use inductive reasoning to make a conjecture: pick any counting number. add 4 to the number and multiply the sum by 3. subtract 7 and then decrease this difference by the triple of the original number.

Explanation:

x

x+4

3(x + 4)

3(x + 4) - 7

3(x + 4) - 7 - 3x

You should always get 12 - 7 = 5 no matter what the starting number was.

20 + 4 = 24

3*24 = 72

72 - 7 = 65

The original number was 20. 3 * 20 = 60

The remainder is 5 when 60 is subtracted. Try it yourself.