Which of the following is the solution to 4 | x + 3 | ≥ 8? a. x ≤ -5 and x ≥ -1 b. x ≥ -1 c. x ≤ -5 or x ≥ -1 d. x ≥ -5 or x ≥ -1

First we get rid of the 4 by dividing by it:

4 | x + 3 | ≥ 8 =>
| x + 3 | ≥ 2

Then eliminate the absolute operator like this:

| x + 3 | ≥ 2 =>

-x-3 ≥ 2 or x+3 ≥ 2

Simplify:

-x ≥ 5 or x ≥ -1=>
x ≤ -5  or x ≥ -1

That's answer C