# Absolute Values

1. Oct 24, 2005

### Jeff Ford

An example in my textbook gives

$$\vert \frac{5-x}{5x} \vert \Leftrightarrow \frac {1}{5} (\frac{1}{\vert x \vert}) (\vert x-5 \vert)$$

Is there something I don't know about absolute values that allows $\vert 5-x \vert$ to become $\vert x-5 \vert$ or is this a mistake in the text?

2. Oct 24, 2005

### TD

What would you say about |x| - |-x|?

3. Oct 24, 2005

### Jeff Ford

It would be zero. So $$\vert 5 \vert + \vert -x \vert \Longleftrightarrow \vert -5 \vert + \vert x \vert$$

Thanks for the push.

4. Oct 24, 2005

### TD

Well yes, but in your case |5-x| doesn't necessarily equal |5| + |-x|, but it does equal |x-5|, as you asked in the first place.

5. Oct 24, 2005

### mathman

By definition |a|=|-a|. Let a=x-5 and the result is obvious.

6. Oct 24, 2005

### eNathan

$$\vert x \vert - \vert-x \vert = 0$$

The absolute value a number simply means that its positive, no matter what. So abs(x) - (abs(-x) would be the same as abs(x) - abs(x). This is actaully quite usfull in the field of programming.

Last edited: Oct 24, 2005