The absolute value function is commonly used to measure distances between points.

Applied problems, such as ranges of possible values, can also be solved using the absolute value function.

The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.

In an absolute value equation, an unknown variable is the input of an absolute value function.

If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable.

An absolute value equation may have one solution, two solutions, or no solutions.

An absolute value inequality is similar to an absolute value equation but takes the form [latex]|A|<B,|A|\le B,|A|>B,\text{ or }|A|\ge B\\[/latex]. It can be solved by determining the boundaries of the solution set and then testing which segments are in the set.

Absolute value inequalities can also be solved graphically.

Glossary

absolute value equation

an equation of the form [latex]|A|=B[/latex], with [latex]B\ge 0[/latex]; it will have solutions when [latex]A=B[/latex] or [latex]A=-B[/latex]

absolute value inequality

a relationship in the form [latex]|{ A }|<{ B },|{ A }|\le { B },|{ A }|>{ B },\text{or }|{ A }|\ge{ B }[/latex]