How can the absolute value of x be negative?

[Joseph1739]

Homework Statement

http://imgur.com/RlIdmFh
http://imgur.com/3dnLK3m

Homework Equations

|x| = -x?

The Attempt at a Solution

I'm trying to make sense of this definition in my book because they are trying to prove the triangle inequality(second link), yet it keeps saying that the absolute value of a number is negative.

 

[vela]

Your interpretation is only true if you're assuming x>0. What if x itself is negative?

 

[Joseph1739]

Your interpretation is only true if you're assuming x>0. What if x itself is negative?

The absolute value would still be positive? Isn't the point of absolute value to obtain positive results only?

 

[vela]

If $x=-1$, what's $-x$ equal to?

 

[Joseph1739]

If $x=-1$, what's $-x$ equal to?

1. How does that explain the definition given though? It says |x| = -x if x<0. So by his definition, if I say x = -3, |x| = |-3| = -3.

 

[Joseph1739]

If $x=-1$, what's $-x$ equal to?

Ohhh. I understand it now. |-3| = -(-3) = 3.

 

[vela]

Yup, you got it.

 

[nuuskur]

A very straightforward definition.
If x is non-negative, then x is just x itself. If x is negative, what do you have to do to make it positive for certain? Put a minus in front, for two minuses give a + :)