Question

If \( |x-3| = 3 \), compare the two quantities:
Quantity A: \( x \)
Quantity B: 2

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined.

Hint:

Absolute value equations often give multiple solutions; always test each solution before comparing.

Answer 1

The Correct Option is D

Step 1: Solve absolute equation: \( |x-3| = 3 \).

Step 2: Two cases:
1. \( x - 3 = 3 \Rightarrow x = 6 \).
2. \( x - 3 = -3 \Rightarrow x = 0 \).

Step 3: Compare with 2. For \( x=6 \), Quantity A>Quantity B. For \( x=0 \), Quantity B>Quantity A.
Thus, no unique relation.
Final Answer: \[ \boxed{\text{Cannot be determined}} \]