Write a conjecture that relates the result of the process to the original number selected.

Question

Add 5. Double the result. Subtract 6. Divide by 2. Subtract the original selected number.

a. Write a conjecture that relates the result of the process to the original number selected.

b. Represent the original number as n​, and use deductive reasoning to prove the conjecture in part​ (a).

1. Add 5.
2. Double the result. (Simplify your​ answer.)
3. Subtract 6. (Simplify your​ answer.)
4. Divide by 2. (Simplify your​ answer.)
5. Subtract the original number. (Simplify your​ answer.)

Answer 1

n+5

2(n+5) = 2n+10

2n+10-6 = 2n+4

(2n+4)/2 = n+2

n+2-n = 2

you always end up with 2, regardless of the value of n

let n=0, you end up with 2

let n=1, you end up with 2

part of the process double, then later it divides by 2, which cancel each other

you start by adding n, then later you subtract n, which cancels each other

n is irrelevant to the process

you really start with 5, double it to get 10, subtract 6 to get 4, divide by 2 to get 2

the n is extraneous, surplusage, irrelevant