How do I solve $N = \lfloor\dfrac{A-B}{B}\rfloor$ for $A$

Question

So I'm not too familiar with the floor function and I was wondering if there was a simple way of solving $N = \lfloor\dfrac{A-B}{B}\rfloor$ with $A$ alone on the LHS?

Answer 1

When $N$ is a known integer, $N=\left\lfloor \frac{A-B}{B} \right\rfloor$ is the same as $$ N \le \frac{A-B}{B} < N+1 $$ which you'll hopefully be able to solve on your own. (The solution set will in general contain several different possible $A$s).