Newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to be using on my set of polynomial equation/inequalitites. Most of the time, I also need to constrain the math on certain domains.

For example if we have:

a x + 1 > 0 && a > 2

and we are solving for x

Refine[Assuming[a > 2, Reduce[a x + 1 > 0, x]]]
output:
    x ? Reals && x > -1/a

works.

So then I want to see if it can detect null sets, so we add the assumption of x < -1:

Refine[Assuming[a > 2 && x < -1, Reduce[a x + 1 > 0, x]]]
output:
    x ? Reals && x > -1/a

it still outputs the same thing... Why?

Another thing... Why does this work (not exactly always the right solution, but at least doesn't produce an error), but using "Solve" instead of "Reduce" doesn't work.