Question
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 2 nd number is 5 . The result is 8 . The 3rd number is 9 . The result is 36 . 20 . The 4 th number is 11 . a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as n . The result is \( \square \). (Simplify your answer.)
Ask by Ayala Wagner. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result is \( 4n \).
Solution
a. **Conjecture:**
Let \( n \) represent the original number. Following the given procedure:
1. **Multiply by 8:** \( 8n \)
2. **Add 12:** \( 8n + 12 \)
3. **Divide by 2:** \( \frac{8n + 12}{2} = 4n + 6 \)
4. **Subtract 6:** \( 4n + 6 - 6 = 4n \)
**The result is \( 4n \).**
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Simplify this solution Extra Insights
Let's break down the procedure step by step for a number \( n \): 1. Multiply the number by 8: \( 8n \) 2. Add 12 to the product: \( 8n + 12 \) 3. Divide this sum by 2: \( \frac{8n + 12}{2} = 4n + 6 \) 4. Subtract 6 from the quotient: \( 4n + 6 - 6 = 4n \) Thus, the result of the process is \( 4n \). So, the conjecture that relates the result of the process to the original number selected is: The result is \( 4n \).
