CAT 2015 Quantitative Ability

By observing we can find that x > 1 and x < 2.
Else the RHS ≠ 8 .
So the combinations are [x] = 1, [2x] = 2 or 3,[3x] = 4 or 5
The combinations that give RHS = 8 are 1 +2 + 5 or 1 + 3 + 4.
For any value of x, the case of “1 +2 + 5" is not possible. Hence it has to be the case of “1 +3 + 4". Which will occur
when x ≥ 3/2 and x < 5/3.
Hence the solution is 3/2 ≤ x < 5/3.