Example problem:

If |x| - 3 = 0, what is x?

Answer:

Clearly, if x = 3, then |x| - 3 = 0.

However, if x = -3, then |x| = | -3| = 3, and once again,

|x| - 3 = 0.

Therefore x, in this equation can be either 3, or -3.

Example problem:

If |x| - 2 = 7, what is |x|?

First we add two to both sides to obtain:

|x| = 9.

Therefore x could be either 9, or -9.

If we are given another condition, such as:

|x| -2 = 7,

and

x < 0,

then we know that the answer must be x = -9.