Example 1. Solve for x:
|x − 2| = 8.
Solution. x − 2 is the argument. Either that argument will be 8, or it will be −8.
x − 2 = 8, or x − 2 = −8.
We must solve these two equations. The first implies
x = 8 + 2 = 10.
The second implies
x = −8 + 2 = −6.
These are the two solutions: x = 10 or −6.