How to solve an absolute value

Question

Please, can someone help me to solve this:
|x - 2| = 1/e
I really don't know the way in which I could solve an absolute value.

Answer 1

From the definition of absolute value, $x$ is a solution of $$\tag{1}|x-2|={1\over e}$$ if and only if $$\tag{2}x-2={1\over e}$$ or $$\tag{3}-(x-2)={1\over e}.$$ (Since $|x-2|$ is either $x-2$ or $-(x-2)\,$.)

For emphasis: if $a$ is a solution of either equation (2) or equation (3), it must be a solution of equation (1). On the other hand, if $a$ is a solution of equation (1), it must be a solution of one of equations (2) or (3).

So, the solution set of equation (1) is precisely the union of the solution sets to equations (1) and (2).

You need to solve both of equations (1) and (2) (which I leave to you). Then you can state that the solutions to equation (1) are all the solutions found in the previous sentence.