# What should a be for the system of inequalities to have one solution? ( 1 )

What should $a$ be for the system of inequalities to have one solution?
$\left(1\right)\frac{3}{x-a}\ge 1\left(2\right)|x-2a-2|\le 1$
For them to have one solution, the solution must be an endpoint of an interval. (1) gives me
$x\le a+3$
but I don't know how to proceed from here. Any hint would be appreciated.
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popman14ee
The first it's
$\frac{3}{x-a}-1\ge 0$
or
$\frac{3+a-x}{x-a}\ge 0$
or
$a
The second it's
$2a+1\le x\le 3+2a.$
Now, we see that an unique possibility it's
$3+a=2a+1.$