a ≠ 0 Quantity A: x/a Quantity B: (a^-1)x

Rationale

Quantity A and Quantity B are equal.

Both expressions, Quantity A (x/a) and Quantity B ((a^-1)x), are mathematically equivalent as they represent the same relationship. When we simplify Quantity B, we find that (a^-1)x is equal to x divided by a, confirming the equality of the two quantities.

A (Quantity A is greater.) YOUR ANSWER

This choice suggests that x/a is greater than (a^-1)x, but since we have established that both expressions are equivalent, this statement is incorrect. The two quantities cannot be compared in terms of greater or lesser.

B (Quantity B is greater.) YOUR ANSWER

Claiming that (a^-1)x is greater than x/a also contradicts the established equality. Since both quantities represent the same value, this choice misrepresents their relationship.

C (The two quantities are equal.) CORRECT

This choice is correct as both quantities simplify to the same expression. Since x/a equals (a^-1)x, we can confidently state that they are equal.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This choice implies uncertainty regarding the relationship between the two quantities. However, the equivalence of x/a and (a^-1)x is clear through algebraic manipulation, making this choice invalid.

Conclusion

The expressions for Quantity A and Quantity B are shown to be equal through algebraic simplification, confirming that both represent the same value. Therefore, the only accurate conclusion is that Quantity A and Quantity B are equal, aligning with mathematical principles of equivalency in fractions.

a ≠ 0 Quantity A: x/a Quantity B: (a^-1)x

Quantity A and Quantity B are equal.

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