Solve quadratic inequalities

Question

(x+2) (x+6) ≤ 0 (x-2) (x-4) ≥ 0

-6 ≤ x ≤ -2 x ≤ 2 or x ≥4

In these two examples I am able to find the positive and negative regions on a number line, but am having trouble figuring out how write the inequality.

I am assuming the signs (≤ or ≥) have something to do with this, as the regions for both are + - +

Any clarification is deeply appreciated.

Thanks,

Brian

Answer 1

The first one, -6 ≤ x ≤ -2, is correct as written.

The second one is more difficult to write because the two regions are not connected. What you wrote is essentially correct, x ≤ 2 or x ≥4. The symbology for the "or" (union) is U, so the correct way to write it is

(x ≤ 2) U (x ≥4). The union symbol (U) means the answer is the union of those two sets. In logic, it also means "or".