Question

the complete solution set of x which satisfy the inequality
[4/(x-2) ]>=[3/(2x-1)]

Answer 1

watch out for zero in denominators
[4/(x-2) ]>=[3/(2x-1)]
must not include x = 2 or x = 1/2
[4(2x-1)]>=[3(x-2)]
8 x - 4 >/= 3 x - 6
5 x >/= -2
x >/ = -2/5 but exclude x = 2 and x = 1/2

Answer 2

Is [] supposed to be absolute value? If so then
|4/(x-2)| >= |3/(2x-1)|
has solution set
x <= -2/5 or x > 2

Answer 3

By cross-multiplying the inequality.
8x-4>=3x+2
5x>=-2

Answer 4

Yes, you are correct. That is another way to solve the inequality.