Solved Examples and Worksheet for Solving Linear Equations in One Variable

Q1Solve q - 85 = - 17.

A. 101
B. 68
C. - 68
D. 102

Solutions
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Step: 1
q - 85 = - 17
  [Original equation.]
Step: 2
q - 85 + 85 = - 17 + 85
  [Add 85 on each side.]
Step: 3
q = 68
  [Simplify.]
Correct Answer is :   68
Q2Joe bought a shirt for $6 less than the original price. If he paid $36 for the shirt, then what was the original price?
A. $36
B. $216
C. $30
D. $42

Solutions
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Step: 1
Let x be the price on the tag.
Step: 2
The price Joe paid for the shirt = $(x - 6).
Step: 3
x - 6 = 36
  [Write an equation.]
Step: 4
x - 6 + 6 = 36 + 6
  [Add 6 to both sides.]
Step: 5
x = 42
  [Simplify.]
Step: 6
The price on the tag is $42.
Correct Answer is :   $42
Q3The computer science department had 27 students in 2002. If 13 of these students failed, then how many students graduated?
A. 14
B. 40
C. 7
D. 21

Solutions
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Step: 1
Let s be the number of students, who graduated.
Step: 2
s + 13 = 27
  [Write an equation.]
Step: 3
s + 13 - 13 = 27 - 13
  [Subtract 13 from each side.]
Step: 4
s = 14
  [Simplify.]
Step: 5
The number of students who graduated is 14.
Correct Answer is :   14
Q4Solve 27 + q = - 18.

A. 45
B. - 45
C. - 50
D. - 55

Solutions
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Step: 1
27 + q = - 18
  [Original equation.]
Step: 2
27 + q - 27 = - 18 - 27
  [Subtract 27 from each side.]
Step: 3
q = - 45
  [Simplify.]
Correct Answer is :   - 45
Q5The sum of 25 and another number is 32. What is the number?
A. 32
B. 7
C. 6
D. 57

Solutions
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Step: 1
Let a be the another number.
Step: 2
25 + a = 32
  [Original equation.]
Step: 3
25 + a - 25 = 32 - 25
  [Subtract 25 from each side.]
Step: 4
a = 7
  [Simplify.]
Step: 5
The other number is 7.
Correct Answer is :   7
Q6Solve 4475 + k = 4000.

A. 475
B. - 4950
C. 4950
D. - 475

Solutions
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Step: 1
4475 + k = 4000
  [Original equation].
Step: 2
4475 + k - 4475 = 4000 - 4475
  [Subtract 4475 from each side.]
Step: 3
k = - 475
  [Simplify.]
Correct Answer is :   - 475
Q7Which of the following is a solution of the equation x - 37 = 26?
A. 73
B. 26
C. 63
D. 64

Solutions
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Step: 1
x - 37 = 26
  [Original equation.]
Step: 2
x - 37 + 37 = 26 + 37
  [Add 37 on both sides.]
Step: 3
x = 63
  [Simplify.]
Step: 4
So, 63 is the solution of the equation.
Correct Answer is :   63
Q8What is the value of the variable p in the equation p - (- 5) = - 5?

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

Solutions
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Step: 1
p - (- 5) = - 5
  [Original equation.]
Step: 2
p + 5 = - 5
  [Use subtraction rule to simplify.]
Step: 3
p + 5 - 5 = - 5 - 5
  [Subtract 5 from each side.]
Step: 4
p = - 10
  [Simplify.]
Step: 5
The value of the variable p in the equation is - 10.
Correct Answer is :   - 10
Q9Solve the equation a + 12 = 23.

A. a = 11
B. a = 16
C. a = 21
D. a = 6

Solutions
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Step: 1
a + 12 = 23
  [Original equation.]
Step: 2
a + 12 - 12 = 23 - 12
  [Subtract 12 from each side.]
Step: 3
a = 11
  [Simplify.]
Correct Answer is :   a = 11
Q10What is the value of p in the equation p - 17 = 45?
A. 62
B. 68
C. 56
D. 50

Solutions
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Step: 1
p - 17 = 45
  [Original equation.]
Step: 2
p - 17 + 17 = 45 + 17
  [Add 17 on both sides.]
Step: 3
p = 62
  [Simplify.]
Step: 4
The value of the variable p in the equation is 62.
Correct Answer is :   62
Q11Solve for x in the equation x + 17 = 59.

A. 42
B. 47
C. 37
D. 50

Solutions
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Step: 1
x + 17 = 59
  [Original equation.]
Step: 2
x + 17 - 17 = 59 - 17
  [Subtract 17 from each side.]
Step: 3
x = 42
  [Simplify.]
Correct Answer is :   42
Q12Solve - a4 = 4.

A. - 19
B. 15
C. - 16
D. 14

Solutions
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Step: 1
- a4 = 4
  [Original equation.]
Step: 2
(- 4) × - a4 = (- 4) × (4)
  [Multiply each side by - 4.]
Step: 3
a = - 16
  [Simplify.]
Correct Answer is :   - 16
Q13Solve x- 4 = - 5.

A. 22
B. 20
C. - 20
D. - 22

Solutions
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Step: 1
x- 4 = - 5
  [Original equation.]
Step: 2
x- 4 × (- 4) = - 5 × (- 4)
  [Multiply each side by - 4.]
Step: 3
x = 20
  [Simplify.]
Correct Answer is :   20
Q14Mr.John owns one-fourth part of a property. If the value of his share is $1,300, what is the total value of the property?
A. $6,225
B. $5,200
C. $8,250
D. $7,200

Solutions
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Step: 1
Let p be the total value of the property.
Step: 2
p4 = 1300
  [Write an equation.]
Step: 3
p4 × 4 = 1300 × 4
  [Multiply each side by 4.]
Step: 4
p = 5200
  [Simplify.]
Step: 5
Total value of the property is $5,200.
Correct Answer is :   $5,200
Q15Jim drove his car to get to the beach. Gasoline costs about $2 per gallon. For his trip, Jim spent $100 on gasoline. How many gallons of gas did he use?
A. 46 gallons
B. 50 gallons
C. 52 gallons
D. 48 gallons

Solutions
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Step: 1
Let p be the gallons of gasoline consumed for Jim's journey.
Step: 2
100 = 2 × p
  [Write an equation.]
Step: 3
1002 = 2 × p2
  [Divide each side by 2.]
Step: 4
50 = p
  [Simplify.]
Step: 5
So, 50 gallons of gasoline were consumed for Jim's journey.
Correct Answer is :   50 gallons

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