminated the variable from both sides.<\/p>\n<p>Question 17.<br \/>\nCritique Reasoning<br \/>\nMatt said 2x &#8211; 7 = 2(x &#8211; 7) has infinitely many solutions. Is he correct? Justify Matt&#8217;s answer or show how he is incorrect.<br \/>\nMatt is: ____________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n2x &#8211; 7 = 2(x &#8211; 7)<br \/>\n2x &#8211; 7 = 2x &#8211; 14<br \/>\n-7 not equal to -14<br \/>\nThe statement is false, there is no solution. Matt is incorrect.<\/p>\n<h3><a id=\"\u00b7_Equations_with_the_Variable_on_Both_Sides_\u2013_Model_Quiz_\u2013_Page_No._221\"><\/a>7.1 Equations with the Variable on Both Sides &#8211; Model Quiz &#8211; Page No. 221<\/h3>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 1.<br \/>\n4a &#8211; 4 = 8 + a<br \/>\n_______<\/p>\n<p>Answer:<br \/>\na = 4<\/p>\n<p>Explanation:<br \/>\n4a &#8211; 4 = 8 + a<br \/>\n4a &#8211; a = 8 + 4<br \/>\n3a = 12<br \/>\na = 12\/3<br \/>\na = 4<\/p>\n<p>Question 2.<br \/>\n4x + 5 = x + 8<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx = 1<\/p>\n<p>Explanation:<br \/>\n4x + 5 = x + 8<br \/>\n4x &#8211; x = 8 &#8211; 5<br \/>\n3x = 3<br \/>\nx = 3\/3<br \/>\nx = 1<\/p>\n<p>Question 3.<br \/>\nHue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs. Write and solve an equation to find how many chairs are in that row length.<br \/>\n_______ chairs<\/p>\n<p>Answer:<br \/>\n7 chairs<\/p>\n<p>Explanation:<br \/>\nHue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs.<br \/>\n6x + 3 = 8x &#8211; 11<br \/>\n8x &#8211; 6x = 3 + 11<br \/>\n2x = 14<br \/>\nx = 14\/2<br \/>\nx = 7<br \/>\nThere are 7 chairs in each row.<\/p>\n<p><strong>7.2 Equations with Rational Numbers<\/strong><\/p>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{3} n-\\frac{2}{3}=\\frac{n}{6}+\\frac{4}{3}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nn = 4<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{3} n-\\frac{2}{3}=\\frac{n}{6}+\\frac{4}{3}\\)<br \/>\nThe LCM is 6.<br \/>\n6(2\/3n &#8211; 2\/3) = 6(n\/6 + 4\/3)<br \/>\n6(2\/3n) -6(2\/3) = 6(n\/6) + 6(4\/3)<br \/>\n4n &#8211; 4 = n + 8<br \/>\n4n &#8211; n = 8 + 4<br \/>\n3n = 12<br \/>\nn = 12\/3<br \/>\nn = 4<\/p>\n<p>Question 5.<br \/>\n1.5d + 3.25 = 1 + 2.25d<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nd = 3<\/p>\n<p>Explanation:<br \/>\n1.5d + 3.25 = 1 + 2.25d<br \/>\n2.25d &#8211; 1.5d = 3.25 &#8211; 1<br \/>\n0.75d = 2.25<br \/>\nd = 2.25\/0.75<br \/>\nd = 3<\/p>\n<p>Question 6.<br \/>\nHappy Paws charges $19.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $14.00 plus $2.75 per hour. Write and solve an equation to find for how many hours the total cost of the services is equal.<br \/>\n_______ hours<\/p>\n<p>Answer:<br \/>\n3.2 hours<\/p>\n<p>Explanation:<br \/>\nHappy Paws charges $19.00 plus $1.50 per hour to keep a dog during the day.<br \/>\n1.5x + 19<br \/>\nWoof Watchers charges $14.00 plus $2.75 per hour.<br \/>\n2.75x + 15<br \/>\n1.5x + 19 = 2.75x + 15<br \/>\n2.75x &#8211; 1.5x = 19 &#8211; 15<br \/>\n1.25x = 4<br \/>\nx = 4\/1.25<br \/>\nx = 3.2<br \/>\nThe total cost of the services is equal after 3.2 hrs.<\/p>\n<p><strong>7.3 Equations with the Distributive Property<\/strong><\/p>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 7.<br \/>\n14 + 5x = 3(-x + 3) &#8211; 11<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx = -2<\/p>\n<p>Explanation:<br \/>\n14 + 5x = 3(-x + 3) &#8211; 11<br \/>\n14 + 5x = -3x + 9 &#8211; 11<br \/>\n14 + 5x = -3x &#8211; 2<br \/>\n5x + 3x = -2 &#8211;\u00a0 14<br \/>\n8x = &#8211; 16<br \/>\nx = -16\/8<br \/>\nx = -2<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{4}\\)(x &#8211; 7) = 1 + 3x<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx = -1<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{4}\\)(x &#8211; 7) = 1 + 3x<br \/>\n4(\\(\\frac{1}{4}\\)(x &#8211; 7)) = 4(1 + 3x)<br \/>\n(x &#8211; 7) = 4 + 12x<br \/>\n12x &#8211; x = -7 &#8211; 4<br \/>\n11x = -11<br \/>\nx = -11\/11<br \/>\nx = -1<\/p>\n<p>Question 9.<br \/>\n-5(2x &#8211; 9) = 2(x &#8211; 8) &#8211; 11<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx = 6<\/p>\n<p>Explanation:<br \/>\n-5(2x &#8211; 9) = 2(x &#8211; 8) &#8211; 11<br \/>\n-10x + 45 = 2x &#8211; 16 &#8211; 11<br \/>\n-10x + 45 = 2x &#8211; 27<br \/>\n2x + 10x = 45 + 27<br \/>\n12x = 72<br \/>\nx = 72\/12<br \/>\nx = 6<\/p>\n<p>Question 10.<br \/>\n3(x + 5) = 2(3x + 12)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx = -3<\/p>\n<p>Explanation:<br \/>\n3(x + 5) = 2(3x + 12)<br \/>\n3x + 15 = 6x + 24<br \/>\n6x &#8211; 3x = 15 &#8211; 24<br \/>\n3x = -9<br \/>\nx = -9\/3<br \/>\nx = -3<\/p>\n<p><strong>7.4 Equations with Many Solutions or No Solution<\/strong><\/p>\n<p><strong>Tell whether each equation has one, zero, or infinitely many solutions.<\/strong><\/p>\n<p>Question 11.<br \/>\n5(x &#8211; 3) + 6 = 5x &#8211; 9<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThere are infinitely many solutions<\/p>\n<p>Explanation:<br \/>\n5(x &#8211; 3) + 6 = 5x &#8211; 9<br \/>\n5x &#8211; 15 + 6 = 5x &#8211; 9<br \/>\n5x &#8211; 9 = 5x &#8211; 9<br \/>\nThe statement is true. There are infinitely many solutions.<\/p>\n<p>Question 12.<br \/>\n5(x &#8211; 3) + 6 = 5x &#8211; 10<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThere are no solutions<\/p>\n<p>Explanation:<br \/>\n5(x &#8211; 3) + 6 = 5x &#8211; 10<br \/>\n5x &#8211; 15 + 6 = 5x &#8211; 10<br \/>\n5x &#8211; 9 = 5x &#8211; 10<br \/>\n-9 not equal to -10<br \/>\nThe statement is false. There are no solutions.<\/p>\n<p>Question 13.<br \/>\n5(x &#8211; 3) + 6 = 4x + 3<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThere is one solution<\/p>\n<p>Explanation:<br \/>\n5(x &#8211; 3) + 6 = 4x + 3<br \/>\n5x &#8211; 15 + 6 = 4x + 3<br \/>\n5x &#8211; 9 = 4x + 3<br \/>\n5x &#8211; 4x = 3 + 9<br \/>\nx = 12<br \/>\nThere is one solution<\/p>\n<h3><a id=\"Mixed_Review_\u2013_Page_No._222\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 222<\/h3>\n<p>Question 1.<br \/>\nTwo cars are traveling in the same direction. The first car is going 40 mi\/h, and the second car is going 55 mi\/h. The first car left 3 hours before the second car. Which equation could you solve to find how many hours it will take for the second car to catch up to the first car?<br \/>\nOptions:<br \/>\na. 55t + 3 = 40t<br \/>\nb. 55t + 165 = 40t<br \/>\nc. 40t + 3 = 55t<br \/>\nd. 40t + 120 = 55t<\/p>\n<p>Answer:<br \/>\nd. 40t + 120 = 55t<\/p>\n<p>Explanation:<br \/>\nTwo cars are traveling in the same direction. The first car is going 40 mi\/h, and the second car is going 55 mi\/h. The first car left 3 hours before the second car.<br \/>\n3 \u00d7 40 + 40t = 120 + 40t<br \/>\n55t<br \/>\n40t + 120 = 55t<\/p>\n<p>Question 2.<br \/>\nWhich linear equation is represented by the table?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Mixed Review img 13\" width=\"234\" height=\"75\" \/><br \/>\nOptions:<br \/>\na. y = -x + 5<br \/>\nb. y = 2x &#8211; 1<br \/>\nc. y = x + 3<br \/>\nd. y = -3x + 11<\/p>\n<p>Answer:<br \/>\na. y = -x + 5<\/p>\n<p>Explanation:<br \/>\nFind the slope using<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nwhere (x1, y1) = (3, 2), (x2, y2) = (1, 4)<br \/>\nSlope = (4 &#8211; 2)\/(1 &#8211; 3) = -2\/2 = -1<\/p>\n<p>Question 3.<br \/>\nShawn\u2019s Rentals charges $27.50 per hour to rent a surfboard and a wetsuit. Darla\u2019s Surf Shop charges $23.25 per hour to rent a surfboard plus $17 extra for a wetsuit. For what total number of hours are the charges for Shawn\u2019s Rentals the same as the charges for Darla\u2019s Surf Shop?<br \/>\nOptions:<br \/>\na. 3<br \/>\nb. 4<br \/>\nc. 5<br \/>\nd. 6<\/p>\n<p>Answer:<br \/>\nb. 4<\/p>\n<p>Explanation:<br \/>\nShawn\u2019s Rentals charges $27.50 per hour to rent a surfboard and a wetsuit.<br \/>\n27.5x<br \/>\nDarla\u2019s Surf Shop charges $23.25 per hour to rent a surfboard plus $17 extra for a wetsuit.<br \/>\n23.25x + 17<br \/>\n23.25x + 17 = 27.5x<br \/>\n27.5x &#8211; 23.25x = 17<br \/>\n4.25x = 17<br \/>\nx = 17\/4.25<br \/>\nx = 4<br \/>\nThe charge would be equal after 4 hrs<\/p>\n<p>Question 4.<br \/>\nWhich of the following is irrational?<br \/>\nOptions:<br \/>\na. -8<br \/>\nb. 4.63<br \/>\nc. \\(\\sqrt { x } \\)<br \/>\nd. \\(\\frac{1}{3}\\)<\/p>\n<p>Answer:<br \/>\nc. \\(\\sqrt { x } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { x } \\) is irrational<\/p>\n<p>Question 5.<br \/>\nGreg and Jane left a 15% tip after dinner. The amount of the tip was $9. Greg\u2019s dinner cost $24. Which equation can you use to find x, the cost of Jane\u2019s dinner?<br \/>\nOptions:<br \/>\na. 0.15x + 24 = 9<br \/>\nb. 0.15(x + 24) = 9<br \/>\nc. 15(x + 24) = 9<br \/>\nd. 0.15x = 24 + 9<\/p>\n<p>Answer:<br \/>\nb. 0.15(x + 24) = 9<\/p>\n<p>Explanation:<br \/>\nLet x be the cost of Jane&#8217;s dinner. The amount of tip is the 15% of the total cost of dinner.<br \/>\n0.15(x + 24) = 9<\/p>\n<p>Question 6.<br \/>\nFor the equation 3(2x \u2212 5) = 6x + k, which value of k will create an equation with infinitely many solutions?<br \/>\nOptions:<br \/>\na. 15<br \/>\nb. -5<br \/>\nc. 5<br \/>\nd. -15<\/p>\n<p>Answer:<br \/>\nd. -15<\/p>\n<p>Explanation:<br \/>\n3(2x &#8211; 5) = 6x + k<br \/>\n6x &#8211; 15 = 6x + k<br \/>\n6x &#8211; 15 = 6x &#8211; 15<br \/>\nThe statement is true. k = -15<\/p>\n<p>Question 7.<br \/>\nWhich of the following is equivalent to 2<sup>\u22124<\/sup>?<br \/>\nOptions:<br \/>\na. \\(\\frac{1}{16}\\)<br \/>\nb. \\(\\frac{1}{8}\\)<br \/>\nc. -2<br \/>\nd. -16<\/p>\n<p>Answer:<br \/>\na. \\(\\frac{1}{16}\\)<\/p>\n<p>Explanation:<br \/>\n2<sup>\u22124<\/sup><br \/>\n1\/2<sup>4<\/sup><br \/>\n1\/16<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 8.<br \/>\nUse the figures below for parts a and b.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-7-Solving-Linear-Equations-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations Mixed Review img 14\" width=\"328\" height=\"121\" \/><br \/>\na. Both figures have the same perimeter. Solve for x.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx=12<\/p>\n<p>Explanation:<br \/>\n4x+10=3x+22<br \/>\n4x &#8211; 3x = 22 &#8211; 10<br \/>\nx = 12<br \/>\nAnswer: x=12<\/p>\n<p>Question 8.<br \/>\nb. What is the perimeter of each figure?<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nBoth are 58<\/p>\n<p>Explanation:<br \/>\nx + x + 5 + x + x + 5<br \/>\n12 + 12 + 5 + 12 + 12 + 5<br \/>\n58<br \/>\nx + 7 + x + 4 + x + 11<br \/>\n12 + 7 + 12 + 4 + 12 + 11<br \/>\n58<\/p>\n<h3>Conclusion:<\/h3>\n<p>Go Math Grade 8 Answer Key is the best source to enhance your math skills. Learn all the solutions from Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations and complete your homework. Hope the information provided in Go Math Grade 8 Chapter 7 Solving Linear Equations Answer Key is satisfactory for all the 8th standard students. Stay with our CCSS Math Answers website to get the solutions of all grade 8 chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you searching for Go Math Grade 8 Answer Key Chapter 7 Solving Linear Equations? If your answer is yes, then you are on the right page. Students of 8th standard can get the Download link of HMH Go Math Grade 8 Solution Key Chapter 7 Solving Linear Equations for free. 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