Solved Examples and Worksheet for Solving Two-step Linear Equations

Q1Solve: - 4 - 2d = 6
A. - 7
B. - 5
C. - 6
D. - 4

Solutions
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Step: 1
- 4 - 2d = 6
  [Original equation.]
Step: 2
- 4 - 2d + 4 = 6 + 4
  [Add 4 to each side.]
Step: 3
- 2d = 10
  [Simplify.]
Step: 4
- 2d- 2 = 10- 2
  [Divide each side by - 2.]
Step: 5
d = - 5
  [Simplify.]
Correct Answer is :   - 5
Q2Solve: 4d - 1 = 7

A. - 2
B. 2
C. - 1
D. 1

Solutions
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Step: 1
4d - 1 = 7
  [Original equation.]
Step: 2
4d - 1 + 1 = 7 + 1
  [Add 1 to each side.]
Step: 3
4d = 8
  [Simplify.]
Step: 4
4d4 = 84
  [Divide each side by 4.]
Step: 5
d = 2
  [Simplify.]
Correct Answer is :   2
Q3Solve: 2d + 16 = 8

A. - 3
B. 4
C. - 4
D. 3

Solutions
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Step: 1
2d + 16 = 8
  [Original equation.]
Step: 2
2d + 16 - 16 = 8 - 16
  [Subtract 16 from each side.]
Step: 3
2d = -8
  [Simplify.]
Step: 4
2d2 = -82
  [Divide each side by 2.]
Step: 5
d = - 4
  [Simplify.]
Correct Answer is :   - 4
Q4Solve: d5 + 8 = - 5
A. - 65
B. - 14
C. - 13
D. - 12

Solutions
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Step: 1
d5 + 8 = - 5
  [Original equation.]
Step: 2
d5 + 8 - 8 = - 5 - 8
  [Subtract 8 from each side.]
Step: 3
d5 = - 13
  [Simplify.]
Step: 4
(5) × (d5) = (5) × - (13)
  [Multiply each side by 5.]
Step: 5
d = - 65
  [Simplify.]
Correct Answer is :   - 65
Q5Solve: d5 - 3 = 5

A. - 8
B. 40
C. 8
D. - 40

Solutions
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Step: 1
d5 - 3 = 5
  [Original equation.]
Step: 2
d5 - 3 + 3 = 5 + 3
  [Add 3 to each side.]
Step: 3
d5 = 8
  [Simplify.]
Step: 4
(5) × ( d5 ) = (5) × (8)
  [Multiply each side by 5.]
Step: 5
d = 40
  [Simplify.]
Correct Answer is :   40
Q6Solve: -5 - d2 = -6

A. 22
B. 2
C. 12
D. 7

Solutions
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Step: 1
-5 - d2= -6
  [Original equation.]
Step: 2
-5 - d2 + 5 = -6 + 5
  [Add 5 to each side.]
Step: 3
-d2 = -1
  [Simplify.]
Step: 4
-2 x ( -d2) = -1 x -2
  [Multiply each side by -2.]
Step: 5
d = 2
  [Simplify.]
Correct Answer is :   2
Q7Find the value of x, if 8x + 9 = 41.
A. 4
B. 3
C. 5
D. 6

Solutions
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Step: 1
8x + 9 = 41
  [Original function.]
Step: 2
8x = 32
  [Subtract 9 from each side.]
Step: 3
8x8 = 328
  [Divide each side by 8.]
Step: 4
x = 4
  [Simplify.]
Step: 5
So, the value of x is 4.
Correct Answer is :   4
Q8Solve for m, if 13m - 4 = 8m.
A. 54
B. 56
C. 65
D. 45

Solutions
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Step: 1
13m - 4 = 8m
  [Original equation]
Step: 2
13m - 4 - 8m = 8m - 8m
  [Subtract 8m from each side.]
Step: 3
5m - 4 = 0
  
Step: 4
5m - 4 + 4 = 0 + 4
  [Add 4 to each side.]
Step: 5
5m = 4
  
Step: 6
m = 45
  [Divide each side by 5.]
Correct Answer is :   45
Q9A number z is multiplied by 3 and the result is decreased by 15 to give 12. Find z.

A. 14
B. 11
C. 6
D. 9

Solutions
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Step: 1
A number z is multiplied by 3 = 3 × z = 3z
Step: 2
3z is decreased by 15 = 3z - 15
Step: 3
3z - 15 = 12
  [Original equation.]
Step: 4
3z = 12 + 15
  [Add 15 to each side.]
Step: 5
3z = 27
  [Add.]
Step: 6
z = 273 = 9
  [Divide each side by 3 and simplify.]
Step: 7
So, the number z is 9.
Correct Answer is :   9
Q10A number n is multiplied by 6 and the result is increased by 5 to give 17. What is the value of n?

A. 2
B. 5
C. 1
D. 4

Solutions
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Step: 1
A number n multiplied by 6 = 6n.
Step: 2
6n increased by 5 = 5 + 6n
Step: 3
5 + 6n = 17
  [Original equation.]
Step: 4
6n = 17 - 5
  [Subtract 5 from both sides.]
Step: 5
6n = 12
  [Subtract.]
Step: 6
n = 126 = 2
  [Divide each side by 6 and simplify.]
Step: 7
So, the value of n is 2.
Correct Answer is :   2
Q11Find y, if 5(y + 4) = 20.

A. 5
B. 0
C. 15
D. 4

Solutions
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Step: 1
5(y + 4) = 20
  [Original expression.]
Step: 2
5y + 5(4) = 20
  [Solve the grouping symbol.]
Step: 3
5y + 20 = 20
  [Multiply 5 and 4.]
Step: 4
5y + 20 - 20 = 20 - 20
  [Subtract 20 from both the sides.]
Step: 5
5y = 0
  [Simplify.]
Step: 6
y = 05
  
Step: 7
y = 0
  
Correct Answer is :   0
Q12Solve:
4x - 2x + 4 = 0
A. -2
B. 2
C. -1
D. 1

Solutions
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Step: 1
4x - 2x + 4 = 0
  [Original equation.]
Step: 2
2x + 4 = 0
  [Combine like terms.]
Step: 3
2x = -4
  [Subtract 4 from both sides.]
Step: 4
x = -2
  [Divide both sides by 2.]
Correct Answer is :   -2
Q13Find the value of k in the equation 4(k - 18) = 16.
A. 18
B. 22
C. 24
D. 20

Solutions
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Step: 1
4(k - 18) = 16
  [Original equation.]
Step: 2
4(k - 18)/4 = 164
  [Divide each side by 4.]
Step: 3
k - 18 = 4
  [Simplify.]
Step: 4
k - 18 + 18 = 4 + 18
  [Add 18 on both sides.]
Step: 5
k = 22
  [Simplify.]
Correct Answer is :   22
Q14Find y, if 3(y + 2) = 6.

A. 3
B. 2
C. 0
D. 13

Solutions
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Step: 1
3(y + 2) = 6
  [Original expression.]
Step: 2
3y + 3(2) = 6
  [Solve the grouping symbol.]
Step: 3
3y + 6 = 6
  [Multiply 3 and 2.]
Step: 4
3y + 6 - 6 = 6 - 6
  [Subtract 6 from both the sides.]
Step: 5
3y = 0
  [Simplify.]
Step: 6
y = 03
  
Step: 7
y = 0
  
Correct Answer is :   0
Q15What is the value of x, if 5x - 15 = 15?
A. 5
B. 8
C. 6
D. 7

Solutions
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Step: 1
5x - 15 = 15
  [Original equation.]
Step: 2
5x - 15 + 15 = 15 + 15
  [Add 15 to each side.]
Step: 3
5x = 30
  [Simplify.]
Step: 4
5x5 = 305
  [Divide each side by 5.]
Step: 5
x = 6
  [Simplify.]
Step: 6
The value of x is 6.
Correct Answer is :   6

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