Whenever one has an inequality, an interesting problem is to characterize the cases of equality. Consider the triangle inequality, which says that x + y ≤ x + y for all real numbers x and y. True or false: If x and y are real numbers for which x + y = |x|+|y, then either x and y are both positive, or x and y are both negative, or at least one of the numbers x and y is zero. True False

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Q: 3. Prove the triangle inequality: For any real numbers x, y, |x + y ≤ |x| + |y].

A: For any real number  we have to prove