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: 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
Q3Find 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
Q4A 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
Q5Solve: 5x = 18 - x
A. 4
B. 3
C. 2
D. 1

Solutions
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Step: 1
5x = 18 - x
  [Original equation.]
Step: 2
6x = 18
  [Add x to both sides.]
Step: 3
6x6 = 186
  [Divide each side by 6.]
Step: 4
x = 3
  [Simplify.]
Step: 5
The solution of the equation is x = 3.
Correct Answer is :   3
Q6Solve:
5z + 2 = - 13

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

Solutions
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Step: 1
5z + 2 = - 13
  [Original equation.]
Step: 2
5z + 2 - 2 = - 13 - 2
  [Subtract 2 from each side.]
Step: 3
5z = - 15
  [Simplify.]
Step: 4
5z5 = - 155
  [Divide each side by 5.]
Step: 5
z = - 3
  [Simplify.]
Correct Answer is :   - 3
Q7Solve:
m90 - 3 = - 11

A. - 730
B. 720
C. - 720
D. - 710

Solutions
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Step: 1
m90 - 3 = - 11
  [Original equation.]
Step: 2
m90 - 3 + 3 = - 11 + 3
  [Add 3 on each side.]
Step: 3
m90 = - 8
  [Add.]
Step: 4
90 × m90 = 90(- 8)
  [Multiply each side by 90.]
Step: 5
m = - 720
  [Simplify.]
Correct Answer is :   - 720
Q8Solve:
23 = k- 5 + 20
A. 5
B. - 3
C. - 2
D. - 15

Solutions
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Step: 1
23 = k- 5 + 20
  [Original equation.]
Step: 2
23 - 20 = k(- 5) + 20 - 20
  [Subtract 20 from each side.]
Step: 3
3 = k- 5
  [Simplify.]
Step: 4
(- 5)3 = - 5 × k- 5
  [Multiply each side by - 5.]
Step: 5
- 15 = k
  [Simplify.]
Step: 6
k = - 15
  
Correct Answer is :   - 15
Q9Solve:
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
Q10Solve:
- 12 - 4d = 8

A. - 6
B. - 5
C. - 7
D. - 4

Solutions
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Step: 1
- 12 - 4d = 8
  [Original equation.]
Step: 2
- 12 - 4d + 12 = 8 + 12
  [Add 12 on both sides.]
Step: 3
- 4d = 20
  [Simplify.]
Step: 4
- 4d- 4 = 20- 4
  [Divide each side by - 4.]
Step: 5
d = - 5
  [Simplify.]
Correct Answer is :   - 5
Q11Solve:
d5 + 6 = - 5

A. - 55
B. 11
C. 10
D. 12

Solutions
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Step: 1
d5 + 6 = - 5
  [Original equation.]
Step: 2
d5 + 6 - 6 = - 5 - 6
  [Subtract 6 from each side.]
Step: 3
d5 = - 11
  [Simplify.]
Step: 4
(5) × (d5) = (5) × (- 11)
  [Multiply each side by 5.]
Step: 5
d = - 55
  [Simplify.]
Correct Answer is :   - 55
Q12Solve:
2d + 3 = 11

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

Solutions
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Step: 1
2d + 3 = 11
  [Original equation.]
Step: 2
2d + 3 - 3 = 11 - 3
  [Subtract 3 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

HighSchool Math