Solve: 2|x + 7|−4 ≥ 0 express the answer in set-builder notation. a. {x | 5 < x < 6} b. {x | x ≥ -5} c. {x | x ≤ -9 or x ≥ -5} d. {x | -9 < x < -5}

To solve an absolute inequality first step is to isolate absolute value expression.

Hence remove -4 from the left side. So, add 4 to each sides of the inequality.

2|x + 7|−4 ≥ 0

2|x + 7|−4 +4≥ 0 +4

2|x + 7| ≥ 4 Combine the like terms.

Divide each sides by 2.

|x + 7| ≥2

Next step is to remove the absolute value sign. So,

x + 7≥2 and x+7≤-2.

x≥2-7 and x≤-2-7

x≥-5 and x≤-9

So, the correct choice is C. {x | x ≤ -9 or x ≥ -5}.

The first one is C) {x|x<= -9 or x=> -5 }

The second one is (-infinity, -9] U [-5, infinity)

I just did it

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a. is correct