Let $G = (V,E)$ be a graph with $|V|=n$ and $|E|=e$.
Let $M = \max\_{v\in V} \deg(v)$ and $m = \min\_{v\in V} \deg(v)$.
Show that $m\leq 2e/n \leq M$.

How do I approach this problem? I am especially confused by $m\leq 2e/n \leq M$.