If modulus sign is used, can a value be negative?

Question

|x-3|

If x is less than 3, will |x-3| be negative? I don't think so.

For example, if x=2, |x-3|= |2-3|=1. x-3 can never be negative, I think.

In this link, it has been said that when x<3, x-3 is negative, thus |x-3|=-(x-3).

I think this statement is totally wrong.

Please let me know what the correct is.

Answer 1

$|x|$ is non-negative regardless of any sign. Absolute value is the distance of a number from $0$ and distance can never be negative!

Answer 2

The statement is correct because if x is lesser than 3 , the x -3 is always negative and hence -(x-3) is always positive. And that is always equal to mod x-3