Inequality Calculator
Solve an inequality, track sign changes, and write the answer in interval notation.
Drag & drop or upload an image or PDF
Try an example
An inequality usually has a range of answers
Instead of finding a single value, an inequality asks which values make one side larger or smaller than the other. The result is often shown on a number line or in interval notation.
Linear inequalities follow familiar equation rules with one important exception: multiplying or dividing by a negative number reverses the inequality sign. Polynomial and rational inequalities also require testing intervals around critical points.
How to use the inequality calculator
Enter the problem as written
Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.
Read the working, not only the answer
Each transformation is separated and explained so you can compare it with your own method.
Ask about any step
Continue in the same solution to request another method, check a restriction, or ask why a rule applies.
The sign reversal rule
Multiplying or dividing both sides by a negative number reverses the order.
A reliable way to work through it
Isolate the variable
Use inverse operations just as you would for an equation, while watching for negative division.
Find boundary points
Set polynomial factors or rational numerators and denominators equal to zero.
Test the intervals
Choose a value from each interval to determine where the original inequality is true.
Worked example
Solve -3x + 7 > 19
Subtract 7 from both sides.
Divide by -3 and reverse the inequality sign.
Write the strict inequality in interval notation.
The solution is x < -4.
Common mistakes to check
Forgetting to reverse the sign
The inequality symbol flips only when multiplying or dividing by a negative value.
Including an undefined endpoint
A value that makes a denominator zero is never included.
Testing the simplified expression incorrectly
Test points in the original inequality when you are unsure about a transformation.
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Questions students ask
Does the calculator give interval notation?
Yes. It can show inequality notation and interval notation, including open or closed endpoints.
Can it solve compound inequalities?
Yes. Enter the full statement, such as 2 < 3x - 1 <= 11, and it will preserve both bounds.
Why does the inequality sign sometimes flip?
Multiplication or division by a negative reverses the order of numbers, so the symbol must reverse too.
Can it solve rational inequalities?
Yes. It finds zeros and undefined points, builds sign intervals, and excludes values outside the original domain.