all that the absolute value of a number represents the distance that number is from zero on the number line. The equation | x| = 3 is translated as “ x is 3 units from zero on the number line.” Notice, on the number line shown in Figure 1, that two different numbers are 3 units away from zero, namely, 3 and –3.
Figure 1. Absolute value.
Absolute value.
The solution set of the equation | x| = 3 is {3, –3}, because |3| = 3 and |–3| = 3.
Example 1
Solve for x: |4 x – 2| = 8.
This translates to “4 x – 2 is 8 units from zero on the number line” (see Figure 2).
Check the solution.
These are true statements. The solution set is .