MHB Understanding Inequalities: Why is Option C the Correct Answer?

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View attachment 2918Why is the answer "C" and not "B"?
 

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In B, the magnitude of a number does not depend on its sign. Clearly, for B, if x is 2, and y is -6, the expression is not true.

C essentially boils down to this, if you add 5 to both sides:

$$\frac{x}{3} > \frac{y}{3}$$

Multiply both sides by 3:

$$x > y$$

If x is a positive number and y is a negative number (as stated by the question), this is always true! Since, well, a positive number is always greater than a negative number. (Wait) (Wondering)
Therefore, C is the right answer.
 
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