# Solving Inequalities (using Addition and Subtraction) Worksheet

Solving Inequalities (using Addition and Subtraction) Worksheet
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1.
Which of the following is a solution to the inequality, $n$ + 3 > 49?
 a. 44 b. 49 c. 43 d. 41

#### Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

n + 3 > 49
[Original inequality.]

n + 3 - 3 > 49 - 3
[Subtract 3 from each side.]

n > 46
[Simplify.]

Among the choices, 49 is the only number that is a solution of the inequality n + 3 > 49.

2.
Solve the inequality.
$x$ - 0.7 ≤ 2.1
 a. $x$ ≤ -2.8 b. $x$ ≥ 2.8 c. $x$ ≤ 2.8 d. $x$ ≥ -2.8

#### Solution:

x - 0.7 ≤ 2.1
[Original inequality.]

x - 0.7 + 0.7 ≤ 2.1 + 0.7

x ≤ 2.8
[Simplify.]

3.
Which of the following choices is a solution of the inequality, $n$ + 4 < 74?
 a. 74 b. 68 c. 74 d. 72

#### Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

n + 4 < 74
[Original inequality.]

n + 4 - 4 < 74 - 4
[Subtract 4 from each side.]

n < 70
[Simplify.]

Among the choices, 68 is the only number that is a solution of the inequality n + 4 < 74.

4.
Which of the following choices is the solution for the inequality, $n$ - 5 > 26?
 a. 27 b. 26 c. 30 d. 32

#### Solution:

n - 5 > 26
[Original inequality.]

n - 5 + 5 > 26 + 5

n > 31
[Simplify.]

Among the choices, 32 is the only number that is a solution of the inequality n - 5 > 26.

5.
Which of the following choices is the solution for the inequality, 2$x$ + 1 > 3?
 a. 1 b. -1 c. 2

#### Solution:

2x + 1 > 3
[Original inequality.]

2x + 1 - 1 > 3 - 1
[Subtract 1 from each side.]

2x > 2
[Simplify.]

2x2 > 22
[Divide each side by 2.]

x > 1
[Simplify.]

The solution greater than 1 from the choices is 2.

6.
Which of the following choices is a solution of the inequality, $x$ - $\frac{5}{4}$ > 3?
 a. 4 b. 5 c. 2 d. 3

#### Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

x - 54 > 3
[Original inequality.]

x - 54 + 54 > 3 + 54
[Add 5 / 4 to each side.]

x > 174
[Simplify.]

Among the choices, 5 is the only number that is a solution of the inequality x - 5 / 4 > 3.

7.
Which of the following choices is the solution for the inequality, $x$ - $\frac{3}{4}$ < 2?
 a. 4 b. 2 c. 5 d. 3

#### Solution:

x - 34 < 2
[Original inequality.]

x - 34 + 34 < 2 + 34
[Add 3 / 4 to each side.]

x < 114
[Simplify.]

x < 2.7
[express the fraction as decimal.]

Among the choices, 2 is the only number that is solution for the inequatiy x - 3 / 4< 2.

8.
Which of the following choices is the solution of the inequality, $x$ + $\frac{1}{4}$ < 12?
 a. 13 b. 14 c. 11 d. 12

#### Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

x + 14 < 12
[Original inequality.]

x + 14 - 14 < 12 - 14
[Subtract 1 / 4 from each side.]

x < 474
[Simplify.]

Among the choices, 11 is the only number that is a solution of the inequality x + 1 / 4 < 12 .

9.
Solve the inequality.
$x$ + $\frac{4}{5}$ > 8
 a. $x$ < $\frac{36}{5}$ b. $x$ > $\frac{36}{5}$ c. $x$ ≥ $\frac{36}{5}$ d. $x$ ≤ $\frac{36}{5}$

#### Solution:

x + 45 > 8
[Original inequality.]

x + 45 - 45 > 8 - 45
[Subtract 4 / 5 from each side.]

x > 365
[Simplify.]

10.
Solve the inequality.
$n$ - $\frac{4}{5}$ < $\frac{3}{4}$
 a. $n$ < $\frac{31}{20}$ b. $n$ ≤ $\frac{31}{20}$ c. $n$ ≥ $\frac{31}{20}$ d. $n$ > $\frac{31}{20}$

#### Solution:

n - 45 < 34
[Original inequality.]

n - 45 + 45 < 34 + 45
[Add 4 / 5 to each side.]

n < 15+1620
[Simplify.]

n < 3120
[Simplify.]