1Cademy - Linear Inequality

Learn Before

Inequality Symbols in Algebra

Definition

Linear Inequality

A linear inequality is an inequality in one variable that can be written in one of the following forms, where $a$ , $b$ , and $c$ are real numbers and $a eq 0$ : $ax + b < c$ , $ax + b \leq c$ , $ax + b > c$ , or $ax + b \geq c$ . Like a linear equation, it connects two algebraic expressions, but uses an inequality symbol ( $<$ , $>$ , $\leq$ , or $\geq$ ) instead of an equal sign, and the variable appears only to the first power. Examples include $15 > x$ , $n - 9 < 42$ , and $3a - 12 \geq 7a - 20$ . Unlike a linear equation — which typically yields a single solution — a linear inequality generally has infinitely many solutions, consisting of all values of the variable that make the statement true. These solutions can be visualized by graphing them on a number line. Solving a linear inequality relies on properties of inequality that parallel the Addition, Subtraction, Multiplication, and Division Properties used for solving equations.

Updated 2026-05-03

Contributors are:

Who are from:

University of Michigan - Ann Arbor

✔️ 4

References

Learn Before

Related

Learn After