`{:("Quantity A","Quantity B"),((x)/(2),2x):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem of comparing Quantity A and Quantity B, we have:

- Quantity A: \( \frac{x}{2} \)
- Quantity B: \( 2x \)

We need to determine the relationship between these two quantities for different values of \( x \).

### Step 1: Choose a value for \( x \)
Let's start by choosing a simple value for \( x \). We will first try \( x = 2 \).

### Step 2: Calculate Quantity A and Quantity B for \( x = 2 \)
- Quantity A:
\[ \frac{x}{2} = \frac{2}{2} = 1 \]
- Quantity B:
\[ 2x = 2 \times 2 = 4 \]

### Step 3: Compare Quantity A and Quantity B for \( x = 2 \)
Now we compare:
- Quantity A = 1
- Quantity B = 4

Since \( 1 < 4 \), we find that Quantity B is greater than Quantity A.

### Step 4: Choose another value for \( x \)
Next, let's try a negative value for \( x \). We will use \( x = -2 \).

### Step 5: Calculate Quantity A and Quantity B for \( x = -2 \)
- Quantity A:
\[ \frac{x}{2} = \frac{-2}{2} = -1 \]
- Quantity B:
\[ 2x = 2 \times -2 = -4 \]

### Step 6: Compare Quantity A and Quantity B for \( x = -2 \)
Now we compare:
- Quantity A = -1
- Quantity B = -4

Since \( -1 > -4 \), we find that Quantity A is greater than Quantity B.

### Step 7: Analyze the results
From our calculations:
- For \( x = 2 \), Quantity B is greater than Quantity A.
- For \( x = -2 \), Quantity A is greater than Quantity B.

### Conclusion
Since we have obtained opposing results depending on the value of \( x \), we cannot definitively conclude the relationship between Quantity A and Quantity B for all values of \( x \). Therefore, the answer is that there is no consistent relationship between the two quantities.

### Final Answer
The correct option is D: The relationship cannot be determined from the information given.

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