Why does this math puzzle always solve out to be three?

Question

Ok, How does this come out to three, I understand how I got it, but why is that always the rule?

Start with a number and multiply by 4. Add 6 to that, and divide the answer by 2, then subtract 2 times the origional number.

for example, # = 10
10 x 4 = 40
40 + 6 = 46
46 / 2 = 23
23 - (2 x 10) =
23 - 20 = 3

why does it always work out to be 3?

Answer 1

think of each step in terms of x

1. 4X
2. 4X+6
3. (4X+6)/2 = 2X+3
4. 2X +3 -2X
5. Since 2X minus 2X is 0, you are left with +3

Answer 2

A little algebra shows us why:

Suppose the number you pick is "N". then multiplying it by 4 is times N, or 4N. Adding 6 to this gives you 4N+6. Now the distributive rule of algebra says that if you have two numbers added together, and are dividing their sum by a certain number, you get the same answer if you divide each individual number and THEN add them up. (Actually the distributive rule is usually defined for multiplication, but long story short, it works for division too). So 4N+6 divide by 2 is the same as 4N divided by 2, plus 6 divided by 2. This gives you 2N+3.

Subtracting 2 times the original number from this is just subtracting 2N. So when you take away 2N from 2N+3, you're just left with 3.

We've now proven that regardless of what value "N" is, we'll always wind up with 3.

Answer 3

because it is a mathermatical truth. All the equation works with is the difference from the original number. Think about it with x as the original number. xtimes 4 is 4x. Then it goes 4x+6 then all that divided by 2 is 2x+3. then subtract 2 times the original or 2x and you get 3 regardless of what it is. Hope this helps u understand

Answer 4

Start with a number, call it "X"
Multiply by 4, that gives you 4X
Add 6, that gives you 4X + 6
Divide by 2, you get 2X + 3
Subtract 2X, you get 3

Answer 5

Lets use algebra to see why...
Let n = any number

(((n x 4) + 6) / 2) - (2n) = 3 Then use algebra to solve for 'n'.
(4n+6)/2 - 2n = 3
2n + 3 - 2n = 3

Answer 6

heres how.

X= the number
4x+6 is the second step
2x+3 is after that,
then subract 2x. you get back to 3. theyre very simple.