Inequality Calculator With Steps
This inequality calculator solves one-variable inequalities of two common types. For a linear inequality, enter the coefficients of ax + b on the left and cx + d on the right, pick <, ≤, > or ≥, and it moves terms across, divides, and flips the sign when you divide by a negative number. For a quadratic inequality ax² + bx + c compared with zero, it finds the roots and tests each region to give the solution set. Answers come in inequality form and interval notation. It does not parse free-typed expressions, rational or absolute value inequalities; use the absolute value calculator for those.
Inequality Calculator
Solve one-variable linear and quadratic inequalities with interval notation.
How to use the Inequality Calculator
- Pick linear or quadratic.
- Enter the coefficients.
- Choose the inequality sign.
- Read the solution, interval notation and steps.
Inequality rules
Adding or subtracting keeps the sign. Multiplying or dividing by a negative number flips it. For ax² + bx + c, the sign can only change at the real roots.
Features
- Linear inequalities on both sides
- Quadratic inequalities against zero
- Sign flip when dividing by a negative
- Interval notation
- No-solution and all-real cases
- Step-by-step work
Frequently asked questions
How do you solve a linear inequality?
Solve it like an equation, but flip the sign whenever you multiply or divide by a negative number. 3x - 5 < 2x + 4 becomes x < 9.
How do you solve a quadratic inequality?
Find the roots of ax² + bx + c = 0, then test a point in each region. x² - 5x + 6 ≥ 0 gives x ≤ 2 or x ≥ 3.
What is interval notation?
A compact way to write a range. x < 9 is (-∞, 9) and -1 ≤ x < 4 is [-1, 4). Square brackets include the endpoint.
When does an inequality have no solution?
When it is never true, such as x² + 1 < 0, because x² + 1 is always positive.
Can this solve any inequality I type?
No. It handles linear and quadratic inequalities in one variable from their coefficients. Rational, radical and absolute value inequalities are not covered here.