Let's analyze the sequence of operations described:

1. Add 7 to the original number.
2. Double the result from step 1.
3. Subtract 10 from the result of step 2.
4. Divide by 2 the result of step 3.
5. Subtract the original number from the result of step 4.

Let's use this process on each number and see if it holds true.

For 1:

1. $1 + 7 = 8$
2. $8 \times 2 = 16$
3. $16 - 10 = 6$
4. $\frac{6}{2} = 3$
5. $3 - 1 = 2$

For 6:

1. $6 + 7 = 13$
2. $13 \times 2 = 26$
3. $26 - 10 = 16$
4. $\frac{16}{2} = 8$
5. $8 - 6 = 2$

For 9:

1. $9 + 7 = 16$
2. $16 \times 2 = 32$
3. $32 - 10 = 22$
4. $\frac{22}{2} = 11$
5. $11 - 9 = 2$

For 11:

1. $11 + 7 = 18$
2. $18 \times 2 = 36$
3. $36 - 10 = 26$
4. $\frac{26}{2} = 13$
5. $13 - 11 = 2$

Summary

In each case, the final result after performing the operations is always 2.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How would the result change if the original number was negative?
2. What happens if you change the operations, such as adding or subtracting different values?
3. Can you develop a general formula for this sequence of operations?
4. How would the result differ if you changed the order of operations?
5. What if you replaced the multiplication by 2 with multiplication by 3?

Tip: When working with sequences of operations, it's often helpful to write down each step to see patterns more easily.