If 2x−3(2x−2)>x−1<2+2x; then x can take which of the following values?

Let's break down the compound inequality into two parts:
Part 1:

2x−3(2x−2)>x−1
2x−6x+6>x−1
−4x+6>x−1
6+1>x+4x
7>5x⟹x<
5
7
​
⟹x<1.4
Part 2:

x−1<2+2x
−1−2<2x−x
−3−3
Combining both results, we find the range for x:

−3Now let's check which option falls inside this range (−3,1.4):

A) 2 (False, as 2>1.4)

B) −2 (True, as −3<−2<1.4)

C) 4 (False)

D) −4 (False, as −4<−3)

Thus, x can take the value −2.