What is wrong with this absolute value equation?

Question

|x-6|= -2

x-6= -2 or x-6= 2

x=4 or x=8

Answer 1

Math is a language, and there are rules set up to be followed just like there would be in any other language. The rules may not always make sense until you study the proofs and theorems.

With that said, I think what your instructor is wanting is to see this type of answer:

Since the 'absolute' value of any real number is never negative, the solution set is Ø or empty set.

(Do you see that x values can be negative, BUT the absolute value is never negative? That is what is important to see in this question.)