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PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE! And...

PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE!

And I was thinking of doing 4 cases:

1. x greater than or equal to  0, and y greater than or equal to  0

2. x greater than or equal to 0, y less than 0

3. x less than 0, y greater than or equal to 0

4. x less than 0 , and y is less than 0.

Proofs by cases - absolute value.

Prove each statement

(d)

For real numbers x and y,  |x+y|≤|x|+|y|.

You can use the fact proven in the previous problem that for any real number z, z≤|z| and −z≤|z|.

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