The absolute value of a number a is written as |a| and represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an absolute value expression. The equation |x|= a has two solutions x = a and x = -a because both numbers are at the distance a from 0. To solve an absolute value equation, you begin by making it into two separate equations and then solving them separately. When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.