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

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Option C is correct because it accurately reflects the relationship between positive and negative numbers. The discussion clarifies that in option B, the sign of the numbers affects the truth of the expression, making it invalid. By manipulating the inequality in option C, it shows that if x is positive and y is negative, the inequality holds true. Thus, the conclusion is that a positive number is always greater than a negative number, confirming that C is the correct answer. Understanding these inequalities is crucial for solving similar problems effectively.
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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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