Proof of absolute value identities – math.stackexchange.com

Proof of absolute value identities – math.stackexchange.com

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How to prove that: $\mid x+y \mid$ = $\mid x \mid$ + $\mid y \mid$ if and only if $xy$ $\ge0$ and $\mid x-y \mid$ = $\mid x \mid$ - $\mid y \mid$ if and only if $xy$ $\le0 $ and $\mid x \mid$ ...

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