Question

Blue of
|2x-| x-4|| at x=-5​

Answer 1

x = 0

Correct option is

A

x=0

Given equation

∣x−∣4−x∣∣−2x=4     ....(1)

Case I: When 4−x≥0

⇒x≤4

So, in this case eqn (1) becomes

∣x−(4−x)∣−2x=4

⇒∣2x−4∣−2x=4    ....(2)

Now, when 2x−4≥0 i.e x≥2

So,eqn (2) becomes

2x−4−2x=4

⇒−4=4 which is absurd.

Hence, there is no solution for x≥2

Now, when 2x−4<0 i.e x<2

So, equation (2) becomes

−(2x−4)−2x=4

⇒−4x=0

⇒x=0

Case II: When 4−x<0

∣x+(4−x)∣−2x=4

⇒−2x=0    

⇒x=0

Hence, x=0 is the only solution to the given equation.