Answer: The correct answer is (D), y < 0. Subtracting x from both sides of the inequality gives -y < 0, which means y < 0.
Step-by-step explanation: We can manipulate the inequality x < x - y by using the same operations on both sides. One operation we can use is subtraction. If we subtract x from both sides, we get:
x - x < x - y - x
Simplifying the left side, we get:
0 < x - y - x
Combining the terms with x on the right side, we get:
0 < -y
This inequality tells us that -y is positive, which means y is negative. Therefore, y < 0.
We can check our answer by plugging in some values for x and y that satisfy the condition y < 0. For example, if x = 1 and y = -2, then x - y = 1 + 2 = 3. The original inequality becomes:
1 < 3
This is true, so our answer is correct. If we plug in values for x and y that do not satisfy the condition y < 0, such as x = 1 and y = 2, then x - y = 1 - 2 = -1. The original inequality becomes:
1 < -1
This is false, so our answer is correct.
Hope this helps, and have a great day!