The critical point of this equation is x = 2, as for x < 2, |x - 2| = (2 - x) and for x > 2, |x - 2| = (x - 2)hey_thr67 wrote:Find the number of solutions of the equation
|x - |x - 2|| = 6
Hence, we will analyze the expression at either side of x = 2.
For x < 2,
- |x - 2| = -(x - 2) = (2 - x)
--> |x - |x - 2|| = 6
--> |x - (2 - x)| = 6
--> |2x -2| = 6
--> |x - 1| = 3
--> x = -2 or x = 4
But x = 4 violates our initial assumption of x < 2.
Hence, only valid solution in this range is x = -2
- |x - 2| = (x - 2)
--> |x - |x - 2|| = 6
--> |x - (x - 2)| = 6
--> |2| = 6 --> Impossible
Hence, there are is no valid solution in this range
The correct answer is B.
