# Solve One-step Equations Worksheet

Solve One-step Equations Worksheet
• Page 1
1.
What is the value of $n$ in the equation?
4$n$ = $\frac{4}{13}$
 a. 1 b. $\frac{13}{1}$ c. $\frac{1}{13}$ d. None of the above

#### Solution:

4n = 4 / 13
[Original equation.]

n = 4 / 13 ÷ 4
[Divide each side by 4.]

= 4 / 13 ÷ 4 / 1
[Write 4 as 4 / 1.]

= 4 / 13 × 1 / 4
[Multiply by the reciprocal of 4 / 1, which is 1 / 4.]

= 4×1 / 13×4

= 1×1 / 13×1
[Cancel 4 with 4.]

= 1 / 13
[Simplify.]

So, the value of n is 1 / 13.

2.
Find the value of $x$ + 9, if $x$ + 6 = 15.
 a. 18 b. 23 c. 28 d. 13

#### Solution:

x + 6 = 15
[Original expression.]

(x + 6) + 3 = 15 + 3
[Add 3 on both sides to get 9.]

x + 9 = 18

The value of x + 9 is 18.

3.
7 times a number $n$ equals 14. What is the value of $n$?
 a. 2 b. 3 c. 4 d. 1

#### Solution:

7 times a number n = 7n

7n = 14
[Original equation.]

n = 14 / 7
[Divide each side by 7.]

n = 2

So, the value of the number n is 2.

4.
The quotient, when a number $n$ is divided by 6, equals 16. Find the number.
 a. 96 b. 86 c. 106 d. 101

#### Solution:

n / 6 = 16

n = 16 × 6
[Multiply each side by 6.]

= 96
[Multiply.]

So, the number n is 96.

5.
The difference between 77 times a number $n$ and 23 times the same number $n$ is ____ times the same number.
 a. 54 b. 58 c. 59 d. 52

#### Solution:

77 times a number n = 77n.

23 times the number n = 23n.

77 times n - 23 times n = 77n - 23n.

= 54n
[Subtract.]

So, the difference between 77 times n and 23 times n is 54 times n.

6.
Find the value of $x$ + 3, if $x$ + 24 = 31.
 a. 17 b. 8 c. 10 d. 7

#### Solution:

x + 24 = 31
[Original expression.]

x = 31 - 24
[Subtract 24 from both the sides.]

x = 7
[Subtract 24 from 31.]

x + 3 = 7 + 3
[Substitute x = 7.]

= 10

The value of x + 3, if x + 24 = 31 is 10.

7.
Solve the expression, $m$ + 36 for $m$ = 20.
 a. 41 b. 56 c. 71 d. 86

#### Solution:

m + 36
[Original algebraic expression.]

= 20 + 36
[Substitute m = 20.]

= 56

So, m + 36 = 56 when m = 20.

8.
Solve the expression $b$ × 8 for $b$ = 5.
 a. 55 b. 45 c. 40 d. 25

#### Solution:

b × 8
[Original algebraic expression.]

= 5 × 8
[Substitute b = 5.]

= 40
[Multiply.]

So, b × 8 = 40 when b = 5.