Math Solver Free

Inequality Solver

Solve linear inequalities with steps, interval notation, and number line graphs โ€” free.

Solve ax + b (inequality) c โ€” enter the coefficients below.

x +
x > 4
Interval notation: (4, โˆž)

Step 1: Subtract 3 from both sides: 2x > 8

Step 2: Divide by 2: x > 4

Step 3: Interval notation: (4, โˆž)

-1
4
9

Open dot = endpoint excluded ยท shaded ray = solution set

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How to Solve Linear Inequalities

A linear inequality looks like an equation, except the equals sign is replaced by >, <, โ‰ฅ, or โ‰ค. Instead of one answer, you get a whole range of answers โ€” every number that makes the statement true. Solving works almost exactly like solving equations, with one famous exception.

The Golden Rule: Flip on Negatives

Add, subtract, multiply, or divide both sides just like an equation โ€” except when you multiply or divide by a negative number, you must flip the inequality sign. So โˆ’3x < 9 becomes x > โˆ’3. Forgetting this flip is the #1 mistake students make.

Reading the Answer

  • Inequality form: x > 4 โ€” direct and familiar.
  • Interval notation: (4, โˆž) โ€” compact; round brackets exclude, square brackets include.
  • Number line: a ray starting at the endpoint with an open or filled dot โ€” the graph above draws it for you.

Comfortable with equations first? Try our linear equation solver or the algebra calculator.

Frequently Asked Questions

How do you solve 2x + 3 > 11?

Subtract 3 from both sides to get 2x > 8, then divide by 2 (positive, so the sign stays) to get x > 4. In interval notation: (4, โˆž).

When do you flip the inequality sign?

Flip the inequality sign whenever you multiply or divide both sides by a negative number. For example, โˆ’2x > 6 becomes x < โˆ’3 after dividing by โˆ’2.

What is interval notation?

Interval notation describes a solution set with brackets: (4, โˆž) means all numbers greater than 4. Round brackets exclude the endpoint; square brackets include it.

Is this inequality solver free?

Yes โ€” every tool on Math Solver Free is free with no sign-up, and all calculations run in your browser.