# SOLVING INEQUALITIES WITH ADDITION AND SUBTRACTION WORKSHEET

Problem 1 :

Solve the inequality given below. Graph and check the solution.

x + 5 < -12

Problem 2 :

Solve the inequality given below. Graph and check the solution.

y - 3

Problem 3 :

Solve the inequality given below. Graph and check the solution.

x + 3 < 8

Problem 4 :

Solve the inequality given below. Graph and check the solution.

y -5  -7

Problem 5 :

Solve the inequality given below. Graph and check the solution.

21 > 12 + x

## Detailed Answer Key

Problem 1 :

Solve the inequality given below. Graph and check the solution.

x + 5 < -12

Solution :

Step 1 :

Solve the inequality

x + 5 < -12

Use the Subtraction Property of Inequality.

Subtract 5 on from both sides.

(x + 5) - 5 < -12 - 5

x < -17

Step 2 :

Graph the solution.

Step 3 :

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute -18 for x into x + 5 < -12.

-18 + 5 < -12

-13 < -12

The inequality is true.

Problem 2 :

Solve the inequality given below. Graph and check the solution.

y - 3

Solution :

Step 1 :

Solve the inequality

8 ≤ y - 3

Use the Addition Property of Inequality.

Add 3 to to both sides.

8 + 3 ≤ (y - 3) + 3

11 ≤ y

or y ≥ 11

Step 2 :

Graph the solution.

Step 3 :

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute 12 for y into  y - 3.

12 - 3

9

The inequality is true.

Problem 3 :

Solve the inequality given below. Graph and check the solution.

x + 3 < 8

Solution :

Step 1 :

Solve the inequality

x + 3 < 8

Use the Subtraction Property of Inequality.

Subtract 3 from both sides.

(x + 3) - 3 < 8 - 3

x < 5

Step 2 :

Graph the solution.

Step 3 :

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute 0 for x into x + 3 < 8.

0 + 3 < 8

3 < 8

The inequality is true.

Problem 4 :

Solve the inequality given below. Graph and check the solution.

y -5  -7

Solution :

Step 1 :

Solve the inequality

y -5  -7

Use the Addition property Property of Inequality.

Add 5 to both sides.

(y -5) + 5  -7 + 5

y ≥ -2

Step 2 :

Graph the solution.

Step 3 :

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute 1 for y into y -5  -7.

1 - 5  -7

-4  -7

The inequality is true.

Problem 5 :

Solve the inequality given below. Graph and check the solution.

21 > 12 + x

Solution :

Step 1 :

Solve the inequality

21 > 12 + x

Use the Subtraction property Property of Inequality.

Subtract 12 from both sides.

21 - 12 > (12 + x) - 12

9 > x

or x < 9

Step 2 :

Graph the solution.

Step 3 :

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute 2 for x into 21 > 12 + x.

21 > 12 + 2

21 > 14

The inequality is true.

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