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
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-> 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
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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.
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.
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.
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