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**1. Homework Statement**

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

**2. Homework 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