1 Answer

Reegan Miranda · Answer 1 · 2018-09-09T19:39:33+0000

Recall that

$|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}$

There are three cases to consider:

(1) When
x+2<0

, we have

and

, so

(2) When
$x+2\ge0$ and
x-2<0

, we get

and

, so

(3) When
$x-2\ge0$ , we have
|x+2|=x+2

and

, so

So

$|x-2|+|x+2|=\begin{cases}-2x-4&\text{if }x<-2\\4&\text{if }-2\le x<2\\2x&\text{if }x\ge2\end{cases}$

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