Inequality Calculator

Solve a linear or quadratic inequality in one variable — the solution is shown in interval notation and drawn on a number line.

Solution (interval notation)

How to Solve an Inequality

Type an inequality in one variable to get the solution set and its number line.

1

Enter the inequality

Type it with one relational sign — for example 2x + 3 < 7 or x² − 4 ≥ 0. Both sides may hold expressions.

2

Read the solution

The answer is given in interval notation, using round brackets for excluded (strict) bounds and square brackets for included ones.

3

Check the number line

The solution is drawn on a number line: filled dots are included boundary points, hollow dots are excluded, and the shaded part is the solution.

Frequently Asked Questions

How do you solve a quadratic inequality?
Move everything to one side, find where the quadratic equals zero, then use a sign chart between and outside those roots. For x² − 4 < 0 the roots are −2 and 2, and the expression is negative between them, so the solution is (−2, 2).
What is interval notation?
Interval notation writes a solution set as ranges. A round bracket ( or ) excludes an endpoint (for < or >); a square bracket [ or ] includes it (for ≤ or ≥); ∪ joins separate pieces.
When do you flip the inequality sign?
When you multiply or divide both sides by a negative number. This calculator avoids that pitfall by moving everything to one side and using a sign chart instead.
Is my data sent anywhere?
No. Everything runs in your browser with JavaScript; nothing is uploaded or stored.