Answer
$\delta=0.1$
Work Step by Step
Find a $\delta\gt0$ such that for all $x$ $$0\lt |x-(-3)|\lt\delta\Rightarrow|f(x)-7.5|\lt0.15$$
Looking at the graphs, we can see that for values of $f(x)$ to be restricted between $7.35$ and $7.65$ (which means $|f(x)-7.5|\lt0.15$), $x$ must be placed between $-3.1$ and $-2.9$.
And since $|-3.1-(-3)|=|-3.1+3|=|-0.1|=0.1$, that means $0\lt |x-(-3)|\lt0.1$.
Therefore, $\delta=0.1$ (or any smaller positives number is also fine).
