## 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
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
$$\frac{68}{16}$$=$$\frac{16}{16}$$ x
$$\frac{68}{16}$$ =x
$$\frac{17}{4}$$ =x

Exercise 2.
-(x-7)+$$\frac{5}{3}$$ =2(x+9)
-(x-7)+$$\frac{5}{3}$$ =2(x+9)
-x+7+$$\frac{5}{3}$$ =2x+18
-x+$$\frac{26}{3}$$ =2x+18
-x+x+$$\frac{26}{3}$$ =2x+x+18
$$\frac{26}{3}$$ =3x+18
$$\frac{26}{3}$$ -18=3x+18-18
–$$\frac{28}{3}$$ =3x
$$\frac{1}{3}$$∙$$\frac{-28}{3}$$ =$$\frac{1}{3}$$∙3x
–$$\frac{28}{9}$$ =x

Question 3.
$$\frac{4}{9}$$ +4(x-1)=$$\frac{28}{9}$$ -(x-7x)+1
$$\frac{4}{9}$$ +4(x-1)=$$\frac{28}{9}$$ -(x-7x)+1
$$\frac{4}{9}$$ –$$\frac{4}{9}$$ +4(x-1)=$$\frac{28}{9}$$ –$$\frac{4}{9}$$ -(x-7x)+1
4x-4=2$$\frac{4}{9}$$ -x+7x+1
4x-4=$$\frac{33}{9}$$ +6x
4x-4+4=$$\frac{33}{9}$$ +36/9+6x
4x=$$\frac{69}{9}$$ +6x
4x-6x=$$\frac{69}{9}$$ +6x-6x
-2x=$$\frac{23}{3}$$
$$\frac{1}{-2}$$ ∙-2x=$$\frac{1}{-2}$$∙$$\frac{23}{3}$$
x=-$$\frac{23}{6}$$

Question 4.
5(3x+4)-2x=7x-3(-2x+11)
5(3x+4)-2x=7x-3(-2x+11)
15x+20-2x=7x+6x-33
13x+20=13x-33
13x-13x+20=13x-13x-33
20≠-33
This equation has no solution.

Question 5.
7x-(3x+5)-8=$$\frac{1}{2}$$ (8x+20)-7x+5
7x-(3x+5)-8=$$\frac{1}{2}$$ (8x+20)-7x+5
7x-3x-5-8=4x+10-7x+5
4x-13=-3x+15
4x-13+13=-3x+15+13
4x=-3x+28
4x+3x=-3x+3x+28
7x=28
x=4

Question 6.
Write at least three equations that have no solution.
Answers will vary. Verify that the equations written have no solution.

### Eureka Math Grade 8 Module 4 Lesson 6 Problem Set Answer Key

Students practice using the distributive property to transform equations and solve.

Transform the equation if necessary, and then solve it to find the value of x that makes the equation true.

Question 1.
x-(9x-10)+11=12x+3(-2x+$$\frac{1}{3}$$)
x-(9x-10)+11=12x+3(-2x+$$\frac{1}{3}$$)
x-9x+10+11=12x-6x+1
-8x+21=6x+1
-8x+8x+21=6x+8x+1
21=14x+1
21-1=14x+1-1
20=14x
$$\frac{20}{14}$$=$$\frac{14}{14}$$
$$\frac{10}{7}$$=x

Question 2.
7x+8(x+$$\frac{1}{4}$$ )=3(6x-9)-8
7x+8(x+$$\frac{1}{4}$$ )=3(6x-9)-8
7x+8x+2=18x-27-8
15x+2=18x-35
15x-15x+2=18x-15x-35
2=3x-35
2+35=3x-35+35
37=3x
$$\frac{37}{3}$$ =$$\frac{3}{3}$$ x
$$\frac{37}{3}$$ =x

Question 3.
-4x-2(8x+1)=-(-2x-10)
-4x-2(8x+1)=-(-2x-10)
-4x-16x-2=2x+10
-20x-2=2x+10
-20x+20x-2=2x+20x+10
-2=22x+10
-2-10=22x+10-10
-12=22x
–$$\frac{12}{22}$$ =$$\frac{22}{22}$$ x
–$$\frac{6}{11}$$ =x

Question 4.
11(x+10)=132
11(x+10)=132
($$\frac{1}{11}$$ )11(x+10)=($$\frac{1}{11}$$ )132
x+10=12
x+10-10=12-10
x=2

Question 5.
37x+$$\frac{1}{2}$$ -(x+$$\frac{1}{4}$$ )=9(4x-7)+5
37x+$$\frac{1}{2}$$ -(x+$$\frac{1}{4}$$ )=9(4x-7)+5
37x+$$\frac{1}{2}$$ -x-$$\frac{1}{4}$$ =36x-63+5
36x+$$\frac{1}{4}$$ =36x-58
36x-36x+$$\frac{1}{4}$$ =36x-36x-58
$$\frac{1}{4}$$ ≠-58
This equation has no solution.

Question 6.
3(2x-14)+x=15-(-9x-5)
3(2x-14)+x=15-(-9x-5)
6x-42+x=15+9x+5
7x-42=20+9x
7x-7x-42=20+9x-7x
-42=20+2x
-42-20=20-20+2x
-62=2x
-31=x

Question 7.
8(2x+9)=56
8(2x+9)=56
($$\frac{1}{8}$$ )8(2x+9)=($$\frac{1}{8}$$ )56
2x+9=7
2x+9-9=7-9
2x=-2
($$\frac{1}{2}$$ )2x=($$\frac{1}{2}$$ )-2
x=-1

### Eureka Math Grade 8 Module 4 Lesson 6 Exit Ticket Answer Key

Transform the equation if necessary, and then solve to find the value of x that makes the equation true.

Question 1.
5x-(x+3)=$$\frac{1}{3}$$ (9x+18)-5
5x-(x+3)=$$\frac{1}{3}$$ (9x+18)-5
5x-x-3=3x+6-5
4x-3=3x+1
4x-3x-3=3x-3x+1
x-3=1
x-3+3=1+3
x=4

Question 2.
5(3x+9)-2x=15x-2(x-5)