Algebraic Proofs

Algebraic proofs are another type of proof. Algebraic proofs use algebra to show that a conjecture must be true.

Example 2

Maia has a mathematical "magic trick" she likes to use with her friends. She asks them to think of an Integer. Then she gives them a set of instructions to follow in their head. Once they have followed the set of instructions, she is able to identify the number they ended up with.

Maia's Magic Trick Instructions

  • Think of an Integer
  • Add 5 to your number
  • Double that number
  • Subtract your original number
  • Subtract your original number again

Maia is then able to tell her friends that they ended up with the number 10.

  1. Try Maia's magic trick with two different integers.

    Think of an Integer 12
    Add 5 to your number 17
    Double that number 34
    Subtract your original number 22
    Subtract your original number again 10


    Think of an Integer
    −4
    Add 5 to your number
    1
    Double that number
    2
    Subtract your original number
    6
    Subtract your original number again
    10


  2. Algebraically prove that Maia's trick will always work.

    To prove that Maia's trick will always work, you can show the general case by using x as your original input Integer.

    Think of an Integer
    Add 5 to your number
    Double that number
    Subtract your original number
    Subtract your original number again


    This shows it doesn't matter which number is used to start the trick. The result will always be 10.