Repeat the following procedure for the four given numbers. Rulty 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 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 \( n \). The result is 4 x . (Simplify your answer.)

When you follow the described process, you can break it down into a mathematical equation using \( n \) as the original number. First, multiply \( n \) by 8, giving you \( 8n \). Next, add 12 to that, resulting in \( 8n + 12 \). Now, divide by 2, leading to \( \frac{8n + 12}{2} = 4n + 6 \). Finally, subtract 6, giving you \( 4n + 6 - 6 = 4n \). So, you can conjecture that the result of the process is \( 4n \), which is simply four times the original number. In a nutshell, every time you plug different values of \( n \) into this fun recipe, you’ll always walk away with a result that’s four times the original number. It’s like a magic multiplying trick, but with math!