Saying " the absolute value of number $N$ is equal to $5$" means " I do not know what number is $N$ , but I know for sure that the distance from $N$ to $0$ is $5$ units".
Defining intuitively the absolute value as a distance explains why the
absolute value cannot be negative .
In your example, it is the number $x-2$ that plays the role of $N$.
Also, when $N$ is positive the distance from $N$ to $0$ is $N-0$ and when $N$ is negative, the distance from $N$ to $0$ is $0-N $.
Consequently, the general formula is as follows, and you simply have to apply it mechanically , by replacing $A$ by your specific number $5$, and $N$ by your specific number : $x-2$ :
$|N| = A $
$\iff [ N-0 = A \space $ OR $\space 0-N =A ] $
$\iff [ N=A \space $ OR $\space 0-N =A]$
$\iff [ N=A \space \mathbb {OR}\space -N = A ]$
So, your equation means:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/GYK1T.png)
(1) $(x-2)- 0 = 5 \implies x-2= 5 \implies x=7$
OR
(2)$ 0 - (x-2) = 5 \implies -x +2 =5 \implies -x = 3 \implies x=-3$
The solution set of the equation is : $\{ -3, 7\}$.