Solve linear, quadratic, rational, and absolute value inequalities. Get interval notation, sign chart, number line graph, and step-by-step working — instantly.
Enter any inequality using standard notation. The solver identifies the type — linear, quadratic, rational, or absolute value — and applies the appropriate algebraic method to find the solution set.
The answer is expressed in interval notation, a compact standard used in algebra and calculus. Open parentheses mean the endpoint is excluded (strict inequality), while square brackets mean it is included.
Supported inequality types
Linear: e.g. 2x + 3 < 7. Solved by isolating x, with direction flip when dividing by a negative.
Quadratic: e.g. x² − 9 > 0. Solved by finding roots, then testing intervals using a sign chart.
Rational: e.g. (x−1)/(x+2) ≤ 0. Excludes values that make the denominator zero, then applies sign chart analysis.
Absolute value: e.g. |x − 3| < 2 or |x| > 2. Split into two cases using the absolute value definition.
Reading interval notation
( ) — open endpoint, value excluded | [ ] — closed endpoint, value included | ∪ — union of two separate intervals | ∞ — extends to infinity (always open)
Frequently Asked Questions
This calculator solves linear, quadratic, rational, and absolute value inequalities, returning interval notation, a sign chart, and a number line graph.
Interval notation expresses a solution set using parentheses for open (excluded) endpoints and brackets for closed (included) endpoints. For example, (2, ∞) means all values greater than 2.
The union symbol ∪ joins two or more separate intervals. For example, (−∞, −3) ∪ (3, ∞) means all values less than −3 or greater than 3.
Use abs() notation. For example: abs(x − 3) < 2 or abs(x) > 5. The solver automatically splits into cases.
Enter the expression directly, for example: (x − 1)/(x + 2) <= 0. The solver handles denominator exclusions automatically and marks those points as open on the number line.
The solver handles both cases. All real numbers is shown as (−∞, ∞) and an empty set is shown as ∅. Both include an explanation in the diagnostics section.