Question

Rewrite each of the following expressions without using absolute value: |x-5|+|x+5| if x<-5

Answer 1

For $x < -5$:

$x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5$

So

$|x-5|+|x+5|=-x+5-x-5=-2x$