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

Algebra ->  Inequalities -> SOLUTION: Which answer choice describes the set of all solutions to the inequality |x – 3| < -2? A. There are no solutions. B. x < 1 or x > 5 C. x > 1 and x < 5 D. All real      Log On


   

Question 305359: Which answer choice describes the set of all solutions to the inequality |x – 3| < -2?


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


Found 3 solutions by vleith, Edwin McCravy, stanbon:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
|x – 3| < -2?
Since an absolute value can never be less that 0, there are no values of x that make that statement true.
Answer A

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

|x – 3| < -2

Absolute values are never negative, so it impossible of
the absolute value of any number to be less than -2.

The correct choice is A. There are no solutions.

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Notice that if the problem had been 

|x – 3| > -2

the correct choice would have been D. All real numbers, because
all absolute values are 0 or greater and thus are always greater
than any negative number.

Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Which answer choice describes the set of all solutions to the inequality |x – 3| < -2?
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Absolute values are never negative.
Ans: A
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Cheers,
Stan H.
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A. There are no solutions.
B. x < 1 or x > 5
C. x > 1 and x < 5
D. All real numbers.