Inequality Calculator
Solving an inequality works like solving an equation — with one famous exception: multiply or divide by a negative and the sign flips. Enter your inequality in the form ax + b (sign) c and get the solution set with the reasoning shown.
Results
Formula
How to use this calculator
- Enter a and b from the left side.
- Choose your inequality sign.
- Enter c, then Calculate — the solution accounts for any sign flip.
Worked example
Solve 2x + 4 < 12.
- Subtract 4: 2x < 8.
- Divide by 2 (positive, sign unchanged): x < 4.
Result: x < 4 — every number below 4 is a solution.
Frequently asked questions
Why does the sign flip for negatives?
Multiplying by −1 reverses the order of numbers on the number line: 2 < 5 but −2 > −5. The flip keeps the inequality true.
How is an inequality answer different from an equation answer?
An equation usually has one solution; an inequality has a whole range of solutions, written as x < 4, x ≥ −2, and so on — often shaded on a number line.
What do the ≤ and ≥ signs add?
They include the boundary value itself as a solution. On a number line that is drawn with a filled circle instead of an open one.
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