Inequality Solver
Solve inequalities and get the answer in interval notation, with every sign flip explained.
Press Enter to solve · ^ for powers · sqrt() for roots · separate a system with a comma
The inequality solver handles <, >, ≤ and ≥. It isolates the variable, flips the sign when you divide by a negative number, and writes the final answer in both inequality form and interval notation.
How to use the inequality solver
- Type the inequality using
<,>,<=or>=, e.g.2x - 5 > 7. - Press Enter.
- Read the steps and the interval notation.
The one rule that changes
Solving an inequality works like solving an equation, with one exception: when you multiply or divide both sides by a negative number, flip the inequality sign. For example −2x < 6 becomes x > −3.
Quadratic inequalities
For an inequality like x² − 4 ≤ 0, the solver first finds the boundary points (x = −2 and x = 2), then tests a point in each interval. The answer here is the closed interval [−2, 2].
Interval notation cheat sheet
| Inequality | Interval |
|---|---|
| x > 3 | (3, ∞) |
| x ≥ 3 | [3, ∞) |
| x < 3 | (−∞, 3) |
| −2 ≤ x ≤ 2 | [−2, 2] |
Questions about inequalities
Why do you flip the inequality sign?
Multiplying by a negative number reverses the order of numbers on the number line: 2 < 3 but −2 > −3. Flipping the sign keeps the statement true.
What do round and square brackets mean?
A round bracket ( ) means the endpoint is not included (< or >). A square bracket [ ] means it is included (≤ or ≥). Infinity always gets a round bracket.
What if every number is a solution?
Then the answer is all real numbers, written (−∞, ∞). If no number works, the answer is the empty set ∅.