1.7+Solve+absolute+value+equations+and+inequalities

When you take the [|absolute value] of a number, you always end up with a positive number (or zero). Whether the input was positive or negative (or zero), the output is always positive (or zero). For instance, | 3 | = 3, and | –3 | = 3 also. This property — that both the positive and the negative become positive — makes solving absolute-value equations a little tricky. But once you //learn// the "trick", they're not so bad.

Solving a simple absolute equation media type="youtube" key="eVsG7_GfgmY" width="560" height="315"

When you solve an absolute value equation, its possible for a solution to be extraneous. An __Extraneous solution__ is an apparent solution that must be rejected because it does not satisfy the original equation.

You can solve an absolute value inequality by rewriting it as a compound inequality and then solving each part. ASSESMENT