Quick tip: Why is $\vert \vert x \vert \vert_{\infty}^{q-p} \vert \vert x \vert \vert _{p}^{p}\leq \vert \vert x \vert \vert _{q}^{q}$

Question

I a solution I recently saw the following estimation for $1\leq p < q \leq \infty$ and $x \in \ell^{p}$:

$\vert \vert x \vert \vert_{\infty}^{q-p} \vert \vert x \vert \vert _{p}^{p}\leq \vert \vert x \vert \vert _{q}^{q}$

I may be missing something obvious, but how do I get to the above?