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

## Related Topics

- How to Solve One-Step Equations
- How to Solve Multi-Step Equations
- How to Solve Multi-Step Inequalities
- How to Solve Systems of Equations
- How to Graph Single–Variable Inequalities

## 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.

### One–Step Inequalities – Example 1:

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

**Solution:**

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

### One–Step Inequalities – 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: \(x \ ≤ \ 3\)

### One–Step Inequalities – 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: \(x≥1\)

### One–Step Inequalities – 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 for Solving One–Step Inequalities

### 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- \(\color{blue}{3x > 12}\)