Repeat the following procedure for the four given numbers. 

Multiply the number by 

8

Add 

8

to the product. Divide this sum by 2. Subtract 

4

from the quotient.

Question content area bottom Part 1 The 1st number is  22 The result is  8 Part 2 The 2nd number is  6. The result is  24. Part 3 The 3rd number is  9 The result is  36 Part 4 The 4th number is  11 The result is  44 Part 5 **a.** Write a conjecture that relates the result of the process to the original number selected.  Represent the original number as n.

Let's break down the process step by step. The operations performed on the number \( n \) are as follows:

1. Multiply the number \( n \) by 8: \( 8n \)
2. Add 8 to the product: \( 8n + 8 \)
3. Divide this sum by 2: \( \frac{8n + 8}{2} = 4n + 4 \)
4. Subtract 4 from the quotient: \( (4n + 4) - 4 = 4n \)

### General Result:
The final result after performing these operations is \( 4n \), which is four times the original number \( n \).

### Conjecture:
Based on the above steps, the result of the process is always **four times the original number**. So, the conjecture can be stated as:

**Conjecture**: If you apply the given procedure to a number \( n \), the result will always be \( 4n \).

Do you want further details or have any questions about this process? 

Here are 5 relative questions to expand your understanding:

1. What would the result be if the original number \( n \) were negative?
2. Can you reverse this process to find the original number from the result?
3. What happens if you change the constants (like instead of adding 8, you add a different number)?
4. How does this process relate to linear functions?
5. Could the result of this process ever be negative if \( n \) is positive?

**Tip**: When working with patterns in mathematical procedures, translating them into algebraic expressions can help identify the underlying relationships easily.

Repeat the following procedure for the four given numbers. Multiply the number by 8. Add 8 to the product. Divide this sum by 2. Subtract 4 from the quotient. The 1st number is 22. The result is 8. The 2nd number is 6. The result is 24. The 3rd number is 9. The result is 36. The 4th number is 11. The result is 44. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as n.

Explore how multiplying a number by 8, adding 8, dividing the sum by 2, and subtracting 4 leads to a result that is four times the original number. This problem highlights key algebraic concepts and the linear relationship between the input and the result. Suitable for Grades 6-8 students.

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