Repeat the following procedure for the four given numbers. Multiply the number by 8 . Add 12 to the product. Divide this sum by 2 . Subtract 6 from the quotient. The 1 st number is 2 . The result is 8 . The 2 nd number is 5 . The result is 20 . The 3rd number is 9 . The result is 36 . The 4 th number is 11 . The result is 44 . a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as The result is \( \square \). (Simplify your answer.)

a. **Conjecture:** Let the original number be represented by \( x \). Then, the result of the process is \( 4x \). **Mathematically:** \[ \text{Original number} = x \quad \Rightarrow \quad \text{Result} = 4x \] **Explanation:** Let's simplify the given procedure step by step: 1. **Multiply by 8**: \( 8x \) 2. **Add 12**: \( 8x + 12 \) 3. **Divide by 2**: \( \frac{8x + 12}{2} = 4x + 6 \) 4. **Subtract 6**: \( 4x + 6 - 6 = 4x \) Thus, the final result is **four times the original number**. **Example Verification:** - For \( x = 2 \): \( 4 \times 2 = 8 \) ✓ - For \( x = 5 \): \( 4 \times 5 = 20 \) ✓ - For \( x = 9 \): \( 4 \times 9 = 36 \) ✓ - For \( x = 11 \): \( 4 \times 11 = 44 \) ✓ This confirms that the conjecture holds for the given numbers. **Final Conjecture Statement:** \[ \text{If the original number is } x, \text{ then the result is } 4x. \] Answer: a. Let the original number be \( x \). Then the result is \( 4x \). \[ \text{Original number} = x \quad \Rightarrow \quad \text{Result} = 4x \]