Question

When aaliyah picks any number between 1 and 20, doubles it,adds 6,divide by 2 and subtract 3, she always gets the number she started with. evaluate and use algebraic evidence to support your conclusion.

Answer 1

Lets say x is a number that is 1-20. The equation is

`(((x * 2) + 6) / 2) - 3 = x`
We then work backwards, add 3

`((x * 2) + 6) / 2 = x + 3`
The multiply by 2

`(x * 2) + 6 = 2(x + 3)`
Then simplify

`2x + 6 = 2x + 6`
As you can see, they are equal to each other and can further condense it, making it into

`x = x`

Answer 2

Any number between 1 and 20. Let's choose 3 different numbers. I choose 11, 16, and 6.

(16 + 16 + 6)/2 - 3 = 16
(11 + 11 + 6)/2 - 3 = 11
(6 + 6 + 6)/2 - 3 = 6

It seems Aaliyah is correct. We can she she's using this equation to come up with this "trick."

Evaluation:
(2x + 6) / 2 - 3
= 2(x+3) / 2 - 3
= x + 3 - 3
= x