elementary set theory - Inverse images and containment

I have a question about inverse images and containment.

Let $\;f: A \rightarrow B, D \subseteq A$, and $E \subseteq B$. Show that $\; f^{-1}(B-E) \subseteq A-f^{-1}(E)$.

I have started by letting $x \in f^{-1}(B-E)$ so $f(x) \in (B-E)$, but I am unsure where to go from here.