How to Solve One-Step Inequalities? (+FREE Worksheet!)
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.
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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- \(\color{blue}{3x > 12}\)
Download One-Step Inequalities Worksheet
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