Question

Given x and y are rational numbers, when is [x - y = bxt - b] true?

A) This is true when x and y have the same sign.
B) This is sometimes true.
C) This is always true.
D) This is never true.

Answer 1

The equation [x - y = bxt - b] is true when x and y have the same sign or when b = 0.

Step-by-step explanation:

The equation [x - y = bxt - b] is true when x and y have the same sign.

To see why, let's consider two cases:

1. If x and y are both positive or both negative, then their difference (x - y) is also positive. Multiplying both sides of the equation by b and then adding b, we get b(x - y) + b = bxt. Simplifying, we have bxt = bxt, which is true.
2. If x and y have opposite signs (one is positive and the other is negative), then their difference (x - y) is negative. Multiplying both sides of the equation by b and then adding b, we get b(x - y) + b = bxt. Simplifying, we have bxt = bxt - 2b, which is not true unless b is equal to 0.

Therefore, the equation [x - y = bxt - b] is only true when x and y have the same sign or when b = 0.