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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

 Apr 7, 2020
 #1
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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:

 

x

 

x-10

 

6(x-10)

 

(6(x-10)/2

 

(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...

 

x

 

x-10

 

6(x-10)= 6x-60

 

(6(x-10)/2= 3x-30

 

(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!

 Apr 7, 2020

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