Inequalities Calculator
Inequality Calculator works out Solution in interval notation and Solution in inequality notation from Inequality, Variable and Restrict to. The default figures on this page give solution in interval notation of (-∞, -12); change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
5 steps
- Read as: 3x + 5 < 2x - 7.
- Collect everything on one side: f(x) < 0.
- Critical numbers: -12.
- Test one point in each interval between the critical numbers, and test the critical numbers themselves.
- Solution: (-∞, -12)
Endpoints of the solution settable
Critical numbers testedtable
Sign charttable
| interval | testPoint | value | sign | satisfied |
|---|---|---|---|---|
| (-∞, -12) | -24 | -12 | - | yes |
| (-12, ∞) | 0 | 12 | + | no |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Inequality Calculator calculates
Solves linear, absolute-value, quadratic, polynomial and compound inequalities in one variable and writes the solution set in inequality, interval and set-builder notation.
How to use this Inequality Calculator
Enter Inequality, Variable, Restrict to and Headline answer as. Solution in interval notation updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Solution in interval notation, Solution in inequality notation and Solution in set-builder notation.
The method follows OpenStax, Elementary Algebra 2e, section 2.7: Solve Linear Inequalities, and section 2.7 compound inequalities and OpenStax, Intermediate Algebra 2e, section 9.8: Solve Quadratic Inequalities, and section 2.7: Solve Absolute Value Inequalities.
Linear: 3x + 5 < 2x - 7 example
With Inequality: 3x + 5 < 2x - 7, the calculator returns Solution in interval notation: (-∞, -12), Solution in inequality notation: x < -12, Endpoints of the solution set: see result table. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Solution in interval notation, Solution in inequality notation and Solution in set-builder notation. The inputs you can vary are Inequality, Variable, Restrict to and Headline answer as.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
Can I do inequalities on a TI-84 calculator?
Solves linear, absolute-value, quadratic, polynomial and compound inequalities in one variable and writes the solution set in inequality, interval and set-builder notation. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give (-∞, -12).
How to calculate an inequality?
Solves linear, absolute-value, quadratic, polynomial and compound inequalities in one variable and writes the solution set in inequality, interval and set-builder notation. Open “How this is worked out” beside the result to see each step for your own figures.
How do I solve inequalities?
It needs Inequality, Variable, Restrict to and Headline answer as. Nothing else is required, and the figures stay in your browser.
How to solve inequalities fast?
The result gives Solution in interval notation, Solution in inequality notation, Solution in set-builder notation, Endpoints of the solution set, Critical numbers tested and Shape of the solution set, each labelled with its unit so the figure can be read on its own.
What information do I need for the Inequality Calculator?
You need Inequality, Variable, Restrict to and Headline answer as. The page opens with default figures that give solution in interval notation of (-∞, -12), so you can see the scale before entering your own.
What does this Inequality Calculator show?
It shows Solution in interval notation, Solution in inequality notation, Solution in set-builder notation, Endpoints of the solution set, Critical numbers tested, Shape of the solution set, Number of intervals and Every real number is a solution, with the working and any warnings for your entries.