$X$ and $Y$ are i.i.d. then $\mathbb{E}(|X|) \le \mathbb{E}(|X+Y|)$

I don't know how to solve it .I first want to use conditional expectation. When $\mathbb{E}(X)=0$, I know it is right.$\mathbb{E}(X+Y|X)=X$,so $\mathbb{E}(|X|) \le \mathbb{E}(|X+Y|)$.But with the general situation ,how can i solve it?how can i use the same distribution?