#### Solved Examples and Worksheet for Solving Linear Equations

Q1Solve:
67 + y = 76

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

Step: 1
67 + y = 76
[Original Equation.]
Step: 2
67 + y - 67 = 76 - 67
[Add - 67 on both sides.]
Step: 3
y = 9
[Simplify.]
Step: 4
So, 9 is a solution to the equation 67 + y = 76.
Q2Solve for x.
x2 = 1

A. 0
B. 1
C. 12
D. 2

Step: 1
x2 = 1
[Original equation.]
Step: 2
x = 1 × 2
[Multiply both sides with 2.]
Step: 3
x = 2
[1 × 2 = 2.]
Step: 4
So the value of x is 2.
Q3Find the value of n in the number sentence.
15 = 6 + n

A. 11
B. 10
C. 8
D. 9

Step: 1
15 = 6 + n
[Given.]
Step: 2
15 - 6 = n
[Subtract 6 from each side.]
Step: 3
9 = n
[Simplify.]
Step: 4
So, the value of n is 9.
Q4What is the value of n in the number sentence shown?
20 = 8 + n

A. 11
B. 14
C. 12
D. 13

Step: 1
20 = 8 + n
[Given.]
Step: 2
20 - 8 = n
[Subtract 8 from each side.]
Step: 3
12 = n
[Simplify.]
Step: 4
So, the value of n is 12.
Q5Find out the value of n when 28 = 21 + n.
A. 8
B. 7
C. 0
D. 6

Step: 1
28 = 21 + n
[Given.]
Step: 2
28 - 21 = n
[Subtract 21 from each side.]
Step: 3
7 = n
[Simplify.]
Step: 4
So, the value of n is 7.
Q6Find n if 9 = n + 1.

A. 0
B. 8
C. 10
D. 9

Step: 1
9 = n + 1
[Given.]
Step: 2
9 - 1 = n
[Subtract 1 from each side.]
Step: 3
8 = n
[Simplify.]
Step: 4
So, the value of n is 8.
Q7What is the value of n in the number sentence?
21 = n + 5

A. 17
B. 18
C. 16
D. 15

Step: 1
21 = n + 5
[Given.]
Step: 2
21 - 5 = n
[Subtract 5 from each side.]
Step: 3
16 = n
[Simplify.]
Step: 4
So, the value of n is 16.
Q8What is the value of n in the number sentence?
42 = n + 15

A. 29
B. 26
C. 28
D. 27

Step: 1
42 = n + 15
[Given.]
Step: 2
42 - 15 = n
[Subtract 15 from each side.]
Step: 3
27 = n
[Simplify.]
Step: 4
So, the value of n is 27.
Q9What is the value of n in the number sentence?
46 = n + 15

A. 31
B. 33
C. 29
D. 32

Step: 1
46 = n + 15
[Given.]
Step: 2
46 - 15 = n
[Subtract 15 from each side.]
Step: 3
31 = n
[Simplify.]
Step: 4
So, the value of n is 31.
Q10What is the value of n in the number sentence?
n + 36 = 68

A. 33
B. 32
C. 34
D. 30

Step: 1
n + 36 = 68
[Given.]
Step: 2
n = 68 - 36
[Subtract 36 from each side.]
Step: 3
n = 32
[Simplify.]
Step: 4
So, the value of n is 32.
Q11What is the value of n in the number sentence?
61 = n + 4

A. 57
B. 56
C. 58
D. 55

Step: 1
61 = n + 4
[Given.]
Step: 2
61 - 4 = n
[Subtract 4 from each side.]
Step: 3
57 = n
[Simplify.]
Step: 4
So, the value of n is 57.
Q12What is the value of n in the number sentence?
92 = n + 14

A. 74
B. 79
C. 78
D. 80

Step: 1
92 = n + 14
[Given.]
Step: 2
92 - 14 = n
[Subtract 14 from each side.]
Step: 3
78 = n
[Simplify.]
Step: 4
So, the value of n is 78.
Q13What is the value of n in the number sentence?
246 + n = 257

A. 9
B. 11
C. 12
D. 13

Step: 1
246 + n = 257
[Given.]
Step: 2
n = 257 - 246
[Subtract 246 from each side.]
Step: 3
n = 11
[Simplify.]
Step: 4
So, the value of n is 11.
Q14Find the value of n, if n + 8 = 49.

A. 40
B. 42
C. 41
D. 43

Step: 1
n + 8 = 49
Step: 2
n = 49 - 8 = 41
Q15Identify the inverse operation to solve the number sentence.
12 + n = 20

A. subtract 12
B. subtract 20

Step: 1
12 + n = 20
[Given.]
Step: 2
To find the value of n, we need to subtract 12 on both sides of the number sentence.
Step: 3
12 + n - 12 = 20 - 12
Step: 4
n = 8
[Simplify.]
Step: 5
So, the inverse operation "subtract 12" should be used to solve the number sentence.
[Simplify.]
Correct Answer is :   subtract 12
• Variable