Pick any number and multiply the number by 4. Add 6 to the product. Divide the sum by 2 and subtract 3 from the quotient.

(a) What is the relationship between the number you started with and the final answer? 

(b) Arbitrarily select some different numbers and repeat the process, recording the original number and the results. 

(c) Can you make a conjecture about the relationship between the original number and the final number?

(d) Prove, using deductive reasoning, the conjecture you made in part (c).