\n– 15 = 8x + 1
\nAnswer:
\n
![\"Engage](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-4-End-of-Module-Assessment-Answer-Key-3-1.png\")
\n-2 = x<\/p>\n
Question 1.
\nWrite and solve each of the following linear equations.
\na. Ofelia has a certain amount of money. If she spends $12, then she has \\(\\frac{1}{5}\\) of the original amount left. How much money did Ofelia have originally?
\nAnswer:
\nLet x be the amount of money ofelia had
\nx – 12 = \\(\\frac{1}{5}\\)
\nx – \\(\\frac{1}{5}\\)x – 12 + 12 = \\(\\frac{1}{5}\\) x – \\(\\frac{1}{5}\\) x +12
\n\\(\\frac{4}{5}\\) x = 12
\nx= 12 \u2219 \\(\\frac{5}{4}\\) = \\(\\frac{60}{4}\\)
\nOfelia had $15.00 originally.<\/p>\n
b. Three consecutive integers have a sum of 234. What are the three integers?
\nAnswer:
\nLet x be the first integer
\nx + x + 1 + x + 2 = 234
\n3x + 3 = 234
\n3x = 234 – 3
\n3x = 231
\nx = 77
\nThe integers are 77, 78, and 79<\/p>\n
c. Gil is reading a book that has 276 pages. He already read some of it last week. He plans to read 20 pages tomorrow. By then, he will be \\(\\frac{2}{3}\\)of the way through the book. How many pages did Gil read last week?
\nAnswer:
\nLet x be the number of pages gil read last week.
\nx + 20 = \\(\\frac{2}{3}\\)(276)
\nx + 20 = 184
\nx + 20 – 20 = 184 – 20
\nx = 164
\nGil read 164 pages last week<\/p>\n
Question 2.
\na. Without solving, identify whether each of the following equations has a unique solution, no solution,
\nor infinitely many solutions.
\ni. 3x + 5 = – 2
\nAnswer:
\nUnique<\/p>\n
ii. 6(x – 11) = 15 – 4x
\nAnswer:
\nUnique<\/p>\n
iii. 12x + 9 = 8x + 1 + 4x
\nAnswer:
\nNo solution<\/p>\n
iv. 2(x – 3) = 10x – 6 – 8x
\nAnswer:
\nInfinitely many solutions<\/p>\n
v. 5x + 6 = 5x – 4
\nAnswer:
\nNo solution<\/p>\n
b. Solve the following equation for a number x. Verify that your solution is correct.
\n– 15 = 8x + 1
\nAnswer:
\n
\n-2 = x<\/p>\n
-15 = 8(-2) + 1
\n-15 = -16 + 1
\n-15 = -15<\/p>\n
c. Solve the following equation for a number x. Verify that your solution is correct.
\n7(2x + 5) = 4x – 9 – x
\nAnswer:
\n7(2x + 5) = 4x – 9 – x
\n14x + 35 = 4x – 9 – x
\n14x + 35 = 3x – 9
\n14x – 3x + 35 = 3x – 3x – 9
\n11x + 35 = -9
\n11x + 35 – 35 = -9 – 35
\n11x = -44
\nx = -4<\/p>\n
7(2(-4) + 5) = 4(-4) – 9 – (-4)
\n7(-8 + 5) = -16 – 9 + 4
\n7(-3) = -25 + 4
\n-21 = -21<\/p>\n
Question 3.
\na. Parker paid $4.50 for three pounds of gummy candy. Assuming each pound of gummy candy costs the same amount, complete the table of values representing the cost of gummy candy in pounds.
\n![\"Engage](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-4-End-of-Module-Assessment-Answer-Key-1-1.png\")
\nAnswer:
\n![\"Engage](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-4-End-of-Module-Assessment-Answer-Key-4-1.png\")
<\/p>\n
b. Graph the data on the coordinate plane.
\n![\"Engage](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-4-End-of-Module-Assessment-Answer-Key-2-1.png\")
\nAnswer:
\n![\"Engage](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-8th-Grade-Module-4-End-of-Module-Assessment-Answer-Key-5-1.png\")
<\/p>\n
c. On the same day, Parker\u2019s friend, Peggy, was charged $5 for 1 \\(\\frac{1}{2}\\) lb. of gummy candy. Explain in terms of the graph why this must be a mistake.
\nAnswer:
\nEven though 1\\(\\frac{1}{2}\\) pounds of candy isn’t a point on the graph, it is reasonable to believe it will fall in line with the other points. The cost of 1\\(\\frac{1}{2}\\) pounds of candy does not fit the pattern.<\/p>\n","protected":false},"excerpt":{"rendered":"
Engage NY Eureka Math 8th Grade Module 4 Mid Module Assessment Answer Key Eureka Math Grade 8 Module 4 Mid Module Assessment Task Answer Key Question 1. Write and solve each of the following linear equations. a. Ofelia has a certain amount of money. If she spends $12, then she has of the original amount … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/86374"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=86374"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/86374\/revisions"}],"predecessor-version":[{"id":91395,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/86374\/revisions\/91395"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=86374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=86374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=86374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}