# Solve one-step linear inequalities

A statement involving a variable and a sign of inequality (viz. < , ≤ , > or ≥) is called an

**inequality**. A statement of inequality between two expressions consisting of a single variable, say x, of highest power 1, is called a

**linear inequality in one variable**. It is ussually written in any of the following forms:

ax+b<0

ax+b>0

ax+b≥0

ax+b≤0

where a ≠ 0;

Linear inequalities are solved much the same way as linear equations are solved, with one important exception: when multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.

Solve for x

<\;3\;\Rightarrow\;x\;<\;3\;-\;5\;\Rightarrow\;x\;<\;-2\; align='absmiddle'>

<\;-2\;\}\;\text{=}\;\(-\infty,-2) align='absmiddle'>