Problem Solving

hey_thr67 wrote:Find the number of solutions of the equation

|x - |x - 2|| = 6

• |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