Enter a linear inequality like 2x + 3 > 7 or -x ≤ 5 into the Inequality Expression field, choose your variable, and get back the solution set, the interval notation, and a clear number line visualization showing the solution region.
Solution
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Interval Notation
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Boundary Point
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Inequality Type
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Solution Direction
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An inequality is a mathematical statement that compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Unlike an equation that has one specific solution, an inequality describes a range of values that satisfy the condition.
The main types are strict inequalities (< and >), which exclude the boundary point, and non-strict inequalities (≤ and ≥), which include it. On a number line, strict inequalities use an open circle at the boundary, while non-strict inequalities use a closed (filled) circle.
The boundary point is marked with either an open circle (excluded, for < or >) or a closed circle (included, for ≤ or ≥). A shaded region or arrow extending to the left means all values less than the boundary satisfy the inequality, while shading to the right means all greater values satisfy it.
Interval notation is a compact way to express the solution set. Round parentheses ( ) indicate the endpoint is excluded, while square brackets [ ] indicate it is included. The infinity symbol ∞ is always paired with a parenthesis since infinity is never reached. For example, x > 3 is written as (3, ∞).
When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign flips. For example, -2x > 6 becomes x < -3 after dividing by -2. This calculator handles this automatically when solving.
Type your inequality using standard keyboard characters: use < for less than, > for greater than, <= for less than or equal to, and >= for greater than or equal to. For example, type '2x + 3 >= 7' or '-x <= 5'. Spaces are optional.
This tool is optimized for single linear inequalities (one expression compared to another). Compound inequalities like '1 < x < 5' or systems of inequalities are best handled by entering each part separately and combining the results.
A number line graph is used for single-variable inequalities (e.g. x > 3), showing a one-dimensional solution region. A coordinate plane graph is used for two-variable inequalities (e.g. y > 2x + 1), showing a shaded half-plane. This calculator focuses on single-variable number line graphing.