#### Answer

$x \leq -1, x \geq 3$

#### Work Step by Step

$x^2-2x-3\geq 0$
$(x-3)(x+1) \geq 0$
$x \leq -1, x \geq 3$
(The key numbers are 3 and -1. The interval before -1 and the interval after 3 satisfy the inequality, which can be seen by checking for x=-3 and x=5)