# How can the absolute value of x be negative?

1. Sep 20, 2015

### Joseph1739

1. The problem statement, all variables and given/known data
http://imgur.com/RlIdmFh
http://imgur.com/3dnLK3m

2. Relevant equations
|x| = -x?

3. 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.

2. Sep 20, 2015

### vela

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

3. Sep 20, 2015

### Joseph1739

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

4. Sep 20, 2015

### vela

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

5. Sep 20, 2015

### Joseph1739

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.

6. Sep 20, 2015

### Joseph1739

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

7. Sep 20, 2015

### vela

Staff Emeritus
Yup, you got it.

8. Sep 23, 2015

### 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 + :)