Question

1. alison created a number trick in which she always ended with the original number. when alison tried to prove her trick, however, it did not work. what type of error occurs in the proof? circle the step where the error occurred.

use n to represent any number. add 4. multiply by 2. add 4. divide by 2. subtract 5.
a. a false premise
b. an error in reasoning
c. a calculation error
d. there is no error in the proof.
n n + 4 2n + 8 2n + 4 n + 4 n - 1

Explanation:

Step1: Analyze the steps

Let's follow the operations step - by - step. Starting with a number \(n\).

1. First step: Add 4, we get \(n + 4\).
2. Second step: Multiply by 2, we get \(2(n + 4)=2n+8\).
3. Third step: Add 4, we get \(2n + 8+4=2n + 12\).
4. Fourth step: Divide by 2, we get \(\frac{2n + 12}{2}=n + 6\).
5. Fifth step: Subtract 5, we get \(n+6 - 5=n + 1\).

The expected result should be \(n\) if it is a valid number - trick, but we got \(n + 1\). The error is in the reasoning of the steps of the number - trick.

Answer:

b. an error in reasoning