Inductive reasoning in Math

How in the HELL do you do this???

This is an example of what I am told to do;

Making and Proving Conjectures

Consider this procedure. Select a number. Multiply the number by 9. Add 6 to the product and divide the sum by 3. Subtract 2 from the quotient.

(a) Follow the procedure for four different numbers and make a conjecture about the relationship between the original number and the final result.

(b) Represent the original number by n and prove the conjecture in part (a).

Solution
Let us select four different numbers--say, 5, 10, 21, and 100--and apply the procedure given.

WHAT THE SHIT, MAN!?!

Hello sir,

Let us example the procedure.
"Select a number. Multiply the number by 9. Add 6 to the product and divide the sum by 3. Subtract 2 from the quotient."

5*9 = 45 ----> 45+6 = 51  ----> 51/3 = 17  ----> 17-2 = 15
10*9 = 90 ---> 90+6 = 96 -----> 96 /3 = 32 ----> 32 -2 = 30
21*9 = 189 ---> 189 + 6 = 195 ----> 195/3 = 65 ---> 65 -2 = 63
It seems like the relation is you multiply it by 3.
WHYYYYYY?? Lets do it in the general case.
n*9 = 9n ----> 9n+6 ---->(9n+6)/3 ---->  (9n+6)/3  -2
Now lets simplify
(9n+6)/3 -2 = 9n/3 + 6/3 -2 = 3n +2 -2 = 3n