Question

I think of a number.

I add 5 to it and then double the result.
I then subtract 10 from this answer.
I then subtract the original number I thought of.
Using algebra and a pronumeral to represent the number I think of, explain
why I get back to the number I started with.

Answer 1

Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x

Explanation:

I think of a number, represented by the variable/pronumeral x.

I add 5 to it: x + 5

then double the result: 2(x + 5)

I then subtract 10 from this answer: [2(x + 5)] - 10

I then subtract the original number I thought of: [2(x + 5)] - 10 - x

Simplifying the expression will explain why you get the original number.

[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.