I've been stuck on this problem for quite a while even though it seemed trivial to me at first.
Basically, I have this:
$$\lvert ax+4 \rvert>\frac1x$$
It is quite easy to conclude that only $x>0$ is possible. For the case when $a=0$, it's trivial to solve too.
But other than that, I've been stuck for a while at it. Any help would be appreciated.