Quant Fundamentals: Absolute Value

If $$|x|=x$$ then $$x$$ must be

Incorrect. [[Snippet]] Eliminate this answer choice because the questions says _must be_. While $$x$$ can be 0, the relation $$|x| = x$$ holds for other values of $$x$$ too, such as 3, 7, or any other positive number.

Incorrect. [[Snippet]] Eliminate this answer choice because the relation $$|x| = x$$ holds for positive numbers i.e. $$|x|$$ is equal to $$x$$ when $$x$$ is 3.

Incorrect. [[Snippet]] Eliminate this answer choice because the questions says _must be_. While $$x$$ can be positive, the relation $$|x| = x$$ holds for 0, too.

Incorrect. [[Snippet]] Eliminate this answer choice because the relation $$|x| = x$$ holds for positive numbers i.e. $$|x|$$ is equal to $$x$$ when $$x$$ is 3.

Correct. [[Snippet]] This is the correct answer because the relation $$|x| = x$$ holds for all non-negative values of $$x$$. $$x$$ can be both positive and zero, i.e. $$|8| = 8$$ and $$|0| = 0$$. However, $$x$$ cannot be negative, since an absolute value cannot be negative—if $$x=-5$$, then $$|{-5}|$$ will equal positive 5, which would mean that the equation $$x=|x|$$ will not hold (as –5 is not equal to 5).

negative

positive

non-negative

non-positive

zero