absolute value

| | x - 2 | - 1 | = 1
(| x - 2 | - 1)2 = 1
| x - 2 |2 - 2| x - 2 | + 1 = 1
| x - 2 |2 - 2| x - 2 | = 0
| x - 2 |(| x - 2 | - 2) = 0
| x - 2 | = 0 or | x - 2 | = 2
x = 2 or | x - 2 |2 = 4
x = 2 or x2 - 4x + 4 = 4
x = 2 or x (x - 4) = 0
x = 2 or x = 0 or x = 4

The equation generates into 2 equations :
abs(x -2) - 1 = 1..............(A) and
-[abs(x -2) - 1] = 1............(B).
Equation (A) again generates into 2 equations:
(x-2) - 1 = 1...........(C) and
-(x -2) - 1 = 1..........(D).
From (C) we get x - 3 = 1 so x = 4.
From (D) we get -x + 2 - 1 = 1, so x = 0.
Equation (B) also generates 2 eqautions:
-[(x -2) - 1] = 1..........(E) and
-[-(x-2) - 1] = 1..........(F).
From (E) we get x -2 - 1 = -1 so x = 2.
From (F) we get -x + 2 - 1 = -1, so x = 2.
Therefore, x = 4, 0 and 2.

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