Question

Your younger sibling runs up to you and excitedly exclaims, "I'm thinking of a number. If I add it to the number 2 ten times, that is, 2 + my number + my number + my number, and so on, then the answer is 2. What is my number?" You almost immediately answer, "zero," but are you sure? Can you find a different number (other than zero) that has the same property? If not, can you justify that your answer is the only correct answer?

Answer 1

Answer:

$x = 0$

Step-by-step explanation:

Given

Represent the number with x.

So:

$2 + x + x + x + x + x + x + x + x + x + x = 2$

or

$2 + 10x = 2$

We want to solve for x

Subtract both sides by 2

$2 - 2 + 10x = 2 - 2$

$10x = 0$

Solve for x

$x = \frac{0}{10}$

$x = 0$

No other number aside 0, satisfy the property.