** **

**Use absolute value.**

Geometrically, the **absolute value **of a number *a*, written 0 *a *0, is the distance on the number line from 0 to *a*. For example, the absolute value of 5 is the same as the absolute value of

– 5 because each number lies five units from 0. That is,

**CAUTION**

Because absolute value represents distance, and distance is always positive

(or 0), *the absolute value of a number is always positive (or 0)***.**

** **

The formal definition of absolute value follows.

Absolute Value

The second part of this definition, = –*a if * *a *is negative, requires careful

thought. If *a *is a *negative *number, then – *a*, the additive inverse or opposite

of *a*, is a positive number, so is positive.