inequality 5

Well, you start by analyzing |x| + |y|. Since the absolute value of any number is always positive or equal to 0, you get that |x| + |y| >=0. Now, since xy does not equal 0, both terms must not equal zero. So this means that both |x| and |y| are not equal to zero. This leaves us with |x| + |y| > 0. Now, we get that |x| + |y|= -x-y. This means that - x - y > 0, ot that x + y < 0.
B is your answer.

Dana, Its given that xy not equal yo zero. But, you took x+y not equal to zero. Please check it.

Thanks.

No, I took that |x| + |y| is not equal to zero. Since absolute values are always greater than or equal to zero, then you get that |x| + |y| >=0. This sum is equal to zero only when both x and y are equal to 0. But since xy is not equal to zero, then this means that neither x nor y is equal to zero, so |x| + |y| cannot be equal to zero. Therefore you get that |x| + |y| >0.

Clearly |x| + |y| > =0 and the equality holds only when both x and y are equal to 0. But, since it is given that xy is not equal to 0 none of x and y can be 0.

Thus |x|+|y| > 0.

Given |x|+|y| = -(x+y)

Hence -(x+y) > 0 , which means (x+y) < 0.