Answer: False
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Step-by-step explanation:
Let's pick a positive number for x and negative number for y.
I'll pick x = 2 and y = -3 as the counter-example.
|x+y| = |x| + |y|
|2 + (-3)| = |2| + |-3|
|2 - 3| = 2 + 3
|-1| = 5
1 = 5
We get a false statement at the end, which means the original equation is false when (x, y) = (2, -3)
I'll let you try other counter-examples.
If both x and y are positive together, or negative together, then the original equation would always be true.
If x and y are mixed (one positive the other negative), then the statement is always false.
Overall |x+y| = |x| + |y| is false for any two integers x and y.