Pick a number, subtract 10, multiply the answer by 6, divide the result by 2 and subtract three times the original number.
a) Use induction to find a rule that relates the number selected to the final answer.
B) Use deductive reasoning to prove your conjecture
The neat thing about this process is that you will always get -30 as your answer.
a. If you have a number x, then you do all the steps, you'll get:
(6(x-10)/2-3x...this would be an unsimplified rule.
b. To prove that all numbers make the final result -30, we simplify the rule...
(6(x-10)/2-3x= 3x-30-3x= -30
This proves that all inputs would create the same -30 output.
*I'm not sure if this fits your problems induction and deductive reasoning requirments, but I hope it gives you an idea on how to do so.
Hope it helps!