# How to show if $x,y$ are vectors, $|x - y | \le |x| + |y|$

How do I show this inequality: $|x - y | \le |x| + |y|$?

Somehow use the triangle inequality?

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$x - y = x + (-y)$ –  Dylan Moreland Jul 1 '12 at 18:53
Oh wow..but thanks –  Holden Jul 1 '12 at 18:58

## 2 Answers

Apply triangle inequality for the vectors $\vec{x}$ and $-\vec{y}$ and recall that $\Vert -y \Vert = \Vert y \Vert$

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\begin{eqnarray} |x-y| &\le & |x|+ |-y|&=& |x| + |y| \end{eqnarray}

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