Linear Inequality Solver

Easily solve linear inequalities with one variable and visualize the solution on a number line.

Enter Your Inequality

Input a linear inequality with a single variable (x). For example: 2x + 3 > 7 or 5 - x <= 10.

Inequality:

Solution Set:

Visualization

What is a Linear Inequality?

A linear inequality is a relationship between linear expressions that uses inequality symbols such as >, <, ≥, or ≤. It's used to find a range of values for a variable that satisfy a given condition, rather than a single value as in linear equations.

Examples:

2x + 1 < 7: This inequality asks for all values of 'x' for which '2x + 1' is less than 7.
3 - x ≥ 0: This inequality seeks values of 'x' for which '3 - x' is greater than or equal to 0.

How to Solve:

Solving a linear inequality is similar to solving a linear equation. The goal is to isolate the variable on one side of the inequality. Operations performed on both sides must maintain the inequality. For example, adding or subtracting the same number from both sides preserves the inequality, and multiplying or dividing by a positive number also preserves it. However, multiplying or dividing by a negative number reverses the direction of the inequality.