Distance from a Point

The equation $\left|x-2\right| = 5$ asks which numbers are five steps from 2. Split it into two cases, $x-2 = 5$ or $x-2 = -5$, then add 2 to both sides in each case:

$$x = 7$$

or

$$x = -3$$

-3 and 7 are both five steps from 2

The expression $\left|x-a\right|$ is the distance between $x$ and $a$. So $\left|x-2\right| = 5$ says the distance between $x$ and 2 is 5, and the two solutions are the two numbers five steps from 2. The algebra gives the same answer: split, solve each case, and the two answers are the same distance from 2, one on each side.