|x-6| is less than or equal to -12. How do i solve this?
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there are no solutions to this
how can the absolute value less than or equal to a negative no?
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Thats what it says, hahaha. Im as confused as you are!
\[|a| \le b \iff -b \le a \le b\]
\[|x-6| \le -12 \implies 12 \le x-6 \le -12\]
Which has no solutions, because nothing is both less than -12 and greater than 12.
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