i have to slove this problem
-3/2x > -6
what i did was i multiply 2 to -3/2 and -6
i cancel the 2 and i got -12
so i am left with -3x>-12
i then divide -3 to both sides. and i got
is this correct?
No, you did that when you swapped the sides!
You had -3x> -12. If you had simply divided both sides by -3 without either changing the sign or swapping sides you would have x> 4 which would be wrong. You can either change the sign, to get x< 4 or swap sides to get 4> x (your answer) but not both.
Of course, it is easy to check this yourself. A number less than 4 is 2. Does x= 2 satisfy (-3/2)x> -6?