Understanding Inequalities: Why is Option C the Correct Answer?

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SUMMARY

The correct answer to the inequality question is option C, as it accurately reflects the relationship between positive and negative numbers. The discussion clarifies that in option B, the magnitude of a number does not account for its sign, leading to incorrect conclusions. By manipulating the inequality $\frac{x}{3} > \frac{y}{3}$ and multiplying both sides by 3, it is established that if x is positive and y is negative, then x will always be greater than y. Thus, option C is definitively the correct choice.

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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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