How to prove that $|x| = inf_{(y_1,y_2) \in \mathbb{R^2}} \ y_1 + y_2$

Question

I need to prove that for every real number $x \in \mathbb{R}$ holds:

$$|x| = inf_{(y_1,y_2) \in \mathbb{R^2}} \ y_1 + y_2 \ $$ such that $$x = y_1 - y_2 , \ y_1 \ge 0 , \ y_2 \ge 0$$

I think the direction $\le$ is pretty obvious, but I don't know how to do the other one, i.e. $\ge$. Could you give me a hint on how to do that?