Inequality Solver

What an inequality tells you

An inequality compares two expressions with $<$, $>$, $\le$ or $\ge$. Instead of a single answer it usually has a range of solutions: every $x$ that makes the statement true. $x>3$ includes 3.1, 50 and a million, but not 3 itself.

How to use the inequality solver

1. Type or paste your problem into the box above — for example 3 - 2x > 7. Use ^ for powers, / for fractions and sqrt() for square roots, or describe it in words.
2. Press Enter. The solver works through the problem with every step shown; switch Steps off if you only want the final answer.
3. Ask a follow-up in the same chat — "why did you do that?" or "now check it" — and it answers with the earlier working in context.

The one rule that differs from equations

You can add, subtract, multiply and divide both sides just as you would with an equation, with one exception: multiplying or dividing by a negative number reverses the inequality sign.

Writing the answer

• Inequality notation: $-2<x\le 3$
• Interval notation: $(-2,3]$ — a round bracket excludes an endpoint, a square bracket includes it.
• Number line: an open circle for $<$ or $>$, a filled circle for $\le$ or $\ge$.

Worked example: $x^2-x-6<0$

1. Find the boundary pointsSolve $x^2-x-6=0$: $(x-3)(x+2)=0$, so $x=-2$ or $x=3$.
2. Split the number lineThe boundaries create three intervals: $x<-2$, $-2<x<3$ and $x>3$.
3. Test a point in each$x=-3$ gives $6$, which is positive; $x=0$ gives $-6$, negative; $x=4$ gives $6$, positive.
4. Keep the intervals that workOnly the middle interval is negative, so $-2<x<3$, or $(-2,3)$ in interval notation.

Common mistakes to avoid

Related calculators

• Solve for XLinear and multi-step equations
• Quadratic equationsRoots, discriminant and formula
• GraphingPlot and compare functions
• Systems of equationsSubstitution and elimination

Questions students ask