Answer
See below.
Work Step by Step
a) Let $x$ be the result of the final exam.
To get an A, we need an average of at least $90$. Thus:
$\frac{86+88+x}{3}\geq90\\86+88+x\geq270\\174+x\geq270\\x\geq96$.
Thus the final result has to be greater than or equal to $96$.
b) Let $x$ be the result of the final exam.
To get a grade worse than B, we need an average less than $80$. Thus:
$\frac{86+88+x}{3}\lt80\\86+88+x\lt240\\174+x\lt240\\x\lt66$.
Thus the final result has to be less than $66$.
