For the inequality to be negative either x<0 and 8-3x>0 or x>0 and 8-3x<0

Check when the factors changes signs. x is easy, its when it is smaller then zero.

Like this

Factor/ -8/3 0 8/3

x: - 0 +

8-3x:

this one you have to fill in yourself

Then it is easy to see when both factors have opposite signs..