If 5x+4(1−x)>3x−4>
3
5x
​
−
3
x
​
; then x can take which of the following values?

We need to solve the compound inequality in two parts.
Part 1:

5x+4(1−x)>3x−4
5x+4−4x>3x−4
x+4>3x−4
4+4>3x−x
8>2x⟹x<4
Part 2:

3x−4>
3
5x
​
−
3
x
​

3x−4>
3
4x
​

Multiply the entire inequality by 3 to remove denominators:

3(3x−4)>4x
9x−12>4x
9x−4x>12
5x>12⟹x>
5
12
​
⟹x>2.4
Combining both results, we get the valid range for x:

2.4From the given options:
A) 2 (False, since 2≤2.4)
B) 1 (False)
C) 3 (True, since 2.4<3<4)
D) -2 (False)

Hence, x can take the value 3.