Inequality Calculator — Solve & Graph on a Number Line (Free)

Use this free inequality calculator to solve a one-variable linear inequality such as 2x + 3 ≤ 11. Enter the coefficients and the inequality sign, and you’ll get the solution, the answer in interval notation, and a number-line graph — with the all-important sign-flip handled for you.

How to use the calculator

1. Enter the coefficient of x, the constant, the inequality sign, and the right-hand side.
2. Press Calculate.
3. Read the solution, the interval notation, and the number-line graph.

The sign-flip rule

Solving an inequality is like solving an equation, with one key rule: when you multiply or divide both sides by a negative number, you must flip the inequality sign. The calculator applies this automatically and points it out in the steps.

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Frequently asked questions

When do you flip an inequality sign?

Whenever you multiply or divide both sides by a negative number. For example, dividing −2x > 4 by −2 gives x < −2.

What is interval notation?

A compact way to write a solution set: x ≤ 4 becomes (−∞, 4], where a square bracket includes the endpoint and a parenthesis excludes it.

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What do open and closed circles mean?

On the number line, an open circle (for < or >) excludes the boundary value; a closed circle (for ≤ or ≥) includes it.

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Read the full lesson: learn the method step by step.

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