Let $\displaystyle (X,d)$ be a metric space. Prove that for all $\displaystyle w,x,y,z \in X$:

$\displaystyle |d(w,x)-d(y,z)|\le d(w,y)+d(x,z)$

I haven't been able to prove it, I'm sure the triangle inequality should be used but I don't know how. Thanks in advance.