How to solve: $\frac{3·x-5}{8·x-2}<6$ I'm trying to solve $\frac{3x-5}{8x-2}<6$ ?
I'm not sure which first step to take. I mean if I multiply both sides by $8x-2$ then I'm not sure if the sign would switch, as this could be positive or negative depending on $x$.

Hint
You can't multiply by $8x-2$ without discuss on its sign. The best way to answer the question is:
$$\frac{3x-5}{8x-2}<6\iff\frac{3x-5}{8x-2}-6=\frac{-45x+7}{8x-2}<0$$
and now draw a signs table for this quotient.
Edit The sign table is

so the answer is $$\left(-\infty,\frac7{45}\right)\cup \left(\frac14,+\infty\right)$$
