am i correct?

-12√[2x - 3]  >    -36         

Divide both sides  by -12   and reverse the inequality sign

√[2x - 3 ]  <   3            square both sides

2x - 3   <  9        add 3 to both sides

2x <   12            divide both sides by 2

x < 6   

However.....also remember  that      2x - 3 must be  ≥   0

So the other solution is

2x - 3 ≥  0

2x ≥ 3

x ≥ 3/2

So.....the solution  is

3/2   ≤  x  <  6

The last choice is correct