Pick a number. Double it. Multiply the result by 3. Add 24. Divide by 6. Subtract your original number. Is the result always the same? Write a convincing argument for what happens.
HELP!
AHA! My mistake. 24/6=4, not 6.
Granted I was wrong, you should have caught my error and noted it, rather than just saying we disagreed.
I showed my work. Why not show yours? Maybe we can come to some agreement...
To understand what happens in this sequence of calculations, let's break it down step by step.
1. Pick a number: Let's say our original number is "x".
2. Double it: Multiplying "x" by 2, we get 2x.
3. Multiply the result by 3: Multiplying 2x by 3, we get 6x.
4. Add 24: Adding 24 to 6x, we have 6x + 24.
5. Divide by 6: Dividing 6x + 24 by 6, we get (6x + 24) / 6.
6. Subtract your original number: Subtracting "x" from (6x + 24) / 6, we have (6x + 24)/6 - x.
Now, let's simplify the expression (6x + 24)/6 - x:
First, we can simplify the numerator:
(6x + 24)/6 = (6/6)*(x + 4) = x + 4
So the expression becomes:
(x + 4) - x
When we simplify the above expression, we get:
x + 4 - x = 4
Therefore, no matter what number "x" we start with, the final result of the sequence of calculations is always 4. This means that the result is indeed the same every time.
To summarize, the convincing argument is that regardless of the original number chosen, all the subsequent calculations result in a final value of 4.
I don't get the same number!!
The result of each step is shown below:
x
2x
(2x)(3) = 6x
6x+24
x+6
6
The result is always 6