Clearly, x≠2, as it will lead equation unmeaningful.

Now, two case arise:

Case1: x–2>0

⇒ x>2

In this case |x–2|=x–2

⇒ x ϵ (2, ∞)….(1)

Case 2: x–2<0

⇒ x<2

In this case, |x–2|=–(x–2)

Inequality doesn’t get satisfy

∴, this case gets nullified.

(from 1)

We can verify the answers using graph as well.