**Solving inequalities involving addition and subtraction :**

We can use properties of inequality to solve inequalities involving addition and subtraction with rational numbers.

**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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