Prove that if $\displaystyle |x - x_0| < e/2$ and $\displaystyle |y - y_0| < e/2$, then

$\displaystyle |(x + y) - (x_0 + y_0)| < e$,

$\displaystyle |(x - y) - (x_0 - y_0)| < e$.

I'm not looking for a complete solution, just a hint as to where to begin.

Thanks.