# Linear inequalities in one variable

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;

You can **solve an inequality** in the variable x by finding all values of x for which the inequality is true. Such values are **solutions** and are said to **satisfy** the inequality. The **solution set** of an inequal¡ty is the set of all real numbers that are solutions of the inequality.

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.