Solve one-variable linear inequalities and see when the inequality sign flips. Enter expressions with x on one or both sides.
For 2x + 5 ≤ 17, subtract 5 to get 2x ≤ 12, then divide by 2. The solution is x ≤ 6.
Linear inequality solution
- Move x terms to one side.
- Move constants to the other side.
- Divide by the coefficient of x.
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How to Use the Inequality Calculator
Enter a linear inequality with one variable x. The calculator simplifies both sides, isolates x, and shows whether the inequality sign stays the same or flips.
- Use x as the variable.
- Use <, <=, >, or >= for the inequality sign.
- Review the steps before copying the final interval.
When Does the Inequality Sign Flip?
The inequality sign flips only when both sides are multiplied or divided by a negative number.
The calculator flags this step so the direction of the answer is easier to verify.
Inequality Examples
2x + 5 ≤ 17
Subtract 5 and divide by 2. The solution is x ≤ 6.
-3x + 4 > 10
Subtract 4 to get -3x > 6. Divide by -3 and flip the sign. The solution is x < -2.
4x + 1 < 2x + 9
Move x terms together and constants together. The solution is x < 4.
Common Inequality Mistakes
Not flipping the sign after dividing by a negative
This is the most common inequality error. Division by a negative reverses the comparison.
Treating an inequality like an equation answer
An inequality usually has a range of values, not a single value.
Changing both sides unevenly
Whatever you add, subtract, multiply, or divide must be applied to both sides.
Inequality Calculator FAQs
Can this solve compound inequalities?
This draft is for one linear inequality at a time. Compound inequality support can be added as a later version.
Does it solve inequalities with x on both sides?
Yes. It supports linear inequalities such as 4x + 1 < 2x + 9.
Why did the sign flip?
The sign flips when both sides are divided or multiplied by a negative number.
Does it graph the answer?
This page gives the symbolic solution. A graphing calculator can be used for visual number-line or coordinate-plane work.
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Reviewer
This educational math content is reviewed under the SolverCalc reviewer rule by Prof. Dr. Khalil Mudassar. WordPress adds the author bio automatically, so this page does not include a duplicate author box.
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.