# One–Step Inequalities

To solve one-step inequalities, you only need to do one math operation. Learn how to solve one-step inequalities easily.

## Step by step guide to solve one-step inequalities

• Similar to equations, first isolate the variable by using the inverse operation.
• For dividing or multiplying both sides by negative numbers, flip the direction of the inequality sign.

### Example 1:

Solve and graph the inequality. $$x \ + \ 2 \ ≥ \ 3$$

Solution:

Subtract 2 from both sides. $$x \ + \ 2 \ ≥ \ 3→x \ + \ 2 \ – \ 2 \ ≥ \ 3 \ – \ 2, then: x \ ≥ \ 1$$

### Example 2:

Solve and graph the inequality. $$x \ – \ 1 \ \leq \ 2$$

Solution:

Add $$1$$ to both sides. $$x \ − \ 1 \ ≤ \ 2→x \ − \ 1 \ + \ 1 \ ≤ \ 2 \ + \ 1$$, then: $$x \ ≤ \ 3$$

### Example 3:

Solve and graph the inequality. $$x+5≥6$$.

Solution:

Subtract $$5$$ from both sides. $$x+5≥6→x+5-5≥6-5$$, then: $$x≥1$$

### Example 4:

Solve this inequality. $$x-6≤-3$$

Solution:

Add $$6$$ to both sides. $$x-6≤-3→x-6+6≤-3+6$$, then: $$x≤3$$

## Exercises

### Solve each inequality and graph it.

1- $$\color{blue}{x + 9 ≥ 11}$$

2- $$\color{blue}{x – 4 ≤ 2}$$

3- $$\color{blue}{6x ≥ 36}$$

4- $$\color{blue}{7 + x < 16}$$

5- $$\color{blue}{x + 8 ≤ 1}$$

6- $$\color{blue}{3x > 12}$$