Answer
$\emptyset.$
Work Step by Step
$ 5(x-2)-3(x+4)\geq 2x-20\qquad ...$ distribute
$ 5x-10-3x-12\geq 2x-20\qquad ...$ simplify
$ 2x-22\geq 2x-20\qquad ...$ add $-2x+22$ to both sides
$0\geq 2$
which is not true for any real number x.
The solution set is $\emptyset.$
