When you work with absolute values, recall that the absolute value of a number is its distance from zero. Given the use of the number line, any number and its additive inverse possess the same absolute value. You represent this situation as follows:
|3| = 3
| – 3| = 3
When you translate this set of relations so that you explicitly identify the values of x in a formal way, you can create an expression that assumes this form:
If |x| = 3 ⇒ x = 3, – 3.
Such a statement reads, “Given that the absolute value of some number x is 3, then x can be either 3 and –3.” As Figure 5.4 illustrates, if you employ a number line, you can easily show the two values.