Example: Solve absolute value equations

Solve | 2x – 3 | – 4 = 3

First, I'll isolate the absolute-value part; that is, I'll get the absolute-value expression by itself on one side of the "equals" sign, with everything else on the other side:

| 2x – 3 | – 4 = 3
| 2x – 3 | = 7

Now I'll clear the absolute-value bars by splitting the equation into its two cases, one for each sign:

(2x – 3) = 7 or –(2x – 3) = 7
2x – 3 = 7 or –2x + 3 = 7
2x = 10 or –2x = 4
x = 5 or x = –2

So the solution is x = –2, 5.