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Chapter 14: Problem 2

\(x \neq 0\) Quantity \(\mathbf{A}\) \(\frac{x}{10}\) Quantity B \(\frac{\frac{x}{5}}{2}\) a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
c. The two quantities are equal.

Step by step solution

01

Simplify Quantity A

Quantity A is already in its simplest form, \(\frac{x}{10}\).
02

Simplify Quantity B

Quantity B can be simplified by evaluating the fraction in the numerator first, which gives \(\frac{x}{5}\), then dividing it by 2. This results in \(\frac{x}{5} \div 2 = \frac{x}{10}\).
03

Compare the Quantities

Now that both quantities are in the same form, \(\frac{x}{10}\), it can be determined that they are equal. The assumption given that \(x \neq 0\) is crucial here, as it avoids complication with division by zero.

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