SOLUTION: Which answer choice is the set of all solutions to the inequality |x + 3| > -2? A. There are no solutions. B. x < -5 or x > -1 C. x > -5 and x

SOLUTION: Which answer choice is the set of all solutions to the inequality |x + 3| > -2? A. There are no solutions. B. x < -5 or x > -1 C. x > -5 and x < -1 D. All real num

Question 306247: Which answer choice is the set of all solutions to the inequality |x + 3| > -2?

A. There are no solutions.
B. x < -5 or x > -1
C. x > -5 and x < -1
D. All real numbers.
Found 3 solutions by Edwin McCravy, PRMath, kevwill:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
D because the left side is the absolute value of something and no absolute value of anything can ever be negative and therefore it will ALWAYS be greater than -2 because all non-negative numbers are greater than -2.
Answer by PRMath(133)   (Show Source): You can put this solution on YOUR website!
Which answer choice is the set of all solutions to the inequality |x + 3| > -2?

A. There are no solutions.
B. x < -5 or x > -1
C. x > -5 and x < -1
D. All real numbers.

With all respect to the person who has already answered this problem, I am sorry to say that I think that person is wrong. The answer to this problem is A: There is NO solutions.

Why?

The absolute-value principle reminds us that absolute value is always non negative.

Therefore,your equation of: |x + 3| > -2 has no solution, which is "A" in your choices.

I hope this helps you. :-)
Answer by kevwill(135)   (Show Source): You can put this solution on YOUR website!
I'm going to have to support the original solver and disagree with the responder.

Let x = 0. Then we have:
|0 + 3| > -2
|3| > -2
3 > -2
Since this inequality is true, we have established that x = 0 is one possible value, we have eliminated options A and C.

But as the original solver pointed out, all absolute values are non-negative and consequently greater than -2.

The correct answer is D.

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