1. ## Absolute Value

Does |x - |y-z|| = |x - y + z|?

Thanks

2. ## Re: Absolute Value

$\displaystyle |x - |y-z|| \ne |x - y + z|$ in general. Example take $\displaystyle x=3, y=1, z=2$ then we have $\displaystyle |3 - |1-2|| = |3-(2-1)|=|3-2+1| \ne |3-1+2|$
Can you say in general under what condition $\displaystyle |x - |y-z|| = |x - y + z|$ true?

3. ## Re: Absolute Value

Can it be simplified then? Basically, I trying to determine if |x - |y-z|| = ||x-y| -z|

4. ## Re: Absolute Value

Originally Posted by jzellt
Does |x - |y-z|| = |x - y + z|?

Thanks
Remember that \displaystyle \displaystyle \begin{align*} |X| = X \end{align*} ONLY if \displaystyle \displaystyle \begin{align*} X \geq 0 \end{align*}.

Here you are wanting \displaystyle \displaystyle \begin{align*} \left| x - |y - z| \right| = \left| x - \left( y - z \right) \right| = \left| x - y + z \right| \end{align*}. To do this, you require \displaystyle \displaystyle \begin{align*} y - z \geq 0 \implies y \geq z \end{align*}.

5. ## Re: Absolute Value

Disregard this post. It's been a long day...