SOLUTION: What is the solution set to the inequality: abs value bar x-5 abs value bar is less than -1? The answer is given as the empty set. Why? Can anyone explain? Thank you. Hele

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Question 978256: What is the solution set to the inequality: abs value bar x-5 abs value bar is less than -1?
The answer is given as the empty set. Why? Can anyone explain?
Thank you.
Helen
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x-5%29%3C-1

You're right! I am removing the posted "solution" because an absolute value is NEVER negative. To say that an absolute value is less than some negative VALUE makes no sense.

-solution process & result removed-

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

What is the solution set to the inequality: abs value bar x-5 abs value bar is less than -1?
The answer is given as the empty set. Why? Can anyone explain?
Thank you.
Helen
abs%28x+-+5%29+%3C+-+1

It is an empty set because the left side of the inequality can NEVER be negative, much more less than - 1. The LEAST value that 

the left side can be is 0, and last time I checked, 0 was never less than - 1, hence NO SOLUTION, and therefore an empty set.