How to find the solutions to the inequality $ \tan x < 2 $

Question

I have

$$ \tan x < 2 $$

what are its solutions? (solution-set)

What I've done?

$$ \tan x -2 < 0$$

Now, by analysing the sign-change, or wavy-curve method

So $$ \tan x \in (- \infty, -2) $$

Now- how to find $x$?

EDIT: I would prefer an algebraic method, but in response to a comment I would like to add the required graphs

Answer 1

The simplest way is to help with a drawing:

We deduce the general solution: $$x\in\bigcup_{k\in\mathbf Z}\Bigl(\frac\pi2+2k\pi,\arctan 2+(2k+1)\pi\Bigr)\cup\Bigl(-\frac\pi2+2k\pi,\arctan 2+2k\pi\Bigr).$$