The solution set of the inequation `|2x-3| lt x-1`, is

Options

A. `(4//3, 3//2) cup (3//2, 2)`
B. `(4//3, 2)`
C. `[3//2, 2)`
D. none of these

Answer

B

Explanation

CASE I when `2x-3 ge 0 i.e., x ge (3)/(2)`
In this case, we have
`|2x-3| = 2x-3`
`therefore |2x-3| lt x -1`
`rArr 2x-3 lt x-1`
`rArr x-2 lt 0 rArr x lt 2 rArr x in [3//2, 2) " "[because x ge 3//2]`
CASE II when `2x-3 lt 0 i.e., x lt 3//2`
In this case, we have
`|2x-3|= (2x-3)`
`therefore |2x-3| lt x-1`
`rArr -(2x-3) lt x-1`
`rArr 3x-4 gt 0 rArr x gt (4)/(3) rArr x in (4//3, 3//2) " " [because x lt 3//2]`
Thus, the set of the values of x satisfying the given inequation is `(4//3, 3//2)cup[3//2, 2_=(4//3, 2)`