#### Solved Examples and Worksheet for Solving Multi-Step Linear Equations Using Distributive Property

Q1Solve: 18y - 7y + 9 = 8y + 18

A. 2
B. 5
C. 4
D. 3

Step: 1
18y - 7y + 9 = 8y + 18
[Original equation.]
Step: 2
11y + 9 = 8y + 18
[Combine like terms.]
Step: 3
11y + 9 - 9 = 8y + 18 - 9
[Subtract 9 from each side.]
Step: 4
11y = 8y + 9
[Simplify both sides.]
Step: 5
11y - 8y = 8y + 9 - 8y
[Subtract 8y from each side.]
Step: 6
3y = 9
[Simplify both sides.]
Step: 7
y = 3
[Simplify.]
Correct Answer is :   3
Q2Solve: 10x - 5(x + 10) = 20

A. 13
B. 15
C. 14
D. 16

Step: 1
10x - 5(x + 10) = 20
[Original equation.]
Step: 2
10x - 5(x) - 5(10) = 20
[Use distributive property.]
Step: 3
10x - 5x - 50 = 20
[Simplify.]
Step: 4
5x - 50 = 20
[Combine like terms.]
Step: 5
5x - 50 + 50 = 20 + 50
[Add 50 both sides.]
Step: 6
5x = 70
[Add 20 and 50.]
Step: 7
5x5 = 705
[Divide each side by 5.]
Step: 8
x = 14
[Simplify.]
Correct Answer is :   14
Q3Solve: 613(w - 3) = 18
A. 39
B. 42
C. 45
D. 41

Step: 1
613(w - 3) = 18
[Original equation.]
Step: 2
136 [613 (w - 3)] = 136[18]
[Multiply each side by 136 , the reciprocal of 613.]
Step: 3
w - 3 = 39
[Simplify.]
Step: 4
w - 3 + 3 = 39 + 3
[Add 3 to each side.]
Step: 5
w = 42
[Simplify.]
Correct Answer is :   42
Q4Solve: j2 + 39.24 = 2(j - 3)

A. 33.16
B. 32.16
C. 30.16
D. 34.16

Step: 1
j2 + 39.24 = 2(j - 3)
[Original equation.]
Step: 2
j2 + 39.24 = 2(j) - 2(3)
[Use distributive property.]
Step: 3
j2 + 39.24 + 6 = 2j - 6 + 6
[Add 6 to each side.]
Step: 4
j2 + 45.24 = 2j
[Combine like terms.]
Step: 5
( j2 + 45.24 ) × 2 = 2j × 2
[Multiply each side by 2.]
Step: 6
j + 90.48 = 4j
[Simplify.]
Step: 7
j + 90.48 - j = 4j - j
[Subtract j from each side.]
Step: 8
90.48 = 3j
[Simplify.]
Step: 9
90.483 = 3j3
[Divide each side by 3.]
Step: 10
j = 30.16
[Simplify.]
Correct Answer is :   30.16
Q5Solve:
- a + (17a - 8) = 40

A. 3
B. 5.33
C. 32
D. 2

Step: 1
- a + (17a - 8) = 40
[Original equation.]
Step: 2
16a - 8 = 40
[Combine like terms.]
Step: 3
16a - 8 + 8 = 40 + 8
[Add 8 to both sides.]
Step: 4
16a = 48
[Simplify.]
Step: 5
16a16 = 4816
[Divide each side by 16.]
Step: 6
a = 3
[Simplify.]
Correct Answer is :   3
Q6Solve:
6x - 3(x + 6) = 12

A. 10
B. 9
C. 12
D. 11

Step: 1
6x - 3(x + 6) = 12
[Original equation.]
Step: 2
6x - 3(x) - 3(6) = 12
[Use distributive property.]
Step: 3
6x - 3x - 18 = 12
[Simplify.]
Step: 4
3x - 18 = 12
[Combine like terms.]
Step: 5
3x - 18 + 18 = 12 + 18
[Add 18 on both sides.]
Step: 6
3x = 30
[Add 12 and 18.]
Step: 7
3x3 = 303
[Divide each side by 3.]
Step: 8
x = 10
[Simplify.]
Correct Answer is :   10
Q7Solve 613(w - 4) = 24.
A. 48
B. 1583
C. 56
D. 330

Step: 1
613(w - 4) = 24
[Original equation.]
Step: 2
136 [613 (w - 4)] = 136[24]
[Multiply each side by 136, the reciprocal of 613.]
Step: 3
w - 4 = 52
[Simplify.]
Step: 4
w - 4 + 4 = 52 + 4
[Add 4 on each side.]
Step: 5
w = 56
[Simplify.]
Correct Answer is :   56
Q8Solve:
1029w + 2345 = 5432

A. 4
B. 1
C. 2
D. 3

Step: 1
1029w + 2345 = 5432
[Original equation.]
Step: 2
1029w + 2345 - 2345 = 5432 - 2345
[Subtract 2345 from each side.]
Step: 3
1029w = 3087
[Simplify.]
Step: 4
1029w1029 = 30871029
[Divide each side by 1029.]
Step: 5
w = 3
[Simplify.]
Correct Answer is :   3
Q9Solve:
14q - 9 + 5(q - 2) = 38

A. 2
B. 4
C. 3
D. 5

Step: 1
14q - 9 + 5(q - 2) = 38
[Original equation.]
Step: 2
14q - 9 + 5(q) - 5(2) = 38
[Use distributive property.]
Step: 3
19q - 19 = 38
[Combine like terms.]
Step: 4
19q - 19 + 19 = 38 + 19
[Add 19 to each side.]
Step: 5
19q = 57
[Simplify.]
Step: 6
19q19 = 5719
[Divide each side by 19.]
Step: 7
q = 3
[Simplify.]
Correct Answer is :   3
Q10Solve:
j8 + 10.86 = 8(j - 5)

A. 6.45
B. 18.13
C. 1.98
D. 6.68

Step: 1
j8 + 10.86 = 8(j - 5)
[Original equation.]
Step: 2
j8 + 10.86 = 8(j) - 8(5)
[Use distributive property.]
Step: 3
j8 + 10.86 + 40 = 8j - 40 + 40
[Add 40 on both sides.]
Step: 4
j8 + 50.86 = 8j
[Combine like terms.]
Step: 5
(j8 + 50.86) × 8 = 8j × 8
[Multiply each side by 8.]
Step: 6
j + 406.88 = 64j
[Simplify.]
Step: 7
j + 406.88 - j = 64j - j
[Subtract j from each side.]
Step: 8
406.88 = 63j
[Simplify.]
Step: 9
406.8863 = 63j63
[Divide each side by 63.]
Step: 10
j = 6.45
[Simplify.]
Correct Answer is :   6.45
Q11Solve:
- 4(4 - n5) = 20

A. 45
B. 44
C. 49
D. 41

Step: 1
- 4(4 - n5) = 20
[Original equation.]
Step: 2
- 4(4 - n5)- 4 = 20- 4
[Divide each side by - 4.]
Step: 3
4 - n5 = - 5
[Simplify.]
Step: 4
4 - n5 - 4 = - 5 - 4
[Subtract 4 from each side.]
Step: 5
- n5 = - 9
[Combine like terms.]
Step: 6
- n5 × (- 5) = - 9 × (- 5)
[Multiply each side by - 5.]
Step: 7
n = 45
[Simplify.]
Correct Answer is :   45
Q12Solve: j9 + 30.93 = 9(j - 4)
A. 11.53
B. 10.53
C. 9.53
D. 7.53

Step: 1
j9 + 30.93 = 9(j - 4)
[Original equation.]
Step: 2
j9 + 30.93 = 9(j) - 9(4)
[Use distributive property.]
Step: 3
j9 + 30.93 + 36 = 9j - 36 + 36
[Add 36 to both sides.]
Step: 4
j9 + 66.93 = 9j
[Combine like terms.]
Step: 5
(j9 + 66.93) × 9 = 9j × 9
[Multiply each side by 9.]
Step: 6
j + 602.37 = 81j
[Simplify.]
Step: 7
j + 602.37 - j = 81j - j
[Subtract j from each side.]
Step: 8
602.37 = 80j
[Simplify.]
Step: 9
602.3780 = 80j80
[Divide each side by 80.]
Step: 10
j = 7.53
[Simplify.]
Correct Answer is :   7.53
Q13Solve:
4q - 4 + 5(q - 1) = 9

A. 2
B. 4
C. 1
D. 3

Step: 1
4q - 4 + 5(q - 1) = 9
[Original equation.]
Step: 2
4q - 4 + 5(q) - 5(1) = 9
[Use distributive property.]
Step: 3
9q - 9 = 9
[Combine like terms.]
Step: 4
9q - 9 + 9 = 9 + 9
[Add 9 to each side.]
Step: 5
9q = 18
[Simplify.]
Step: 6
9q9 = 189
[Divide each side by 9.]
Step: 7
q = 2
[Simplify.]
Correct Answer is :   2
Q14Solve:
j8 + 44.82 = 8(j - 2)

A. 53.51
B. 7.72
C. 5.85
D. 7.95

Step: 1
j8 + 44.82 = 8(j - 2)
[Original equation.]
Step: 2
j8 + 44.82 = 8(j) - 8(2)
[Use distributive property.]
Step: 3
j8 + 44.82 + 16 = 8j - 16 + 16
[Add 16 on both sides.]
Step: 4
j8 + 60.82 = 8j
[Combine like terms.]
Step: 5
(j8 + 60.82) × 8 = 8j × 8
[Multiply each side by 8.]
Step: 6
j + 486.56 = 64j
[Simplify.]
Step: 7
j + 486.56 - j = 64j - j
[Subtract j from each side.]
Step: 8
486.56 = 63j
[Simplify.]
Step: 9
486.5663 = 63j63
[Divide each side by 63.]
Step: 10
j = 7.72
[Simplify.]
Correct Answer is :   7.72
Q15Find the value of p, if the area of the parallelogram is 56 cm2.

A. 4
B. 3
C. 5
D. 6

Step: 1
The area of a parallelogram with base length b and height h is A = b × h
Step: 2
56 = 7 × (p + 4)
[Substitute the values.]
Step: 3
56 = 7(p) + 7(4)
[Use distributive property.]
Step: 4
56 - 28 = 7p + 28 - 28
[Subtract 28 from each side.]
Step: 5
28 = 7p
[Combine like terms.]
Step: 6
287 = 7p7
[Divide each side by 7.]
Step: 7
4 = p
[Simplify.]
Step: 8
The value of p is 4.
Correct Answer is :   4