One–Step Inequalities

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

Download One-Step Inequalities Worksheet

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