Verified answer

Lumpy is incorrect. Since the "critical numbers" are 3 and -1, you need to check a number such that x>3, one such that -1 < x < 3, and one such that x < -1.

x> 3. Choose 4. Plug in and see if it works:

4^2 - 2(4) ≥ 3? Yes. So you need to include this set in your solution.

-1 < x < 3. Choose 0 (it's always the easiest to check).

0^2 - 2(0) ≥ 3? No. So exclude this from your answer set.

x < -1. Choose -2.

(-2)^2 - 2(-2) ≥ 3? Yes.

Include in your answer set.

So, the answers are x ≥ 3 and x ≤ -1.

x^2 -2x >= 3

x^2 - 2x - 3 >= 0

factorise

(x - 3)(x + 1) >= 0

x >= 3

x >= -1