Solve each of the following system of equations in R.

Clearly, |x–2|–2≠0

⇒ |x–2|≠2

⇒ x≠0 and x≠4

Now, 2 case arise:

Case 1:–∞ <x<2

For this, |x–2|=–(x–2)

⇒ x ϵ (0,1] …(1)

Case 2: 2<x<∞

For this, |x–2|=x–2

⇒ x ϵ [3,4) …(2)

⇒ x ϵ (0,1] ⋃ [3, 4) (from 1 and 2)

We can verify the answers using graph as well.