## Key Concepts

• 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 $|A|<B,|A|\le B,|A|>B,\text{ or }|A|\ge B\\$. 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 $|A|=B$, with $B\ge 0$; it will have solutions when $A=B$ or $A=-B$
absolute value inequality
a relationship in the form $|{ A }|<{ B },|{ A }|\le { B },|{ A }|>{ B },\text{or }|{ A }|\ge{ B }$