# Absolute Value Inequalities

The absolute value of a number is its distance measured on the number line from 0. Absolute value inequalities are inequality statements containing absolute value expressions.

The simplest form of absolute value inequalities are of one of the following forms:

- | x | < k or | x | $\leq$ k, which can be equivalently represented by correspondingly as -k < x < k and -k $\leq$ x $\leq$ k
- | x | > k or | x | $\geq$ k, which are written correspondingly in equivalent form as x < -k or x > k and x $\leq$ -k or x $\geq$ k.

Absolute value inequalities are solved algebraically, by taking the expression inside the absolute value notation as both positive and negative. The inequalities are also solved by writing the inequality in expanded form. The solution of an absolute value inequality is often graphically on a number line. The graphical representation of absolute value inequalities are shown below.