Explain This...and you Win...umm...Something..

[Hossfly]

1. (2x+8)/2 - 4 = x
2. (2x+8)/2 = x + 4
3. (2x+8) = 2(x+4)
4. 2x+8=2x+8
5. x can be any number

Like edthecynic said, but my algebra teacher back in '69 slap me across the head for skipping steps and not showing my work. So this is how we were forced to show it.

I can sympathize with you. I would use my own shortcuts and not show my work and even if I made a perfect score on a test, the teacher would threaten to give me an F and I would go back and show my work.

 

[Bonzi]

How about this one.

Take a deck of cards. Don't look, but remove 3 of them and set them aside.

Start placing the rest of the cards face up on a table. Any cards that add up to 10 place more cards on top, like if you have a 5 and a 5, put cards on top of them.
Or, if there is a 10 put a card on top of that, in this trick, J+Q+K = 10. Ace+9=10 etc.

Once you are done, match up the piles where the top card equals 10 based on the rules above. You will be left with random stack where the top card didn't match up with another stack to make 10. Like 9, 6 and 2

The 3 cards you put to the side will be A, 4 and 8 (to make 10 with the stack that had no match)

 

[g5000]

Think of a number 1 to 10. Now double it. Add 8 to it. Divide by 2. Subtract 1st number you thought of. The answer will be 4.

Try the same trick, except instead of adding 8, add 10. Your final answer will be 5.

Or add 6 instead of 8, and you final answer will be 3.

Or add 52,768 instead of 8, and your final answer will be 26,384.

And so forth.