Question

Choose any number. Double it. Subtract six and add the original number. Now divide by three. Repeat this process with other numbers until a pattern develops. By using a variable such as x in place of your number, show that the pattern does not depend on which number you choose initially.

a. ( 2x - 6 + x3 )
b. ( 3x - 63 )
c. ( 2x + 63 )
d. ( x + 63 )

Answer 1

The pattern when doubling a number, subtracting six, adding the original number, and dividing by three results in the original number minus two, as demonstrated using the variable x in the steps of the operation.

Step-by-step explanation:

To find the pattern when choosing any number, doubling it, subtracting six, adding the original number, and then dividing by three, we can use a variable x to represent the initial number. We start by doubling x to get 2x. We then subtract six to get 2x - 6. Next, we add the original number x to the result to get 2x - 6 + x, which simplifies to 3x - 6. Finally, we divide this by three, which simplifies to x - 2.

Now, let's conduct the operation step by step:

1. Choose any number (x).
2. Double the number: 2x.
3. Subtract six: 2x - 6.
4. Add the original number: 3x - 6.
5. Divide by three: (3x - 6) / 3 or x - 2

This pattern shows that no matter which number you start with, after following these operations, you always end with the original number minus two.