Another absolute value question?

Question

| x - 2 |

How do I solve for x? Wouldn't there be tons of answers? I need a bit of review.

Answer 1

Hi,
This is not an equation, i.e., it is not set equal to anything, so there is no answer. To solve for x, you would need something like this:
|x-2| = 7
In which case you would solve it as follows:
x-2 = 7
x = 9 (Add 2 to both sides.)

The term inside the bars can be either negative or positive, so we must also solve this:
x-2=-7
x = 5 (Add 2 to both sides.)

You could also have this:
|x-2| > 7 or |x-2| < 7 or some other relationship, but to have a specific answer or a specifiable range of values you must have a relational sign of = or <, > or other relations.

Hope this helps.
FE

Answer 2

For x >= 2: |x - 2| == x - 2, (== means identical).
For x < 2: |x - 2| == 2 - x.

That's all.

Answer 3

The anwser is in fact is x-2 without the lines.