Question

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

Answer 1

either 4(x + 3) >= 8 or 4(x + 3) <= -8

4x + 12 >=8
4x >= =4
x >= -1
or

4x + 12 <= -8
4x <= -20
x <= -5

Answer is C

Answer 2

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