`xlt0`
`{:("Quantity A","Quantity B"),(x-2,-(x-2)):}`

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, we need to compare Quantity A and Quantity B given the condition \( x < 0 \).

**Step 1: Define the quantities.**
- Quantity A: \( x - 2 \)
- Quantity B: \( - (x - 2) = -x + 2 \)

**Step 2: Analyze Quantity A.**
Since \( x < 0 \):
\[ x - 2 < 0 - 2 = -2 \]
Thus, we can conclude:
\[ \text{Quantity A} < -2 \]

**Step 3: Analyze Quantity B.**
Now let's simplify Quantity B:
\[ -(x - 2) = -x + 2 \]
Since \( x < 0 \), we know that \( -x > 0 \). Therefore:
\[ -x + 2 > 0 + 2 = 2 \]
Thus, we can conclude:
\[ \text{Quantity B} > 2 \]

**Step 4: Compare the two quantities.**
From our analysis:
- Quantity A is less than -2.
- Quantity B is greater than 2.

Since \( -2 < 2 \), we can conclude that:
\[ \text{Quantity A} < \text{Quantity B} \]

**Final Conclusion:**
Quantity B is greater than Quantity A.

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