Question

Suppose that XNY are in rational numbers such that x>y. Which of the following inequalities must be true

Answer 1

Answer:

  D.  2x > 2y

Step-by-step explanation:

This question illustrates some of the difficulties you can run into with inequalities.

Consider each of the expressions when x = 1 and y = -2. We know that

  x > y

  1 > -2

__

A. x^2 = 1, y^2 = 4 . . . . x^2 > y^2 is not true

B. -x = -1, -y = 2 . . . . -x > -y is not true

C. 1/x = 1/1 = 1, 1/y = 1/-2 = -1/2 . . . . 1/x > 1/y is true

  Now consider x=2, y=1. x > y because 2 > 1, but ...

  1/x = 1/2, 1/y = 1 . . . . 1/x > 1/y is not true

D. We know that multiplying the numbers by 2 only stretches them apart on the number line. It does not change their order. For our example, ...

  2x = 2, 2y = -4 . . . . 2 > -4 is true