Education
Inequality Calculator
Type a linear inequality in one variable. The calculator moves the variable to one side, divides by its coefficient (flipping the direction if that coefficient is negative), and reports the solution as both an inequality and an interval.
Inequality
Linear inequality in one variable. Use <, <=, >, or >= between the two sides.
e.g. 2x + 3 < 11
Single letter. · e.g. x
What is supported
- One-variable linear inequalities, any side mix of variable and constant terms.
- All four comparison operators, including the ≤ and ≥ characters.
- Automatic flip when both sides are divided by a negative coefficient.
Quadratic and compound inequalities are not supported. For nonlinear cases, solve each piece and intersect the intervals by hand.
Solution
x < 4, so x ∈ (−∞, 4)
For an inequality that compares ratios, see the proportion calculator. For checking the resulting bound against a numeric test value, use the scientific calculator.
Examples
2x + 3 < 11
x < 4
5 − x ≥ 2x − 4
x ≤ 3
−3x > 9
x < −3 (flip)
x + 1 > x
Always true
How it works
The calculator rewrites the inequality as A · x + B ◊ 0 by subtracting one side from the other, then divides both sides by A.
Solve · x ◊ −B / A (flip ◊ when A < 0)
If A = 0, the variable cancels: the inequality is always true or has no solution depending on B and the operator.
Related ratio and algebra calculators
- Proportion calculator for solving A : B = C : D with one unknown.
- Ratio calculator for simplifying A : B and checking equivalent ratios.
- Scientific calculator for arithmetic checks of the solution interval.
- All education calculators.
Frequently asked questions
An inequality where both sides are linear expressions in the same variable, like 2x + 3 < 11 or 5 − x ≥ 2x − 4. Solving means describing every value of x that makes the inequality true.
Whenever you multiply or divide both sides by a negative number. For example, −2x > 6 divided by −2 becomes x < −3 (the > flipped to <). The calculator does this automatically when the coefficient of x is negative.
Both as an inequality like x < 4 and as an interval like (−∞, 4). Closed brackets like [ or ] mean the endpoint is included (≤ or ≥); open parentheses like ( or ) mean the endpoint is excluded (< or >).
When the variable cancels out, the inequality reduces to a comparison of constants. If the constants make the comparison true, every real number satisfies the inequality. If they make it false, no real number does.
Not directly. Solve each piece on its own and intersect the intervals by hand.
Decimals and negatives are fine. Fractions written with the / character are not parsed; convert to decimals first or use the fraction-to-decimal calculator.
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