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

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

Answer 2

Lets say x is a number that is 1-20. The equation is
$(((x \times 2) + 6) \div 2) - 3 = x$
We then work backwards, add 3
$((x \times 2) + 6) \div 2 = x + 3$
The multiply by 2
$(x \times 2) + 6 = 2(x + 3)$
Then simplify
$2x + 6 = 2x + 6$
As you can see, they are equal to each other and can further condense it, making it into
$x = x$