Inequality Solver

A linear inequality is a mathematical statement with a less than (<), greater than (>), less than or equal to (<=), or greater than or equal to (>=) symbol, involving a linear expression. Examples include 2x + 3 < 7, 5x - 2 >= 8, and -3x + 4 > 1. Unlike equations, inequalities have a range of solutions rather than a single value.

Solving a linear inequality uses the same steps as solving an equation: isolate the variable by adding, subtracting, multiplying, or dividing both sides. The key difference is that when you multiply or divide by a negative number, you must flip the inequality sign. For example, -2x > 4 becomes x < -2 after dividing both sides by -2.

The inequality sign flips because multiplying by a negative number reverses the order of numbers. For example, 2 < 5 is true, but -2 > -5 is also true. The negative multiplication reverses the relationship, so to keep the inequality valid, the sign must flip.

A number line is a visual way to show the solution set of an inequality. An open circle at a point (like 3) means that value is not included (< or >). A closed circle means the value is included (<= or >=). An arrow or line extending in one direction shows all values that satisfy the inequality.

Yes. For example, x > x + 1 has no solution because no number is greater than itself plus one. Similarly, x + 2 < x simplifies to 2 < 0, which is false. Some inequalities are always true (like x + 1 > x), meaning all real numbers satisfy them.