Question

If x < x-y, which of the following must be true?

(A) x = 0
(B) x < 0
(C) x > 0
(D) y < 0
(E) y > 0

Answer 1

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!