Question

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

Answer 1

there are no solutions to this

Answer 2

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

Answer 3

\[|x-6|\le -12\]

Answer 4

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

Answer 5

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.

Answer 6

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

Answer 7

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