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.
![How to Solve One-Step Inequalities? (+FREE Worksheet!)](https://www.effortlessmath.com/wp-content/uploads/2019/12/One–Step-Inequalities-Cover-512x240.jpg)
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: \(x \ ≥ \ 1\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/123.png)
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: \(x \ ≤ \ 3\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/454.png)
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- \(\color{blue}{x + 9 ≥ 11}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/33-5.png)
2- \(\color{blue}{x – 4 ≤ 2}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/33-6.png)
3- \(\color{blue}{6x ≥ 36}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/33-7.png)
4- \(\color{blue}{7 + x < 16}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/33-8.png)
5- \(\color{blue}{x + 8 ≤ 1}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/33-9.png)
6- \(\color{blue}{3x > 12}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/33-10.png)
Download One-Step Inequalities Worksheet
![This image has an empty alt attribute; its file name is answer-3.png](https://www.effortlessmath.com/wp-content/uploads/2020/04/answer-3.png)
Answers
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/y-1.png)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/y1.png)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/y3.png)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/y4.png)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/y5.png)
![](https://www.effortlessmath.com/wp-content/uploads/2019/09/y6.png)
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