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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

Solutions
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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

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