katmalfoy14
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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

Respuesta :

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
tonb
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

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