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

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) (Show Source): You can put this solution on YOUR website!

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) (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

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.
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