{"id":5952,"date":"2022-03-25T16:27:48","date_gmt":"2022-03-25T10:57:48","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=5952"},"modified":"2022-04-07T12:56:40","modified_gmt":"2022-04-07T07:26:40","slug":"go-math-grade-7-answer-key-chapter-6-algebraic-expressions","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-7-answer-key-chapter-6-algebraic-expressions\/","title":{"rendered":"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions"},"content":{"rendered":"<p>Access the answers by downloading the 7th Grade HMH Go Math Answer Key Chapter 6 Algebraic Expressions pdf. We have prepared the solutions for all the questions in an easy manner. Thus we advise the students who are willing to score the highest marks to go through the <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-7-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 7 Answer Key<\/a> Chapter 6 Algebraic Expressions. The solutions seen in Go Math 7th Grade Solution Key Chapter 6 Algebraic Expressions are prepared by the math experts. So don&#8217;t worry about the solutions just go through the topics and start your preparation.<\/p>\n<h2>Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions<\/h2>\n<p>Download Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions pdf on this page. The topics covered in chapter 6 algebraic expressions are combining like terms using the properties. Refer to our Go Math Grade 7 Chapter 6 Algebraic Expression to prove yourself in the exams. Test and enhance your math skills by solving the questions provided at the end of the chapter.<\/p>\n<p><strong>Chapter 6 Algebraic Expressions &#8211; Lesson:1<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_176\">Guided Practice &#8211; Page No. 176<\/a><\/li>\n<li><a href=\"#Independent_Practice_Page_No_177\">Independent Practice &#8211; Page No. 177<\/a><\/li>\n<li><a href=\"#Page_No_178\">Page No. 178<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 6 Algebraic Expressions &#8211; Lesson:2<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_182\">Guided Practice &#8211; Page No. 182<\/a><\/li>\n<li><a href=\"#Independent_Practice_Page_No_183\">Independent Practice &#8211; Page No. 183<\/a><\/li>\n<li><a href=\"#Page_No_184\">Page No. 184<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 6 Algebraic Expressions &#8211; Lesson:3<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_188\">Guided Practice &#8211; Page No. 188<\/a><\/li>\n<li><a href=\"#Independent_Practice_Page_No_189\">Independent Practice &#8211; Page No. 189<\/a><\/li>\n<li><a href=\"#Page_No_190\">Page No. 190<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 6 Algebraic Expressions &#8211; Lesson:4<\/strong><\/p>\n<ul>\n<li><a href=\"#Guided_Practice_Page_No_194\">Guided Practice &#8211; Page No. 194<\/a><\/li>\n<li><a href=\"#Page_No_195\">Page No. 195<\/a><\/li>\n<li><a href=\"#Page_No_196\">Page No. 196<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 6 Algebraic Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#6.1_Algebraic_Expressions_Page_No_197\">6.1 Algebraic Expressions &#8211; Page No. 197<\/a><\/li>\n<li><a href=\"#Selected_Response_Page_No_198\">Selected Response &#8211; Page No. 198<\/a><\/li>\n<\/ul>\n<h3><a id=\"Guided_Practice_Page_No_176\"><\/a>Guided Practice &#8211; Page No. 176<\/h3>\n<p>Question 1.<br \/>\nThe manager of a summer camp has 14 baseballs and 23 tennis balls. The manager buys some boxes of baseballs with 12 baseballs to a box and an equal number of boxes of tennis balls with 16 tennis balls to a box. Write an expression to represent the total number of balls.<br \/>\n______ + ______ n<\/p>\n<p>Answer: 37 + 28n<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe manager of a summer camp has 14 baseballs and 23 tennis balls.<br \/>\nThe manager buys some boxes of baseballs with 12 baseballs to a box and an equal number of boxes of tennis balls with 16 tennis balls to a box.<br \/>\nLet n be the number of boxes of each type<br \/>\nBaseballs: 14 + 12n<br \/>\nTennis Balls: 23 + 16n<br \/>\nNow add the like terms<br \/>\n14 + 12n + 23 + 16n<br \/>\n(14 + 23) + (12 + 16)n<br \/>\n37 + 28n<br \/>\nThus the expression for the total number of balls is 37 + 28n<\/p>\n<p>Question 2.<br \/>\nUse the expression you found above to find the total number of baseballs and tennis balls if the manager bought 9 boxes of each type.<\/p>\n<p>Answer: 289<\/p>\n<p>Explanation:<br \/>\nThe expression we found in the above question is 37 + 28n<br \/>\nn = 9 boxes<br \/>\nSubstitute the value of n in the expression<br \/>\n37 + 28(9) = 37 + 252 = 289<br \/>\nThus the total number of balls = 289<\/p>\n<p><strong>Use the Distributive Property to expand each expression.<\/strong><\/p>\n<p>Question 3.<br \/>\n0.5(12m &#8211; 22n)<br \/>\n______ m &#8211; ______ n<\/p>\n<p>Answer: 6m &#8211; 11n<\/p>\n<p>Explanation:<br \/>\nWe use the Distributive Property to expand the expression.<br \/>\n0.5(12m &#8211; 22n) = 0.5(12m) &#8211; 0.5(22n)<br \/>\n= 16m &#8211; 11n<br \/>\nThus the expansion of 0.5(12m &#8211; 22n) is 16m &#8211; 11n<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{3}\\)(18x + 6z)<br \/>\n______ x + ______ z<\/p>\n<p>Answer: 12x + 4z<\/p>\n<p>Explanation:<br \/>\nWe use the Distributive Property to expand the expression.<br \/>\n\\(\\frac{2}{3}\\)(18x + 6z) = \\(\\frac{2}{3}\\)(18x) + \\(\\frac{2}{3}\\)(6z)<br \/>\n= \\(\\frac{36}{3}\\) + \\(\\frac{12}{3}\\)<br \/>\n= 12x + 4z<br \/>\nThus the expansion of \\(\\frac{2}{3}\\)(18x + 6z) is 12x + 4z<\/p>\n<p><strong>Factor each expression.<\/strong><\/p>\n<p>Question 5.<br \/>\n2x + 12<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 2(x + 6)<\/p>\n<p>Explanation:<br \/>\nThe common factor is 2. We factor the expression,<br \/>\n2x + 12 = 2(x + 6)<\/p>\n<p>Question 6.<br \/>\n12x + 24<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 12(x + 2)<\/p>\n<p>Explanation:<br \/>\nThe common factor is 12. We factor the expression,<br \/>\n12x + 24 = 12(x + 2)<\/p>\n<p>Question 7.<br \/>\n7x + 35<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 7(x + 5)<\/p>\n<p>Explanation:<br \/>\nThe common factor is 7. We factor the expression,<br \/>\n7x + 35 = 7(x + 5)<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 8.<br \/>\nWhat is the relationship between multiplying and factoring?<\/p>\n<p>Answer:<br \/>\nFactoring a number means writing it as a product &#8211; a list of numbers which when multiplied, give you the original number, thus factoring implies multiplication.<br \/>\nOn the other hand, we can interpret the relationship between factoring and multiplication as one opposition because factoring an expression means dividing each term of the expression by the same number\/factor.<\/p>\n<h3><a id=\"Independent_Practice_Page_No_177\"><\/a>Independent Practice &#8211; Page No. 177<\/h3>\n<p><strong>Write and simplify an expression for each situation.<\/strong><\/p>\n<p>Question 9.<br \/>\nA company rents out 15 food booths and 20 game booths at the county fair. The fee for a food booth is $100 plus $5 per day. The fee for a game booth is $50 plus $7 per day. The fair lasts for d days, and all the booths are rented for the entire time. Write and simplify an expression for the amount in dollars that the company is paid.<br \/>\n______ + ______ d<\/p>\n<p>Answer: 2500 + 215d<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA company rents out 15 food booths and 20 game booths at the county fair.<br \/>\nThe fee for a food booth is $100 plus $5 per day.<br \/>\nThe fee for a game booth is $50 plus $7 per day.<br \/>\nLet d be the number of days for which the booths are rented.<br \/>\nWe have to write the expression for the amount of money for the food booths<br \/>\n15(100 + 5d)<br \/>\nWe have to write the expression for the amount of money for the game booths<br \/>\n20(50 + 7d)<br \/>\nWe have to write the expression for the amount of money for all the booths<br \/>\n15(100 + 5d) + 20(50 + 7d)<br \/>\n1500 + 75d + 1000 + 140d<br \/>\nCombine the like terms<br \/>\n2500 + 215d<br \/>\nThus the expression for the amount in dollars that the company is paid is 2500 + 215d<\/p>\n<p>Question 10.<br \/>\nA rug maker is using a pattern that is a rectangle with a length of 96 inches and a width of 60 inches. The rug maker wants to increase each dimension by a different amount. Let l and w be the increases in inches of the length and width. Write and simplify an expression for the perimeter of the new pattern.<br \/>\n______ + ______ l + ______ w<\/p>\n<p>Answer:<br \/>\nA rug maker is using a pattern that is a rectangle with a length of 96 inches and a width of 60 inches. The rug maker wants to increase each dimension by a different amount.<br \/>\nThe formula for the perimeter of a rectangle is 2 Length+ 2 Width<br \/>\n2 \u00d7(96+l+60+w)<br \/>\n=2\u00d7(156+l+w)<br \/>\n=(312+2l+2w) inches<\/p>\n<p><strong>In 11 &#8211; 12, identify the two factors that were multiplied together to form the array of tiles. Then identify the product of the two factors.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-1.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 1\" width=\"61\" height=\"101\" \/><br \/>\n______ x + ______<\/p>\n<p>Answer: 3x + 6<\/p>\n<p>Explanation:<br \/>\nThe two factors are<br \/>\nWidth = 3<br \/>\nLength = x + 2<br \/>\nThe area is the product of the two numbers:<br \/>\n3(x + 2) = 3(x) + 3(2)<br \/>\n3x + 6<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-2.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 2\" width=\"83\" height=\"140\" \/><br \/>\n______ x &#8211; ______<\/p>\n<p>Answer: 8x &#8211; 4<\/p>\n<p>Explanation:<br \/>\nThe two factors are<br \/>\nWidth = 4<br \/>\nLength = 2x &#8211; 1<br \/>\nThe area is the product of the two numbers:<br \/>\n4(2x &#8211; 1) = 4(2x) + 4(-1) = 8x &#8211; 4<\/p>\n<p>Question 13.<br \/>\nExplain how the figure illustrates that 6(9) = 6(5) + 6(4).<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-3.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 3\" width=\"188\" height=\"125\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNote that the left part of the figure has 6 units from top to bottom and 5 units from left to right making it 6 \u00d7 5. On the other hand, the right part has also 6 units from top to bottom but 4 units from left to right making it 6 \u00d7 4. Adding the two expressions will give (6 \u00d7 5) + (6 \u00d7 4).<\/p>\n<p><strong>In 14\u201315, the perimeter of the figure is given. Find the length of the indicated side.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-4.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 4\" width=\"246\" height=\"147\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 3x &#8211; 7<\/p>\n<p>Explanation:<br \/>\nWe know that the perimeter of a figure is the sum of all sides. Therefore, we can identify the length of the other side by representing it with a variable, s<br \/>\nside + side + side = perimeter<br \/>\ns + (x + 3) + (2x +4) = 6x<br \/>\ns + 3x + 7 = 6x<br \/>\ns = 6x &#8211; 3x &#8211; 7<br \/>\nCombine the like terms<br \/>\ns = 3x &#8211; 7<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-5.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 5\" width=\"228\" height=\"137\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 2x + 6<\/p>\n<p>Explanation:<br \/>\nWe know that the perimeter of a figure is the sum of all sides. Therefore, we can identify the length of the other side by representing it with a variable, s<br \/>\n2side + 2side = perimeter<br \/>\n2s + 2(3x &#8211; 3) = 10x + 6<br \/>\n2s + 6x &#8211; 6 = 10x + 6<br \/>\n2s = 10x + 6 -6x + 6<br \/>\n2s = 4x + 12<br \/>\n2s = 2(2x+ 6)<br \/>\ns = 2x + 6<\/p>\n<h3><a id=\"Page_No_178\"><\/a>Page No. 178<\/h3>\n<p>Question 16.<br \/>\nPersevere in Problem Solving<br \/>\nThe figures show the dimensions of a tennis court and a basketball court given in terms of the width x in feet of the tennis court.<br \/>\na. Write an expression for the perimeter of each court.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-6.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 6\" width=\"477\" height=\"143\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSince the courts are rectangle, we can add all sides of the court using the given expressions:<br \/>\nTennis:<br \/>\nx + x + (2x + 6) + (2x + 6)<br \/>\n= 2x + 4x + 12<br \/>\n= 6x + 12<br \/>\nBasketball:<br \/>\n(1\/2 x + 32) + (1\/2 x + 32) + (3x &#8211; 14) + (3x &#8211; 14)<br \/>\nx + 64 + 6x &#8211; 28<br \/>\nNow combine the like terms<br \/>\n7x + 36<\/p>\n<p>Question 16.<br \/>\nb. Write an expression that describes how much greater the perimeter of the basketball court is than the perimeter of the tennis court.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: x + 24<\/p>\n<p>Explanation:<br \/>\nSince the perimeter of the basketball court is larger, we subtract the perimeter of the tennis court from this.<br \/>\nTherefore the expression is (7x + 36) &#8211; (6x + 12)<br \/>\n= 7x + 36 &#8211; 6x &#8211; 12 = x + 24<\/p>\n<p>Question 16.<br \/>\nc. Suppose the tennis court is 36 feet wide. Find all dimensions of the two courts.<br \/>\nWidth of the tennis court: _________ feet<br \/>\nLength of the tennis court: _________ feet<br \/>\nWidth of basketball court: _________ feet<br \/>\nLength of the basketball court: _________ feet<\/p>\n<p>Answer:<br \/>\nTo find all dimensions, we substitute 36 in x of the tennis court and solve for the length.<br \/>\nFor the tennis court:<br \/>\nWidth: x = 36 feet<br \/>\nLength: 2x + 6 = 2(36) + 6 = 72 + 6 = 78 feet<br \/>\nFor the basketball court:<br \/>\nWidth: 1\/2 x + 32 = 1\/21(36) + 32 = 18 + 32 = 50 feet<br \/>\nLength: 3x &#8211; 14 = 3(36) &#8211; 14 = 108 &#8211; 14 = 94 feet<\/p>\n<p>Question 17.<br \/>\nDraw Conclusions<br \/>\nUse the figure to find the product (x + 3)(x + 2). (Hint: Find the area of each small square or rectangle, then add.)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-7.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 7\" width=\"126\" height=\"114\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: x\u00b2 + 5x + 6<\/p>\n<p>Explanation:<br \/>\nWe can add the area of the smaller squares to find the area of the entire figure.<br \/>\nNote that there is one x.x = x\u00b2<br \/>\nThere are 3(x.1) = 3x<br \/>\nThere are 2(x.1) = 2x<br \/>\nThere are 6(1.1) = 6<br \/>\nAdding these together we get x\u00b2 + 3x + 2x + 6 = x\u00b2 + 5x + 6<\/p>\n<p>Question 18.<br \/>\nCommunicate Mathematical Ideas<br \/>\nDesmond claims that the product shown at the right illustrates the Distributive Property. Do you agree? Explain why or why not.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-8.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 8\" width=\"56\" height=\"114\" \/><br \/>\n________<\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nThe multiplication can be written:<br \/>\n58 \u00d7 23 = 58(20 + 3)<br \/>\n58(20) + 58(3)<br \/>\n1160 + 174<br \/>\nWe notice that the products 174 and 1160 were obtained using the Distributive Property.<\/p>\n<p>Question 19.<br \/>\nJustify Reasoning<br \/>\nDescribe two different ways that you could find the product 8 \u00d7 997 using mental math. Find the product and explain why your methods work.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWe are given the product<br \/>\n8 \u00d7 997<br \/>\nFor a mental computation, we use the fact that 997 is close to 1000<br \/>\n8 \u00d7 997 = 8 . (1000 &#8211; 3)<br \/>\n8 \u00d7 1000 &#8211; 8 \u00d7 3<br \/>\n8000 &#8211; 24<br \/>\n7976<br \/>\nOther method:<br \/>\n8 \u00d7 997 = 8 . (900 + 90 + 7)<br \/>\n8(900) + 8(90) + 8(7)<br \/>\n7200 + 720 + 56<br \/>\n7976<\/p>\n<h3><a id=\"Guided_Practice_Page_No_182\"><\/a>Guided Practice &#8211; Page No. 182<\/h3>\n<p><strong>The table shows the average temperature in Barrow, Alaska, for three months during one year.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-9.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 9\" width=\"251\" height=\"139\" \/><\/p>\n<p>Question 1.<br \/>\nHow many degrees warmer is the average temperature in November than in January?<br \/>\n________ \u00b0F<\/p>\n<p>Answer: 11.7\u00b0F<\/p>\n<p>Explanation:<br \/>\nLet x represent the number of degrees the temperature in November is warmer than in January.<br \/>\nx + (-13.4) = -1.7<br \/>\nx &#8211; 13.4 + 13.4 = -1.7 + 3.4<br \/>\nx = 11.7<br \/>\nThus the average temperature in November is 11.7\u00b0F warmer.<\/p>\n<p>Question 2.<br \/>\nSuppose that during one period of extreme cold, the average daily temperature decreased 1 \\(\\frac{1}{2}\\) \u00b0F each day. How many days did it take for the temperature to decrease by 9 \u00b0F?<br \/>\n________ days<\/p>\n<p>Answer: 6 days<\/p>\n<p>Explanation:<br \/>\nLet x be the number of days it took for the temperature to decrease by 9 \u00b0F<br \/>\n(-1 1\/2)x = -9<br \/>\n-3\/2x = -9<br \/>\n-3x = -18<br \/>\nx = 6<br \/>\nIt took 6 days for the temperature to decrease by 9\u00b0F.<\/p>\n<p><strong>Use inverse operations to solve each equation.<\/strong><\/p>\n<p>Question 3.<br \/>\n\u22122x = 34<br \/>\n________<\/p>\n<p>Answer: -17<\/p>\n<p>Explanation:<br \/>\nWe are given the equation:<br \/>\n\u22122x = 34<br \/>\nx = -17<\/p>\n<p>Question 4.<br \/>\ny \u2212 3.5 = \u22122.1<br \/>\n________<\/p>\n<p>Answer: 1.4<\/p>\n<p>Explanation:<br \/>\nWe are given the equation:<br \/>\ny \u2212 3.5 = \u22122.1<br \/>\ny = -2.1 + 3.5<br \/>\ny = 1.4<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{2}{3}\\) z = \u22126<br \/>\n________<\/p>\n<p>Answer: -9<\/p>\n<p>Explanation:<br \/>\nWe are given the equation:<br \/>\n\\(\\frac{2}{3}\\) z = \u22126<br \/>\nz = -6 \u00d7 \\(\\frac{3}{2}\\)<br \/>\nz = -9<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nHow does writing an equation help you solve a problem?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWriting an equation helps us model a problem. Once the equation is written, we can apply mathematical rules to determine the unknown in the equation.<\/p>\n<h3><a id=\"Independent_Practice_Page_No_183\"><\/a>Independent Practice &#8211; Page No. 183<\/h3>\n<p><strong>The table shows the elevation in feet at the peaks of several mountains. Use the table for 7\u20139.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-10.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 10\" width=\"324\" height=\"152\" \/><\/p>\n<p>Question 7.<br \/>\nMt. Everest is 8,707.37 feet higher than Mt. McKinley. What is the elevation of Mt. Everest?<br \/>\n________ feet<\/p>\n<p>Answer: 29,087.87<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nMt. Everest is 8,707.37 feet higher than Mt. McKinley.<br \/>\nAdd 8707.37 to the height of the Mt. McKinley to find the height of the Mt. Everest.<br \/>\n20,321.5 + 8,707.37 = 29,028.87<br \/>\nThus the elevation of Mt. Everest is 29,087.87 feet<\/p>\n<p>Question 8.<br \/>\nLiam descended from the summit of K2 to an elevation of 23,201.06 feet. How many feet did Liam descend? What was his change in elevation?<br \/>\n________ feet<\/p>\n<p>Answer: 5050.25 feet<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nLiam descended from the summit of K2 to an elevation of 23,201.06 feet.<br \/>\nSubtract the height of the K2 mountain and his elevation after descending to find the number of feet he descended. Since he descended down the mountain the change in elevation is the negative of the number of feet he descended.<br \/>\ndescent: 28,251.31 &#8211; 23,201.06 = 5050.25 feet<br \/>\nchange in elevation: -5050.25 feet<\/p>\n<p>Question 9.<br \/>\nK2 is 11,194.21 feet higher than Mt. Kenya. Write and solve an equation to find the elevation of Mt. Kenya.<br \/>\n________ feet<\/p>\n<p>Answer: 17,057.1<\/p>\n<p>Explanation:<br \/>\nLet h be the height of Mt. Kenya.<br \/>\nWrite the equation using the given information that K2, with a height of 28,251.31 feet, is 11,194.21 feet higher than Mt. Kenya.<br \/>\nh + 11,194.21 = 28, 251.31<br \/>\nh = 17057.1 feet<\/p>\n<p>Question 10.<br \/>\nA hot air balloon begins its descent at a rate of 22 \\(\\frac{1}{2}\\) feet per minute. How long will it take for the balloon&#8217;s elevation to change by -315 feet?<br \/>\n________ minutes<\/p>\n<p>Answer: 14 minutes<\/p>\n<p>Explanation:<br \/>\nA hot air balloon begins its descent at a rate of 22 \\(\\frac{1}{2}\\) feet per minute.<br \/>\n315\/22 \\(\\frac{1}{2}\\) = 315\/\\(\\frac{45}{2}\\)<br \/>\n= 315 \u00d7 \\(\\frac{2}{45}\\) = 14 minutes<\/p>\n<p>Question 11.<br \/>\nDuring another part of its flight, the balloon in Exercise 10 had a change in elevation of -901 feet in 34 minutes. What was its rate of descent?<br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\) feet per minute<\/p>\n<p>Answer:<\/p>\n<p>Divide the number of feet by the number of minutes<br \/>\n\\(\\frac{901}{34}\\) = 26.5 feet per minute<br \/>\n(Or)<br \/>\n\\(\\frac{901}{10}\\) = 90.1 feet per minute<\/p>\n<p><strong>The table shows the average temperatures in several states from January through March. Use the table for 12\u201314.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-11.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 11\" width=\"321\" height=\"153\" \/><\/p>\n<p>Question 12.<br \/>\nWrite and solve an equation to find how much warmer Montana&#8217;s average 3-month temperature is than Minnesota&#8217;s.<br \/>\n________ \u00b0C<\/p>\n<p>Answer: 1.8\u00b0C<\/p>\n<p>Explanation:<br \/>\nWrite an equation where t is the number of degrees warmer than Montana&#8217;s temperature is compared to Minnesota&#8217;s<br \/>\n-2.5 + t = -0.7<br \/>\nt = -0.7 + 2.5<br \/>\nt = 1.8\u00b0C<\/p>\n<p>Question 13.<br \/>\nHow much warmer is Florida&#8217;s average 3-month temperature than Montana&#8217;s?<br \/>\n________ \u00b0C<\/p>\n<p>Answer: 18.8\u00b0C<\/p>\n<p>Explanation:<br \/>\nSubtract Florida and Montana&#8217;s temperatures<br \/>\n18.1 &#8211; (-0.7) = 18.1 + 0.7 = 18.8\u00b0C<\/p>\n<p>Question 14.<br \/>\nHow would the average temperature in Texas have to change to match the average temperature in Florida?<br \/>\n________ \u00b0C<\/p>\n<p>Answer: increase by 5.6\u00b0C<\/p>\n<p>Explanation:<br \/>\nSubtract Florida and Texas&#8217;s temperatures<br \/>\n18.1 &#8211; 12.5 = 5.6 \u00b0C<\/p>\n<p>Question 15.<br \/>\nA football team has a net yardage of \u221226 \\(\\frac{1}{3}\\) yards on a series of plays. The team needs a net yardage of 10 yards to get a first down. How many yards do they have to get on their next play to get a first down?<br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\) yards<\/p>\n<p>Answer: 36 \\(\\frac{1}{3}\\) yards<\/p>\n<p>Explanation:<br \/>\nSubtract the final net yardage and the current net yardage to find how many more yards they need<br \/>\n10 &#8211; (\u221226 \\(\\frac{1}{3}\\)) = 10 + 26 \\(\\frac{1}{3}\\)<br \/>\n= 36 \\(\\frac{1}{3}\\)<br \/>\nThey have to get 36 \\(\\frac{1}{3}\\) yards on their next play to get the first down.<\/p>\n<h3><a id=\"Page_No_184\"><\/a>Page No. 184<\/h3>\n<p>Question 16.<br \/>\nA diver begins at sea level and descends vertically at a rate of 2 \\(\\frac{1}{2}\\) feet per second. How long does the diver take to reach -15.6 feet?<br \/>\n________ seconds<\/p>\n<p>Answer: 6.24 seconds<\/p>\n<p>Explanation:<br \/>\nDivide the number of feet the diver descends by the rate of descent.<br \/>\ntime = distance\/rate<br \/>\n\\(\\frac{-15.6}{-2.5}\\)<br \/>\n= 6.24 seconds<\/p>\n<p>Question 17.<br \/>\nAnalyze Relationships<br \/>\nIn Exercise 16, what is the relationship between the rate at which the diver descends, the elevation he reaches, and the time it takes to reach that elevation?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: The elevation he reaches (y) is directly proportional to the time it takes to reach that elevation (x) and the rate of descent is (k) the constant of proportionality.<\/p>\n<p>Question 18.<br \/>\nCheck for Reasonableness<br \/>\nJane withdrew money from her savings account in each of 5 months. The average amount she withdrew per month was $45.50. How much did she withdraw in all during the 5 months? Show that your answer is reasonable.<br \/>\n$ ________<\/p>\n<p>Answer: $227.50<\/p>\n<p>Explanation:<br \/>\nMultiply the amount she withdrew per month by the number of months.<br \/>\n45.50 \u00d7 5 = 227.50<br \/>\nSince 45.50 \u2248 50 and 50 \u00d7 5 = 250 which is close to 227.50, the answer is reasonable.<\/p>\n<p>Question 19.<br \/>\nJustify Reasoning<br \/>\nConsider the two problems below. Which values in the problems are represented by negative numbers? Explain why.<\/p>\n<p>(1) A diver below sea level ascends 25 feet to a reef at -35.5 feet. What was the elevation of the diver before she ascended to the reef?<\/p>\n<p>(2) A plane descends 1.5 miles to an elevation of 3.75 miles. What was the elevation of the plane before its descent?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe elevation of -35.5 and the elevation after ascending are both represented by the negative numbers. The change in elevation is represented by a negative number since the plane is descending.<\/p>\n<p>Question 20.<br \/>\nAnalyze Relationships<br \/>\nHow is solving -4x = -4.8 different from solving \u2212 \\(\\frac{1}{4}\\) x = -4.8? How are the solutions related?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWhen you are solving -4x = -4.8, you are dividing both sides by -4 to solve for x.<br \/>\nWhen you are solving \u2212 \\(\\frac{1}{4}\\) x = -4.8, you are multiplying both sides by -4 to solve for x.<br \/>\nThe answers for the second equation is then 16 times the answer to the first problem since 4 \u00d7 4 = 16<\/p>\n<p>Question 21.<br \/>\nCommunicate Mathematical Ideas<br \/>\nFlynn opens a savings account. In one 3-month period, he makes deposits of $75.50 and $55.25. He makes withdrawals of $25.15 and $18.65. His balance at the end of the 3-month period is $210.85. Explain how you can find his initial deposit amount.<br \/>\n$ ________<\/p>\n<p>Answer: $123.90<\/p>\n<p>Explanation:<br \/>\nLet x be his initial deposit. Write the equation for his balance after making the additional deposits and withdrawals.<br \/>\nx + 75.50 + 55.25 &#8211; 25.15 &#8211; 18.65 = 210.58<br \/>\nx + 86.95 = 210.85<br \/>\nSimplify the left side of the equation<br \/>\nx = 123.90<br \/>\nThus the initial deposit amount is $123.90<\/p>\n<h3><a id=\"Guided_Practice_Page_No_188\"><\/a>Guided Practice &#8211; Page No. 188<\/h3>\n<p><strong>Draw algebra tiles to model the given two-step equation.<\/strong><\/p>\n<p>Question 1.<br \/>\n2x + 5 = 7<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-6-Answer-Key-solution-img-1-300x147.jpg\" alt=\"Go Math Grade 7 Chapter 6 Answer Key solution img-1\" width=\"300\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-6-Answer-Key-solution-img-1-300x147.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-6-Answer-Key-solution-img-1.jpg 483w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFirst, draw two positive rectangles on the left to represent 2x and five positive squares to represent 5. One the right side, draw 7 positive squares to represent 7.<\/p>\n<p>Question 2.<br \/>\n\u22123 = 5 \u2212 4x<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<\/p>\n<p>Draw 3 negative squares on the left side to represent -3. On the right side, draw 5 positive squares to represent 5 and 4 negative rectangles to represent -4x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-6-answer-key-solution-img-2-300x147.jpg\" alt=\"Go Math Grade 7 Chapter 6 answer key solution img-2\" width=\"300\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-6-answer-key-solution-img-2-300x147.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Chapter-6-answer-key-solution-img-2.jpg 483w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\nA group of adults plus one child attend a movie at Cineplex 15. Tickets cost $9 for adults and $6 for children. The total cost for the movie is $78. Write an equation to find the number of adults in the group.<br \/>\n________ adults<\/p>\n<p>Answer: 8 adults<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA group of adults plus one child attend a movie at Cineplex 15.<br \/>\nTickets cost $9 for adults and $6 for children.<br \/>\nThe total cost for the movie is $78.<br \/>\nWrite the equation for the total cost letting a be the number of adults.<br \/>\n9a + 6 = 78<br \/>\n9a = 72<br \/>\na = 8<br \/>\nTherefore there are 8 adults in the group.<\/p>\n<p>Question 4.<br \/>\nBreak down the equation 2x + 10 = 16 to analyze each part.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSince x is the value we are trying to find, x is the solution. This means that 2x is the quantity we are looking for multiplied by 2. The 10 is added to 2x = 16 means the result is 16.<\/p>\n<p>Question 5.<br \/>\nWrite a corresponding real-world problem to represent 2x &#8211; 125 = 400.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nA real-world problem could be: You are selling lemonade one summer. You paid a total of $125 for all the supplies you needed. If you charge customers $2 per cup of lemonade, how many cups of lemonade do you have to sell to make a profit of $400?<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nDescribe the steps you would follow to write a two-step equation you can use to solve a real-world problem.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nFirst you must define what you are looking for with a variable. In the real-world problem I wrote a problem 5, the variable, x represents the number of cups sold. Next, decide how the remaining information is related to the variable. Since x is the number of cups sold and $2 is the price per cup, then the equation needs to have 2x.<br \/>\nSince profit = income &#8211; the cost of supplies, the cost of $125 needs to be subtracted from 2x and the equation needs to equal to the profit of $400. This would give an equation of 2x &#8211; 125 = 400.<\/p>\n<h3><a id=\"Independent_Practice_Page_No_189\"><\/a>Independent Practice &#8211; Page No. 189<\/h3>\n<p>Question 7.<br \/>\nDescribe how to model -3x + 7 = 28 with algebra tiles.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nOn the left side, draw 3 negative rectangles to represent -3x and 7 positive squares to represent 7. On the right side, draw 28 positive squares to represent 28.<\/p>\n<p>Question 8.<br \/>\nVal rented a bicycle while she was on vacation. She paid a flat rental fee of $55.00, plus $8.50 each day. The total cost was $123. Write an equation you can use to find the number of days she rented the bicycle.<br \/>\n________ days<\/p>\n<p>Answer: 8 days<\/p>\n<p>Explanation:<br \/>\nLet x be the number of days then the daily fees are 8.50x.<br \/>\nSince there is a flat fee of $55, the total fees are 8.50x + 55<br \/>\n8.50x + 55 = 123<br \/>\n8.50x = 123 &#8211; 55<br \/>\n8.50x = 68<br \/>\nx = 68\/8.50<br \/>\nx = 8<br \/>\nThus she rented the bicycle for 8 days.<\/p>\n<p>Question 9.<br \/>\nA restaurant sells a coffee refill mug for $6.75. Each refill costs $1.25. Last month Keith spent $31.75 on a mug and refills. Write an equation you can use to find the number of refills that Keith bought.<br \/>\n________ refills<\/p>\n<p>Answer: 20 refills<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA restaurant sells a coffee refill mug for $6.75.<br \/>\nEach refill costs $1.25. Last month Keith spent $31.75 on a mug and refills.<br \/>\nLet x represent the number of refills then the total for refills is 1.25x.<br \/>\nSince the cost of the mug was $6.75, the total cost is 6.75 + 1.25x<br \/>\n6.75 + 1.25x = 31.75<br \/>\n1.25x = 31.75 &#8211; 6.75<br \/>\n1.25x = 25<br \/>\nx = 25\/1.25<br \/>\nx = 20<br \/>\nThus the number of refills that Keith bought is 20 refills.<\/p>\n<p>Question 10.<br \/>\nA gym holds one 60-minute exercise class on Saturdays and several 45-minute classes during the week. Last week all of the classes lasted a total of 285 minutes. Write an equation you can use to find the number of weekday classes.<br \/>\n________ classes<\/p>\n<p>Answer: 5 classes<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA gym holds one 60-minute exercise class on Saturdays and several 45-minute classes during the week.<br \/>\nLast week all of the classes lasted a total of 285 minutes.<br \/>\nLet x be the number of 45 minute classes then the total time of 45 minute classes if 45x the total time of all classes is then 60 + 45x = 285<br \/>\n45x = 285 &#8211; 60<br \/>\n45x = 225<br \/>\nx = 225\/45<br \/>\nx = 5<br \/>\nThus the number of weekday classes is 5.<\/p>\n<p>Question 11.<br \/>\nMultiple Representations<\/p>\n<p>There are 172 South American animals in the Springdale Zoo. That is 45 more than half the number of African animals in the zoo. Write an equation you could use to find n, the number of African animals in the zoo.<br \/>\n________ animals<\/p>\n<p>Answer: 254 animals<\/p>\n<p>Explanation:<br \/>\nThere are 172 South American animals in the Springdale Zoo. That is 45 more than half the number of African animals in the zoo.<br \/>\nn\/2 + 45 = 172<br \/>\nn\/2 = 172 &#8211; 45<br \/>\nn\/2 = 127<br \/>\nn = 127 \u00d7 2<br \/>\nn = 254 animals<br \/>\nThus the number of African animals in the zoo is 254.<\/p>\n<p>Question 12.<br \/>\nA school bought $548 in basketball equipment and uniforms costing $29.50 each. The total cost was $2,023. Write an equation you can use to find the number of uniforms the school purchased.<br \/>\n________ uniforms<\/p>\n<p>Answer: 50 uniforms<\/p>\n<p>Explanation:<br \/>\nThe total cost is equal to the cost of the basketball equipment plus the cost of the uniforms.<br \/>\nLet x represent the number of uniforms. Since each uniform costs $29.50, then the cost of x uniforms is 29.50x dollars.<br \/>\nThe cost of the basketball equipment is $548 so the total cost is 548 + 29.50x<br \/>\nIt is given that the total cost is $2023 so setting this equal to the expression we obtained for the total cost gives the equation 548 + 29.50x = 2023<br \/>\n29.50x = 2023 &#8211; 548<br \/>\n29.50x = 1475<br \/>\nx = 1475\/29.50<br \/>\nx = 50<br \/>\nThus the number of uniforms the school purchased is 50.<\/p>\n<p>Question 13.<br \/>\nFinancial Literacy<br \/>\nHeather has $500 in her savings account. She withdraws $20 per week for gas. Write an equation Heather can use to see how many weeks it will take her to have a balance of $220.<br \/>\n________ weeks<\/p>\n<p>Answer: 14 weeks<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nHeather has $500 in her savings account. She withdraws $20 per week for gas.<br \/>\nLet x be the number of weeks. Since she is withdrawing $20 each week, then after x weeks her account has changed by -20x dollars.<br \/>\nHer original balance was $500 so after x weeks, her ending balance is 500 &#8211; 20x dollars.<br \/>\nIt is given that her ending balance is $220 so the equation is<br \/>\n500 &#8211; 20x = 220<br \/>\n-20x = 220 &#8211; 500<br \/>\n-20x = -280<br \/>\nx = 280\/20<br \/>\nx = 14<br \/>\nIt will take 14 weeks to have a balance of $220.<\/p>\n<p>Question 14.<br \/>\nCritique Reasoning<br \/>\nFor 9x + 25 = 88, Deena wrote the situation \u201cI bought some shirts at the store for $9 each and received a $25 discount. My total bill was $88. How many shirts did I buy?\u201d<br \/>\na. What mistake did Deena make?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Her mistake was that a discount would decrease the amount she paid so her equation should have 25 subtracted, not added.<\/p>\n<p>Question 14.<br \/>\nb. Rewrite the equation to match Deena\u2019s situation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Changing the addition in 9x + 25 = 88 to subtraction gives 9x &#8211; 25 = 88<\/p>\n<p>Question 14.<br \/>\nc. How could you rewrite the situation to make it fit the equation?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: Instead of a discount, the situation could be rewritten to have her buying another item, like pants or a sweater, that cost $25.<\/p>\n<h3><a id=\"Page_No_190\"><\/a>Page No. 190<\/h3>\n<p>Question 15.<br \/>\nMultistep<br \/>\nSandy charges each family that she babysits a flat fee of $10 for the night and an extra $5 per child. Kimmi charges $25 per night, no matter how many children a family has.<br \/>\na. Write a two-step equation that would compare what the two girls charge and find when their fees are the same.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 10 + 5x = 25<\/p>\n<p>Explanation:<br \/>\nLet x be the number of children.<br \/>\nSandy charges each family that she babysits a flat fee of $10 for the night and an extra $5 per child. Kimmi charges $25 per night, no matter how many children a family has.<br \/>\nThis means that she charges a total of 10 + 5x per night.<br \/>\nKimmi only charges a flat fee of $25 per night,<br \/>\nSince you need to compare their charges, set these expressions equal to each other.<br \/>\nSandy: 10 + 5x<br \/>\nKimmi:\u00a0 25<br \/>\nThe equation is 10 + 5x = 25<\/p>\n<p>Question 15.<br \/>\nb. How many children must a family have for Sandy and Kimmi to charge the same amount?<br \/>\n________ children<\/p>\n<p>Answer: 3 children<\/p>\n<p>Explanation:<br \/>\nSubtract 10 on both sides and then divide both sides by 5 to solve for x.<br \/>\n10 + 5x = 25<br \/>\n5x = 25 &#8211; 10<br \/>\n5x = 15<br \/>\nx = 3 children<\/p>\n<p>Question 15.<br \/>\nc. The Sanderson family has five children. Which babysitter should they choose if they wish to save some money on babysitting, and why?<br \/>\n_____________<\/p>\n<p>Answer: Kimmi, saves them $10<\/p>\n<p>Explanation:<br \/>\nSubstitute x = 5 in the above equation for Sandy.<br \/>\n10 + 5(5) = 10 + 25 = 35<br \/>\nThis is $10 more than the $25 that Kimmi Charges so they should choose Kimmi because it will save them $10.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 16.<br \/>\nAnalyze Relationships<br \/>\nEach student wrote a two-step equation. Peter wrote the equation 4x &#8211; 2 = 10, and Andres wrote the equation 16x &#8211; 8 = 40. The teacher looked at their equations and asked them to compare them. Describe one way in which the equations are similar.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nEach student wrote a two-step equation. Peter wrote the equation 4x &#8211; 2 = 10, and Andres wrote the equation 16x &#8211; 8 = 40.<br \/>\n4x &#8211; 2 = 10<br \/>\n4x = 10 + 2<br \/>\n4x = 12<br \/>\nx = 3<br \/>\n16x &#8211; 8 = 40<br \/>\n16x = 40 + 8<br \/>\n16x = 48<br \/>\nx = 48\/16<br \/>\nx = 3<br \/>\nThey are also similar because if you multiply both sides of 4x &#8211; 2 = 10 by 4, you get 16x &#8211; 8 = 40<\/p>\n<p>Question 17.<br \/>\nWhat\u2019s the Error?<br \/>\nDamon has 5 dimes and some nickels in his pocket, worth a total of $1.20. To find the number of nickels Damon has, a student wrote the equation 5n + 50 = 1.20. Find the error in the student\u2019s equation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe error is that he wrote the amount of money on the left side of the equation in cents but wrote the amount of money on the left side of the equation in dollars. He needs to write the equation as either 5n + 50 = 120. or 0.05n + 0.50 = 1.20<\/p>\n<p>Question 18.<br \/>\nRepresent Real-World Problems<br \/>\nWrite a real-world problem you could answer by solving the equation -8x + 60 = 28.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nA possible real-world problem could be: You have $60 to spend on clothes. You want to buy some T-shirts that cost $8 each. After you went shopping, you had $28 left. How many T-shirts did you buy?<\/p>\n<h3><a id=\"Guided_Practice_Page_No_194\"><\/a>Guided Practice &#8211; Page No. 194<\/h3>\n<p><strong>The equation 2x + 1 = 9 is modeled below<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-6-Algebraic-Expressions-img-12.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 6 Algebraic Expressions img 12\" width=\"331\" height=\"87\" \/><\/p>\n<p>Question 1.<br \/>\nTo solve the equation with algebra tiles, first remove _____<br \/>\nThen divide each side into _____<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe first step is to remove one positive square on each side. Then divide each side into 2 equal groups.<\/p>\n<p>Question 2.<br \/>\nThe solution is x = _____<br \/>\nx = ______<\/p>\n<p>Answer: x = 4<\/p>\n<p>Explanation:<br \/>\nThe solution is x = 4 since removing one square on each side gives 2x = 8 and then dividing each side into two equal groups gives x = 4.<\/p>\n<p><strong>Solve each problem by writing and solving an equation.<\/strong><\/p>\n<p>Question 3.<br \/>\nA rectangular picture frame has a perimeter of 58 inches. The height of the frame is 18 inches. What is the width of the frame?<br \/>\n______ inches<\/p>\n<p>Answer: 11 inches<\/p>\n<p>Explanation:<br \/>\nA rectangular picture frame has a perimeter of 58 inches. The height of the frame is 18 inches.<br \/>\nThe perimeter of a rectangle is P = 2w + 2h.<br \/>\nIt is given that the perimeter of the rectangular frame is P = 58 inches and the height is h = 18 inches.<br \/>\nP = 2w + 2h<br \/>\n58 = 2w + 2(18)<br \/>\n2w = 58 &#8211; 36<br \/>\n2w = 22<br \/>\nw = 11 inches<br \/>\nThus the width of the frame is 11 inches.<\/p>\n<p>Question 4.<br \/>\nA school store has 1200 pencils in stock and sells an average of 24 pencils per day. The manager reorders when the number of pencils in stock is 500. In how many days will the manager have to reorder?<br \/>\n______ days<\/p>\n<p>Answer: 30 days<\/p>\n<p>Explanation:<br \/>\nA school store has 1200 pencils in stock and sells an average of 24 pencils per day.<br \/>\nThe manager reorders when the number of pencils in stock is 500.<br \/>\nLet x be the number of days<br \/>\n1200 &#8211; 24x = 500<br \/>\n-24x = -700<br \/>\nx \u2248 30<br \/>\nThus the manager has to reorder 30 days.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 5.<br \/>\nHow can you decide which operations to use to solve a two-step equation?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYou must use inverse operations when solving a two-step equation. You remove addition by subtracting the inverse operation of subtraction. You get rid of multiplication by using the inverse operation of division.<\/p>\n<h3><a id=\"Page_No_195\"><\/a>Page No. 195<\/h3>\n<p>Question 6.<br \/>\n9s + 3 = 57<br \/>\n______<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n9s + 3 = 57<br \/>\n9s = 57 &#8211; 3<br \/>\n9s = 54<br \/>\ns = 54\/9<br \/>\ns = 6<\/p>\n<p>Question 7.<br \/>\n4d + 6 = 42<br \/>\n______<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n4d + 6 = 42<br \/>\n4d = 42 &#8211; 6<br \/>\n4d = 36<br \/>\nd = 36\/4<br \/>\nd = 9<\/p>\n<p>Question 8.<br \/>\n\u22123y + 12 = \u221248<br \/>\n______<\/p>\n<p>Answer: 20<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22123y + 12 = \u221248<br \/>\n-3y = -48 &#8211; 12<br \/>\n-3y = -60<br \/>\n3y = 60<br \/>\ny = 20<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{k}{2}\\) + 9 = 30<br \/>\n______<\/p>\n<p>Answer: 42<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{k}{2}\\) + 9 = 30<br \/>\n\\(\\frac{k}{2}\\) = 30 &#8211; 9<br \/>\nk\/2 = 21<br \/>\nk = 42<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{g}{3}\\) \u2212 7 = 15<br \/>\n______<\/p>\n<p>Answer: 66<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{g}{3}\\) \u2212 7 = 15<br \/>\n\\(\\frac{g}{3}\\) = 15 + 7<br \/>\ng\/3 = 22<br \/>\ng = 22 \u00d7 3<br \/>\ng = 66<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{z}{5}\\) + 3 = \u221235<br \/>\n______<\/p>\n<p>Answer: -190<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{z}{5}\\) + 3 = \u221235<br \/>\n\\(\\frac{z}{5}\\) = \u221235 &#8211; 3<br \/>\nz\/5 = -38<br \/>\nz = -38 \u00d7 5<br \/>\nz = -190<\/p>\n<p>Question 12.<br \/>\n\u22129h \u2212 15 = 93<br \/>\n______<\/p>\n<p>Answer: -12<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22129h \u2212 15 = 93<br \/>\n-9h = 93 + 15<br \/>\n-9h = 108<br \/>\n-h = 108\/9<br \/>\nh = -12<\/p>\n<p>Question 13.<br \/>\n\u22123(n + 5) = 12<br \/>\n______<\/p>\n<p>Answer: -9<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22123(n + 5) = 12<br \/>\n-3n &#8211; 15 = 12<br \/>\n-3n = 12 + 15<br \/>\n-3n = 27<br \/>\n-n = 27\/3<br \/>\nn = -9<\/p>\n<p>Question 14.<br \/>\n\u221217 + \\(\\frac{b}{8}\\) = 13<br \/>\n______<\/p>\n<p>Answer: 240<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u221217 + \\(\\frac{b}{8}\\) = 13<br \/>\nb\/8 = 13 + 17<br \/>\nb\/8 = 30<br \/>\nb = 30 \u00d7 8<br \/>\nb = 240<\/p>\n<p>Question 15.<br \/>\n7(c \u2212 12) = \u221221<br \/>\n______<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n7(c \u2212 12) = \u221221<br \/>\n7c &#8211; 84 = -21<br \/>\n7c = -21 + 84<br \/>\n7c = 63<br \/>\nc = 63\/7<br \/>\nc = 9<\/p>\n<p>Question 16.<br \/>\n\u22123 + \\(\\frac{p}{7}\\) = \u22125<br \/>\n______<\/p>\n<p>Answer: -14<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22123 + \\(\\frac{p}{7}\\) = \u22125<br \/>\n\\(\\frac{p}{7}\\) = -5 + 3<br \/>\n\\(\\frac{p}{7}\\) = -2<br \/>\np = -2 \u00d7 7<br \/>\np = -14<\/p>\n<p>Question 17.<br \/>\n46 = \u22126t \u2212 8<br \/>\n______<\/p>\n<p>Answer: -9<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n46 = \u22126t \u2212 8<br \/>\n-6t &#8211; 8 = 46<br \/>\n-6t = 46 + 8<br \/>\n-6t = 54<br \/>\n-t = 54\/6<br \/>\nt = -9<\/p>\n<p>Question 18.<br \/>\nAfter making a deposit, Puja had $264 in her savings account. She noticed that if she added $26 to the amount originally in the account and doubled the sum, she would get the new amount. How much did she originally have in the account?<br \/>\n$ ______<\/p>\n<p>Answer: $106<\/p>\n<p>Explanation:<br \/>\nLet x be the original amount. Adding $26 to the original amount gives a sum of x + 26.<br \/>\nDoubling the sum then gives 2(x + 26) so the new amount is 2(x + 26) dollars.<br \/>\nIt is given that the new amount is $264 so 2(x + 26) = 264<br \/>\n2(x + 26) = 264<br \/>\nx + 26 = 264\/2<br \/>\nx + 26 = 132<br \/>\nx = 132 &#8211; 26<br \/>\nx = 106<br \/>\nThus she originally has $106 in the account.<\/p>\n<p>Question 19.<br \/>\nThe current temperature in Smalltown is 20 \u00b0F. This is 6 degrees less than twice the temperature that it was six hours ago. What was the temperature in Smalltown six hours ago?<br \/>\n______ \u00b0F<\/p>\n<p>Answer: 13\u00b0F<\/p>\n<p>Explanation:<br \/>\nThe current temperature in Smalltown is 20 \u00b0F. This is 6 degrees less than twice the temperature that it was six hours ago.<br \/>\nLet x be the temperature six hours ago<br \/>\n2x &#8211; 6 = 20<br \/>\n2x = 20 + 6<br \/>\n2x = 26<br \/>\nx = 13<br \/>\nThus the temperature is 13\u00b0F in Smalltown six hours ago.<\/p>\n<p>Question 20.<br \/>\nOne reading at an Arctic research station showed that the temperature was -35 \u00b0C. What is this temperature in degrees Fahrenheit?<br \/>\n______ \u00b0F<\/p>\n<p>Answer: -31\u00b0F<\/p>\n<p>Explanation:<br \/>\nOne reading at an Arctic research station showed that the temperature was -35 \u00b0C.<br \/>\nSubstitute C = -35 into the formula for converting Celsius and Fahrenheit temperatures<br \/>\nC = 5\/9 (F &#8211; 32)<br \/>\n-35 = \\(\\frac{5}{9}\\)(F &#8211; 32)<br \/>\n-35 \u00d7 \\(\\frac{9}{5}\\) = F &#8211; 32<br \/>\n-7 \u00d7 9 = F &#8211; 32<br \/>\n-63 = F &#8211; 32<br \/>\nF = -63 + 32<br \/>\nF = -31\u00b0F<br \/>\nThus the temperature in degrees Fahrenheit is -31\u00b0F<\/p>\n<p>Question 21.<br \/>\nArtaud noticed that if he takes the opposite of his age and adds 40, he gets the number 28. How old is Artaud?<br \/>\n______ years old<\/p>\n<p>Answer: 12 years old<\/p>\n<p>Explanation:<br \/>\nArtaud noticed that if he takes the opposite of his age and adds 40, he gets the number 28.<br \/>\nLet x be his age<br \/>\n-x + 40 = 28<br \/>\nx = 40 &#8211; 28<br \/>\nx = 12<br \/>\nThus Artaud is 12 years old.<\/p>\n<p>Question 22.<br \/>\nSven has 11 more than twice as many customers as when he started selling newspapers. He now has 73 customers. How many did he have when he started?<br \/>\n______ costumers<\/p>\n<p>Answer: 31 customers<\/p>\n<p>Explanation:<br \/>\nLet x be the number of customers he started with<br \/>\n11 + 2x = 73<br \/>\n2x = 73 &#8211; 11<br \/>\n2x = 62<br \/>\nx = 62\/2<br \/>\nx = 31<br \/>\nThus Sven has 31 customers when he started.<\/p>\n<p>Question 23.<br \/>\nPaula bought a ski jacket on sale for $6 less than half its original price. She paid $88 for the jacket. What was the original price?<br \/>\n$ ______<\/p>\n<p>Answer: $188<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nPaula bought a ski jacket on sale for $6 less than half its original price. She paid $88 for the jacket.<br \/>\nLet x be the original price<br \/>\n1\/2 x &#8211; 6 = 88<br \/>\n1\/2 x = 88 + 6<br \/>\n1\/2 x = 94<br \/>\nx = 94 \u00d7 2<br \/>\nx = 188<br \/>\nThus the original price is $188.<\/p>\n<p>Question 24.<br \/>\nThe McIntosh family went apple picking. They picked a total of 115 apples. The family ate a total of 8 apples each day. After how many days did they have 19 apples left?<br \/>\n______ days<\/p>\n<p>Answer: 12 days<\/p>\n<p>Explanation:<br \/>\nThe McIntosh family went apple picking. They picked a total of 115 apples. The family ate a total of 8 apples each day<br \/>\nLet x be the number of days.<br \/>\n115 &#8211; 8x = 19<br \/>\n115 &#8211; 19 = 8x<br \/>\n8x = 96<br \/>\nx = 96\/8<br \/>\nx = 12<br \/>\nThus the answer for the above question is 12 days.<\/p>\n<p><strong>Use a calculator to solve each equation.<\/strong><\/p>\n<p>Question 25.<br \/>\n\u22125.5x + 0.56 = \u22121.64<br \/>\n______<\/p>\n<p>Answer: 0.4<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22125.5x + 0.56 = \u22121.64<br \/>\nSubtract 0.56 on both sides<br \/>\n-5.5x = -2.2<br \/>\nDivide both sides by -5.5<br \/>\nx = 0.4<\/p>\n<p>Question 26.<br \/>\n\u22124.2x + 31.5 = \u221265.1<br \/>\n______<\/p>\n<p>Answer: 23<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22124.2x + 31.5 = \u221265.1<br \/>\nSubtract 31.5 on both sides<br \/>\n-4.2x = -96.6<br \/>\n4.2x = 96.6<br \/>\nx = 96.6\/4.2<br \/>\nx = 23<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{k}{5.2}\\) + 81.9 = 47.2<br \/>\n______<\/p>\n<p>Answer: -180.44<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{k}{5.2}\\) + 81.9 = 47.2<br \/>\nk\/5.2 = 47.2 &#8211; 81.9<br \/>\nk\/5.2 = -34.7<br \/>\nk = -180.44<\/p>\n<h3><a id=\"Page_No_196\"><\/a>Page No. 196<\/h3>\n<p>Question 28.<br \/>\nWrite a two-step equation that involves multiplication and subtraction, includes a negative coefficient, and has a solution of x = 7.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA possible two-step equation that involves multiplication and subtraction, includes a negative coefficient and has a solution of x = 7 is -2x &#8211; 7 = -21<br \/>\n-2x = -21 + 7<br \/>\n-2x = -14<br \/>\n2x = 14<br \/>\nx = 14\/2<br \/>\nx = 7<\/p>\n<p>Question 29.<br \/>\nWrite a two-step equation involving division and addition that has a solution of x = -25<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: \\(\\frac{x}{5}\\) + 20 = 15<\/p>\n<p>Explanation:<br \/>\nA possible two-step equation that involves division and addition and has a solution of x = -25 is \\(\\frac{x}{5}\\) + 20 = 15<br \/>\n\\(\\frac{x}{5}\\) = 15 &#8211; 20<br \/>\n\\(\\frac{x}{5}\\) = -5<br \/>\nx = -25<\/p>\n<p>Question 30.<br \/>\nExplain the Error<br \/>\nA student\u2019s solution to the equation 3x + 2 = 15 is shown. Describe and correct the error that the student made.<br \/>\n3x + 2 = 15\u00a0 \u00a0 \u00a0 \u00a0 Divide both sides by 3.<br \/>\nx + 2 = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Subtract 2 from both sides.<br \/>\nx = 3<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\nHer error was when she divided both sides by 3.<br \/>\nShe didn&#8217;t divide the 2 by 3. She should have gotten x + \\(\\frac{2}{3}\\) = 5 after dividing both sides by 3.<br \/>\nHer first step should have been subtracting both sides by 2 instead of dividing both sides by 3.<br \/>\n3x + 2 = 15<br \/>\n3x = 15 &#8211; 2<br \/>\n3x = 13<br \/>\nx = 13\/2<\/p>\n<p>Question 31.<br \/>\nMultiple Representations<br \/>\nExplain how you could use the work backward problem-solving strategy to solve the equation \\(\\frac{x}{4}\\) \u2212 6 = 2.<br \/>\n______<\/p>\n<p>Answer: Working backward would mean talking the result of 2 and adding 6 to it to get 8. Then multiplying this by 4 to get 32.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 32.<br \/>\nReason Abstractly<br \/>\nThe formula F = 1.8C + 32 allows you to find the Fahrenheit (F) temperature for a given Celsius (C) temperature. Solve the equation for C to produce a formula for finding the Celsius temperature for a given Fahrenheit temperature.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nF = 1.8C + 32<br \/>\nF &#8211; 32 = 1.8C<br \/>\n1.8C = F &#8211; 32<br \/>\nC = (F &#8211; 32)\/1.8<\/p>\n<p>Question 33.<br \/>\nReason Abstractly<br \/>\nThe equation P = 2(l + w) can be used to find the perimeter P of a rectangle with length l and width w. Solve the equation for w to produce a formula for finding the width of a rectangle given its perimeter and length.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nP = 2(l + w)<br \/>\nP\/2 = l + w<br \/>\nP\/2 &#8211; l = w<br \/>\nw = P\/2 &#8211; l<\/p>\n<p>Question 34.<br \/>\nReason Abstractly<br \/>\nSolve the equation ax + b = c for x.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSubtract both sides by b<br \/>\nax = c &#8211; b<br \/>\nx = (c &#8211; b)\/a<\/p>\n<h3><a id=\"6.1_Algebraic_Expressions_Page_No_197\"><\/a>6.1 Algebraic Expressions &#8211; Page No. 197<\/h3>\n<p>Question 1.<br \/>\nThe Science Club went on a two-day field trip. The first day the members paid $60 for transportation plus $15 per ticket to the planetarium. The second day they paid $95 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost for two days for the n members of the club.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: 155 + 27n<\/p>\n<p>Explanation:<br \/>\nLet n be the number of members. Then n also represents the number of tickets.<br \/>\nFor the first day, tickets are $15 each so for n members, the ticket cost is 15n dollars. The members must also pay $60 for transportation so the total cost for the first day is 60 + 15n dollars.<br \/>\nFor the second day, tickets are $12 each so for n members, the ticket cost is 12n dollars. The members must also pay $95 for transportation so the total cost for the first day is 95 + 12n dollars.<br \/>\nThe total cost for the two days is then (60 + 15n) + (95 + 12n).<br \/>\nCombine the like terms.<br \/>\n27n + 155<\/p>\n<p><strong>6.2 One-Step Equations with Rational Coefficients<\/strong><\/p>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 2.<br \/>\nh + 9.7 = \u22129.7<br \/>\n______<\/p>\n<p>Answer: h = -19.4<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\nh + 9.7 = \u22129.7<br \/>\nh = -9.7 &#8211; 9.7<br \/>\nh = -19.4<\/p>\n<p>Question 3.<br \/>\n\\(-\\frac{3}{4}+p=\\frac{1}{2}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: p = 1 \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(-\\frac{3}{4}+p=\\frac{1}{2}\\)<br \/>\n-3\/4 + p = 1\/2<br \/>\np = 1\/2 + 3\/4<br \/>\np = 1 \\(\\frac{1}{4}\\)<\/p>\n<p>Question 4.<br \/>\n\u221215 = \u22120.2k<br \/>\n______<\/p>\n<p>Answer: k = 75<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u221215 = \u22120.2k<br \/>\n0.2k = 15<br \/>\nk = 15\/0.2<br \/>\nk = 150\/2<br \/>\nk = 75<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{y}{-3}=\\frac{1}{6}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: y = &#8211; \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{y}{-3}=\\frac{1}{6}\\)<br \/>\ny = -3\/6<br \/>\ny = -1\/2<\/p>\n<p>Question 6.<br \/>\n\u2212\\(\\frac{2}{3}\\) m = \u221212<br \/>\n______<\/p>\n<p>Answer: m = 18<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u2212\\(\\frac{2}{3}\\) m = \u221212<br \/>\n\\(\\frac{2}{3}\\) m = 12<br \/>\nm = 12 \u00d7 3\/2<br \/>\nm = 6 \u00d7 3<br \/>\nm = 18<\/p>\n<p>Question 7.<br \/>\n2.4 = \u2212\\(\\frac{t}{4.5}\\)<br \/>\n______<\/p>\n<p>Answer: t = -10.8<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n2.4 = \u2212\\(\\frac{t}{4.5}\\)<br \/>\n-t = 2.4 \u00d7 4.5<br \/>\nt = -10.8<\/p>\n<p><strong>6.3 Writing Two-Step Equations<\/strong><\/p>\n<p>Question 8.<br \/>\nJerry started doing sit-ups every day. The first day he did 15 sit-ups. Every day after that he did 2 more sit-ups than he had done the previous day. Today Jerry did 33 sit-ups. Write an equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day.<br \/>\n______ days<\/p>\n<p>Answer: 2x + 15 = 33<\/p>\n<p>Explanation:<br \/>\nLet x be the number of days then the number of additional sit-ups is 2x since he does 2 more sit-ups for each day, not counting the first day.<br \/>\nSince he started doing 15 sit-ups on the first day, the total number of sit-ups after x would be 2x +15<br \/>\n2x + 15 = 33<\/p>\n<p><strong>6.4 Solving Two-Step Equations<\/strong><\/p>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 9.<br \/>\n5n + 8 = 43<br \/>\n______<\/p>\n<p>Answer: n = 7<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n5n + 8 = 43<br \/>\n5n = 43 &#8211; 8<br \/>\n5n = 35<br \/>\nn = 35\/5<br \/>\nn = 7<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{y}{6}\\) \u2212 7 = 4<br \/>\n______<\/p>\n<p>Answer: y = 66<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{y}{6}\\) \u2212 7 = 4<br \/>\n\\(\\frac{y}{6}\\) = 4 + 7<br \/>\n\\(\\frac{y}{6}\\) = 11<br \/>\ny = 11 \u00d7 6<br \/>\ny = 66<\/p>\n<p>Question 11.<br \/>\n8w \u2212 15 = 57<br \/>\n______<\/p>\n<p>Answer: w = 9<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n8w \u2212 15 = 57<br \/>\n8w = 57 + 15<br \/>\n8w = 72<br \/>\nw = 72\/8<br \/>\nw = 9<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{g}{3}\\) + 11 = 25<br \/>\n______<\/p>\n<p>Answer: g = 42<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{g}{3}\\) + 11 = 25<br \/>\n\\(\\frac{g}{3}\\) = 25 &#8211; 11<br \/>\n\\(\\frac{g}{3}\\) = 14<br \/>\ng = 14 \u00d7 3<br \/>\ng = 42<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{f}{5}\\) \u2212 22 = \u221225<br \/>\n______<\/p>\n<p>Answer: f = -15<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\\(\\frac{f}{5}\\) \u2212 22 = \u221225<br \/>\n\\(\\frac{f}{5}\\) = -25 + 22<br \/>\n\\(\\frac{f}{5}\\) = -3<br \/>\nf = -3 \u00d7 5<br \/>\nf = -15<\/p>\n<p>Question 14.<br \/>\n\u22124p + 19 = 11<br \/>\n______<\/p>\n<p>Answer: p = 2<\/p>\n<p>Explanation:<br \/>\nWe are given the equation<br \/>\n\u22124p + 19 = 11<br \/>\n-4p = 11 &#8211; 19<br \/>\n-4p = -8<br \/>\np = 2<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 15.<br \/>\nHow can you use two-step equations to represent and solve real-world problems?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nYou can step two-step equations to represent and solve real-world problems by translating the words into an algebraic equation, solving the equation, and then interpreting the solution to the equation.<\/p>\n<h3><a id=\"Selected_Response_Page_No_198\"><\/a>Selected Response &#8211; Page No. 198<\/h3>\n<p>Question 1.<br \/>\nA taxi cab costs $1.50 for the first mile and $0.75 for each additional mile. Which equation could be solved to find how many miles you can travel in a taxi for $10, given that x is the number of additional miles?<br \/>\nOptions:<br \/>\na. 1.5x + 0.75 = 10<br \/>\nb. 0.75x + 1.5 = 10<br \/>\nc. 1.5x \u2212 0.75 = 10<br \/>\nd. 0.75x \u2212 1.5 = 10<\/p>\n<p>Answer: 0.75x + 1.5 = 10<\/p>\n<p>Explanation:<br \/>\nLet x be the number of additional miles then the charge for the additional miles is 0.75x the total cost is then 1.50 + 0.75x = 10<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 2.<br \/>\nWhich is the solution of \\(\\frac{t}{2.5}\\) = \u22125.2?<br \/>\nOptions:<br \/>\na. -13<br \/>\nb. -2.08<br \/>\nc. 2.08<br \/>\nd. 13<\/p>\n<p>Answer: -13<\/p>\n<p>Explanation:<br \/>\nt\/2.5 = -5.2<br \/>\nt = -5.2 \u00d7 2.5<br \/>\nt = -13<br \/>\nThus the correct answer is option is A.<\/p>\n<p>Question 3.<br \/>\nWhich expression is equivalent to 5x \u2212 30?<br \/>\nOptions:<br \/>\na. 5(x \u2212 30)<br \/>\nb. 5(x \u2212 6)<br \/>\nc. 5x(x \u2212 6)<br \/>\nd. x(5 \u2212 30)<\/p>\n<p>Answer: 5(x \u2212 6)<\/p>\n<p>Explanation:<br \/>\nFactor out 5 from each term.<br \/>\n5x &#8211; 30 = 5(x &#8211; 6)<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 4.<br \/>\nIn a science experiment, the temperature of a substance is changed from 42 \u00b0F to -54 \u00b0F at an average rate of -12 degrees per hour. Over how many hours does the change take place?<br \/>\nOptions:<br \/>\na. -8 hours<br \/>\nb. 18 hour<br \/>\nc. 1 hour<br \/>\nd. 8 hours<\/p>\n<p>Answer: 8 hours<\/p>\n<p>Explanation:<br \/>\nIn a science experiment, the temperature of a substance is changed from 42 \u00b0F to -54 \u00b0F at an average rate of -12 degrees per hour.<br \/>\nLet x be the number of hours.<br \/>\n42 &#8211; 12x = -54<br \/>\n-12x = -54 &#8211; 42<br \/>\n-12x = -96<br \/>\n12x = 96<br \/>\nx = 96\/12<br \/>\nx = 8 hours<br \/>\nThus the correct answer is option D.<\/p>\n<p>Question 5.<br \/>\nWhich statement best represents the distance on a number line between -14 and -5?<br \/>\nOptions:<br \/>\na. \u221214 \u2212 (\u22125)<br \/>\nb. \u221214 + (\u22125)<br \/>\nc. \u22125 \u2212 (\u221214)<br \/>\nd. \u22125 + (\u221214)<\/p>\n<p>Answer: \u22125 \u2212 (\u221214)<\/p>\n<p>Explanation:<br \/>\nDistance is the difference between the biggest number and the smallest number so the distance between -5 and -14 is -5 &#8211; (-14) since -5 bigger than -14.<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 6.<br \/>\nWhich cereal costs the most per ounce?<br \/>\nOptions:<br \/>\na. $4.92 for 12 ounces<br \/>\nb. $4.25 for 10 ounces<br \/>\nc. $5.04 for 14 ounces<br \/>\nd. $3.92 for 8 ounces<\/p>\n<p>Answer: $3.92 for 8 ounces<\/p>\n<p>Explanation:<br \/>\nFind the unit rates for each answer choice by dividing the cost by the number of ounces and rounding to two decimal places if necessary.<br \/>\na. $4.92 for 12 ounces<br \/>\n4.92\/12 = $0.41 per ounce<br \/>\nb. $4.25 for 10 ounces<br \/>\n4.25\/10 \u2248 0.43 per ounce<br \/>\nc. $5.04 for 14 ounces<br \/>\n5.04\/14 = 0.36 per ounce<br \/>\nd. $3.92 for 8 ounces<br \/>\n3.92\/8 = 0.49 per ounce<br \/>\nThus the correct answer is option D.<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 7.<br \/>\nCasey bought 9 tickets to a concert. The total charge was $104, including a $5 service charge.<br \/>\na. Write an equation you can solve to find c, the cost of one ticket.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: 9c + 5 = 104<\/p>\n<p>Explanation:<br \/>\nLet c be the cost of each ticket, the total cost of 9 tickets before the service charge is 9c adding the service charge gives a total charge of 9c + 5<\/p>\n<p>Question 7.<br \/>\nb. Explain how you could estimate the solution of your equation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n104 is about 105. subtracting 5 from this gives 100. 9 is about 10 and 100 divided by 10 is 10 so the ticket price is around $10.<\/p>\n<p>Question 7.<br \/>\nc. Solve the equation. How much did each ticket cost?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n9c = 99<br \/>\nc = 99\/9<br \/>\nc = 11<\/p>\n<p><em>Final Words:<\/em><\/p>\n<p>I hope the details mentioned in this article is beneficial for all the students of 7th standard. Enhance your math skills by practicing the problems from HMH Go Math Grade 7\u00a0 Chapter 6 Algebraic Expressions. Download the Go Math Grade 7 Key Algebraic Expressions pdf and share it with your besties. All the Best Guys!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Access the answers by downloading the 7th Grade HMH Go Math Answer Key Chapter 6 Algebraic Expressions pdf. We have prepared the solutions for all the questions in an easy manner. 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