⚖️Inequality Calculator
Solve linear, quadratic, and compound inequalities with steps, interval notation, and a number line.
Free Inequality Calculator
Solving inequalities is easy to get wrong — especially remembering to flip the sign. Our free inequality calculator solves linear, quadratic, and compound inequalities and shows every step, with the sign-flip rule called out explicitly whenever you multiply or divide by a negative number.
Type in your inequality and get the solution in both inequality notation and interval notation, plus a visual number line showing exactly which values satisfy it — with open or closed circles and shading that match the boundary conditions.
For quadratic inequalities, the calculator finds the roots, builds a sign chart across the intervals, and combines them into the correct solution set. Special cases like "no solution" or "all real numbers" are explained in plain English rather than left blank. No sign-up, no downloads, no limits.
About the Inequality Calculator
Features
Sign-flip rule
Explicitly called out whenever multiplying or dividing by a negative number.
Quadratic sign chart
Roots and a sign-chart method combine into the correct solution intervals.
Compound inequalities
Expressions like -3 < 2x + 1 < 5 split, solved, and recombined.
Number line + interval notation
Solution shown visually with open/closed circles and as interval notation.
Frequently Asked Questions
How does the inequality calculator work?
Type in your inequality and it solves step by step, showing the solution as an inequality, an interval, and a number line.
Is it free?
Completely free, no sign-up, downloads, or limits.
Does it handle quadratic inequalities?
Yes, it finds the roots and builds a sign chart to determine the correct solution intervals.
What about compound inequalities?
Yes, inequalities like -3 < 2x + 1 < 5 are split, solved, and recombined correctly.
Why does the sign flip sometimes?
Multiplying or dividing both sides by a negative number reverses the inequality direction — the calculator highlights this step explicitly since it's the most common mistake.
What does interval notation mean?
A compact way to write a solution set, like (2, ∞) for "all values greater than 2" — shown alongside the inequality form.
What if there's no solution?
The calculator explains clearly when an inequality has no solution, rather than leaving the answer blank.
What if all real numbers satisfy it?
Cases like x² ≥ 0 are identified and explained as true for all real numbers.
Is my data stored?
No; everything runs in your browser and isn't stored or sent.
Does it work on mobile?
Yes, fully responsive; the number line and steps adapt to smaller screens.