Answer:
D. 2x > 2y
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
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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