(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that |x+y|</|x|+|y|

2. Relevant equations

3. The attempt at a solution

Assume that x and y are real numbers.

|5+2|</|5|+|7|

7</7

|-5-2|</|-5|+|-2|

7</7

I know that it is true by testing different numbers, but I'm not sure how to prove it. Could someone please show me how or give me a hint?

Thank you very much

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# Triangle inequality proof

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