![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Eureka-Math-Grade-8-Module-4-Lesson-6-Problem-Set-Answer-Key.png\")
<\/p>\nExercises
\nFind the value of x that makes the equation true.<\/p>\n
Exercise 1.
\n17-5(2x-9)=-(-6x+10)+4
\nAnswer:
\n17-5(2x-9)=-(-6x+10)+4
\n17-10x+45=6x-10+4
\n62-10x=6x-6
\n62-10x+10x=6x+10x-6
\n62=16x-6
\n62+6=16x-6+6
\n68=16x
\n\\(\\frac{68}{16}\\)=\\(\\frac{16}{16}\\) x
\n\\(\\frac{68}{16}\\) =x
\n\\(\\frac{17}{4}\\) =x<\/p>\n
Exercise 2.
\n-(x-7)+\\(\\frac{5}{3}\\) =2(x+9)
\nAnswer;
\n-(x-7)+\\(\\frac{5}{3}\\) =2(x+9)
\n-x+7+\\(\\frac{5}{3}\\) =2x+18
\n-x+\\(\\frac{26}{3}\\) =2x+18
\n-x+x+\\(\\frac{26}{3}\\) =2x+x+18
\n\\(\\frac{26}{3}\\) =3x+18
\n\\(\\frac{26}{3}\\) -18=3x+18-18
\n–\\(\\frac{28}{3}\\) =3x
\n\\(\\frac{1}{3}\\)\u2219\\(\\frac{-28}{3}\\) =\\(\\frac{1}{3}\\)\u22193x
\n–\\(\\frac{28}{9}\\) =x<\/p>\n
Question 3.
\n\\(\\frac{4}{9}\\) +4(x-1)=\\(\\frac{28}{9}\\) -(x-7x)+1
\nAnswer;
\n\\(\\frac{4}{9}\\) +4(x-1)=\\(\\frac{28}{9}\\) -(x-7x)+1
\n\\(\\frac{4}{9}\\) –\\(\\frac{4}{9}\\) +4(x-1)=\\(\\frac{28}{9}\\) –\\(\\frac{4}{9}\\) -(x-7x)+1
\n4x-4=2\\(\\frac{4}{9}\\) -x+7x+1
\n4x-4=\\(\\frac{33}{9}\\) +6x
\n4x-4+4=\\(\\frac{33}{9}\\) +36\/9+6x
\n4x=\\(\\frac{69}{9}\\) +6x
\n4x-6x=\\(\\frac{69}{9}\\) +6x-6x
\n-2x=\\(\\frac{23}{3}\\)
\n\\(\\frac{1}{-2}\\) \u2219-2x=\\(\\frac{1}{-2}\\)\u2219\\(\\frac{23}{3}\\)
\nx=-\\(\\frac{23}{6}\\)<\/p>\n
Question 4.
\n5(3x+4)-2x=7x-3(-2x+11)
\nAnswer:
\n5(3x+4)-2x=7x-3(-2x+11)
\n15x+20-2x=7x+6x-33
\n13x+20=13x-33
\n13x-13x+20=13x-13x-33
\n20\u2260-33
\nThis equation has no solution.<\/p>\n
Question 5.
\n7x-(3x+5)-8=\\(\\frac{1}{2}\\) (8x+20)-7x+5
\nAnswer:
\n7x-(3x+5)-8=\\(\\frac{1}{2}\\) (8x+20)-7x+5
\n7x-3x-5-8=4x+10-7x+5
\n4x-13=-3x+15
\n4x-13+13=-3x+15+13
\n4x=-3x+28
\n4x+3x=-3x+3x+28
\n7x=28
\nx=4<\/p>\n
Question 6.
\nWrite at least three equations that have no solution.
\nAnswer:
\nAnswers will vary. Verify that the equations written have no solution.<\/p>\n
<\/p>\n
Students practice using the distributive property to transform equations and solve.<\/p>\n
Transform the equation if necessary, and then solve it to find the value of x that makes the equation true.<\/p>\n
Question 1.
\nx-(9x-10)+11=12x+3(-2x+\\(\\frac{1}{3}\\))
\nx-(9x-10)+11=12x+3(-2x+\\(\\frac{1}{3}\\))
\nx-9x+10+11=12x-6x+1
\n-8x+21=6x+1
\n-8x+8x+21=6x+8x+1
\n21=14x+1
\n21-1=14x+1-1
\n20=14x
\n\\(\\frac{20}{14}\\)=\\(\\frac{14}{14}\\)
\n\\(\\frac{10}{7}\\)=x<\/p>\n
Question 2.
\n7x+8(x+\\(\\frac{1}{4}\\) )=3(6x-9)-8
\nAnswer:
\n7x+8(x+\\(\\frac{1}{4}\\) )=3(6x-9)-8
\n7x+8x+2=18x-27-8
\n15x+2=18x-35
\n15x-15x+2=18x-15x-35
\n2=3x-35
\n2+35=3x-35+35
\n37=3x
\n\\(\\frac{37}{3}\\) =\\(\\frac{3}{3}\\) x
\n\\(\\frac{37}{3}\\) =x<\/p>\n
Question 3.
\n-4x-2(8x+1)=-(-2x-10)
\nAnswer:
\n-4x-2(8x+1)=-(-2x-10)
\n-4x-16x-2=2x+10
\n-20x-2=2x+10
\n-20x+20x-2=2x+20x+10
\n-2=22x+10
\n-2-10=22x+10-10
\n-12=22x
\n–\\(\\frac{12}{22}\\) =\\(\\frac{22}{22}\\) x
\n–\\(\\frac{6}{11}\\) =x<\/p>\n
Question 4.
\n11(x+10)=132
\nAnswer:
\n11(x+10)=132
\n(\\(\\frac{1}{11}\\) )11(x+10)=(\\(\\frac{1}{11}\\) )132
\nx+10=12
\nx+10-10=12-10
\nx=2<\/p>\n
Question 5.
\n37x+\\(\\frac{1}{2}\\) -(x+\\(\\frac{1}{4}\\) )=9(4x-7)+5
\nAnswer:
\n37x+\\(\\frac{1}{2}\\) -(x+\\(\\frac{1}{4}\\) )=9(4x-7)+5
\n37x+\\(\\frac{1}{2}\\) -x-\\(\\frac{1}{4}\\) =36x-63+5
\n36x+\\(\\frac{1}{4}\\) =36x-58
\n36x-36x+\\(\\frac{1}{4}\\) =36x-36x-58
\n\\(\\frac{1}{4}\\) \u2260-58
\nThis equation has no solution.<\/p>\n
Question 6.
\n3(2x-14)+x=15-(-9x-5)
\nAnswer:
\n3(2x-14)+x=15-(-9x-5)
\n6x-42+x=15+9x+5
\n7x-42=20+9x
\n7x-7x-42=20+9x-7x
\n-42=20+2x
\n-42-20=20-20+2x
\n-62=2x
\n-31=x<\/p>\n
Question 7.
\n8(2x+9)=56
\nAnswer:
\n8(2x+9)=56
\n(\\(\\frac{1}{8}\\) )8(2x+9)=(\\(\\frac{1}{8}\\) )56
\n2x+9=7
\n2x+9-9=7-9
\n2x=-2
\n(\\(\\frac{1}{2}\\) )2x=(\\(\\frac{1}{2}\\) )-2
\nx=-1<\/p>\n
![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Eureka-Math-Grade-8-Module-4-Lesson-6-Exit-Ticket-Answer-Key.png\")
<\/p>\n
Transform the equation if necessary, and then solve to find the value of x that makes the equation true.<\/p>\n
Question 1.
\n5x-(x+3)=\\(\\frac{1}{3}\\) (9x+18)-5
\nAnswer:
\n5x-(x+3)=\\(\\frac{1}{3}\\) (9x+18)-5
\n5x-x-3=3x+6-5
\n4x-3=3x+1
\n4x-3x-3=3x-3x+1
\nx-3=1
\nx-3+3=1+3
\nx=4<\/p>\n
Question 2.
\n5(3x+9)-2x=15x-2(x-5)
\nAnswer:
\n5(3x+9)-2x=15x-2(x-5)
\n15x+45-2x=15x-2x+10
\n13x+45=13x+10
\n13x-13x+45=13x-13x+10
\n45\u226010
\nSince 45\u226010, the equation has no solution.<\/p>\n","protected":false},"excerpt":{"rendered":"
Engage NY Eureka Math 8th Grade Module 4 Lesson 6 Answer Key Eureka Math Grade 8 Module 4 Lesson 6 Exercise Answer Key Exercises Find the value of x that makes the equation true. Exercise 1. 17-5(2x-9)=-(-6x+10)+4 Answer: 17-5(2x-9)=-(-6x+10)+4 17-10x+45=6x-10+4 62-10x=6x-6 62-10x+10x=6x+10x-6 62=16x-6 62+6=16x-6+6 68=16x = x =x =x Exercise 2. -(x-7)+ =2(x+9) Answer; -(x-7)+ … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":171384,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Eureka-Math-Grade-8-Module-4-Lesson-6-Answer-Key.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85051"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=85051"}],"version-history":[{"count":3,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85051\/revisions"}],"predecessor-version":[{"id":171388,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85051\/revisions\/171388"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/171384"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=85051"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=85051"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=85051"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}