|x-6| is less than or equal to -12. How do i solve this?

Question

anonymous · Answer

there are no solutions to this

anonymous · Answer

how can the absolute value less than or equal to a negative no?

anonymous · Answer

$$|x-6|\le -12$$

anonymous · Answer

Thats what it says, hahaha. Im as confused as you are!

anonymous · Answer

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 · Answer

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 · Answer

It was just an empty set, haha. My bad!