What should $a$ be for the system of inequalities to have one solution?
$$(1) \frac{3}{x-a}\geq 1 (2)\left | x-2a-2 \right | \leq 1$$
For them to have one solution, the solution must be an endpoint of an interval. (1) gives me $$x\leq a+3$$, but I don't know how to proceed from here. Any hint would be appreciated.
The first it's $$\frac{3}{x-a}-1\geq0$$ or $$\frac{3+a-x}{x-a}\geq0$$ or $$a<x\leq 3+a.$$ The second it's $$2a+1\leq x\leq3+2a.$$ Now, we see that an unique possibility it's $$3+a=2a+1.$$ Can you end it now?