I thought that I do not have any probs with absolute value questions, but apparently I do. That's the prob with solution. IMO the correct answer is "all three are correct". I do not understand why III is incorrect. Why do they say in the second last line that x = +- |x| = -x . Doesn't the +- mean that we can choose between + and - since the questions say which of the following could be correct.

garuhape wrote:I thought that I do not have any probs with absolute value questions, but apparently I do. That's the prob with solution. IMO the correct answer is "all three are correct". I do not understand why III is incorrect. Why do they say in the second last line that x = +- |x| = -x . Doesn't the +- mean that we can choose between + and - since the questions say which of the following could be correct. All I can see is a frog trapped in ice

Hi there! You are 100% correct, garuhape! The explanation is bad-written, and the question stem is bad-posed because "+ or - something" is bad notation. (I will explain why at the end of this post.) [In the problem posed, the usual interpretation of the notation will give the answer "all of them", as garuhape believes and correctly explores at the end of his post. What I mean is that I do not like the "+ or -" notation ANYWHERE.] Just to rephrase what you said: when x is positive, then |x| = x therefore x IS equal to |x| or -|x|, because in this case (x>0) we have the first choice: "is x equal to x or to -x ?" Yes, x is equal to x... Regards, Fabio. Explanation promised: I like to write that the set of integers is given by {0, 1, -1, 2, -2, 3, -3, ...} and I do NOT like to write that the set of integers is given by {0, +- 1, +- 2, ...} why? because I believe the student "has the right" to understand (wrongly) that I am "giving the option of choosing between say 1 and -1", therefore it seems as 1 or -1 could be left out of the set of integers, what is NOT the case, for sure. I hope you got the point! Original question (for people who cannot access it):