why is this compund inequality not following the rules of divideing a negative number?

Here's how I would solve this question; that might clear up some confusion. 

12x - 39 < 9

12x < 48

x < 4

and 

-4x + 3 < -6

-4x < -9

x > (9/4)

So, 9/4 < x < 4

If you need any clarification in terms of the steps I used, please let me know and I can elaborate.