SOLVING INEQUALITIES INVOLVING ADDITION AND SUBTRACTION

Example 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.

Example 2 : 

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

8 ≤ 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 8 ≤ y - 3.

8 ≤ 12 - 3

8 ≤ 9

The inequality is true.

Example 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.

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