If 2x−2(4−x)<2x−3<3x+3, then x can take which of the following values?

The given compound inequality consists of two parts:
Part 1: 2x−2(4−x)<2x−3
Part 2: 2x−3<3x+3

Let's solve Part 1:

2x−8+2x<2x−3
4x−8<2x−3
4x−2x<8−3
2x<5⟹x<2.5
Let's solve Part 2:

2x−3<3x+3
−3−3<3x−2x
−6−6
Combining both parts, the range of x is:

−6Among the given choices (2,3,4,5), only 2 lies within this range (−6 to 2.5).