Math  /  Measurement

Question Determine if the statement x+y=x+y|x| + |y| = |x + y| is true for all real numbers x,yx, y.

Studdy Solution
Conclusion:
The statement x+y=x+y|x| + |y| = |x + y| holds true for Cases 1 and 2, and for certain situations in Cases 3 and 4. However, it does not hold true for all x,yRx, y \in \mathbb{R}, as demonstrated by the counterexample in Case 3, subcase 2.
Therefore, the statement is not true for all x,yRx, y \in \mathbb{R}.

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