How would you interpret the word problem: "Write the statement where the sum of the absolute values of two numbers is less than the absolute value of the sum of the two numbers." If this interprets to |x|+|y|

Question

How would you interpret the word problem: "Write the statement where the sum of the absolute values of two numbers is less than the absolute value of the sum of the two numbers." If this interprets to |x|+|y|<|x+y| as I suspect, what set of numbers would work for this equation?

anonymous · Answer

I don't think that's true for any pair of numbers.
|x| + |y| will always be at least equal to |x + y|.
In the case of either x or y being negative, |x| + |y| > |x + y|