Inequality Solver
Solve linear and quadratic inequalities on a number line
About this calculator
The Inequality Solver solves linear and quadratic inequalities ax² + bx + c (<, ≤, >, ≥) 0 exactly, reporting the solution set as intervals on a number line. For quadratics it computes the discriminant b² − 4ac and the roots in 30-digit decimal arithmetic, then reads off whether the answer is a bounded interval, two rays, a single point, all reals, or empty — honoring strict versus inclusive boundaries. When a = 0 it falls back to the linear (or constant) case automatically.
How to use the Inequality Solver calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- x² − 5x + 6 < 0 → 2 < x < 3 (between the roots)
- x² − 4 ≥ 0 → x ≤ −2 or x ≥ 2 (two rays, endpoints included)
- 2x − 6 > 0 → x > 3 (linear case, one open ray)
- x² + 1 > 0 → all real numbers (discriminant −4, no real roots)
Frequently asked questions
How does the Inequality Solver calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Inequality Solver calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.