anonymous
  • anonymous
|x-6| is less than or equal to -12. How do i solve this?
Mathematics
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anonymous
  • anonymous
|x-6| is less than or equal to -12. How do i solve this?
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
there are no solutions to this
anonymous
  • anonymous
how can the absolute value less than or equal to a negative no?
anonymous
  • anonymous
\[|x-6|\le -12\]

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anonymous
  • anonymous
Thats what it says, hahaha. Im as confused as you are!
anonymous
  • anonymous
Recall that: \[|a| \le b \iff -b \le a \le b\] Therefore \[|x-6| \le -12 \implies 12 \le x-6 \le -12\] Which has no solutions, because nothing is both less than -12 and greater than 12.
amistre64
  • amistre64
i assume that these problems are designed to test that you comprehend what is going on and not just simply trying to follow a mechanical step to get an answer. There are many illogical ways to put together a sentence in math; just as there is in speech
anonymous
  • anonymous
It was just an empty set, haha. My bad!

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