Find the range of x if 8x<3x^2.
$\displaystyle 8x <3x^2$
$\displaystyle 8x-3x^2<0$
$\displaystyle x(8-3x)<0$
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..