Write a number you like, add 2 to this number, multiply the result by 5, subtract 10, and divide it by 5 to get the original number.
(1) Assuming that the number written at the beginning is n, list the final expression according to each step of the game;
(2) Simplify the expression obtained in (1). Use your results to prove why this game applies to any number;
(3) Write a math game by yourself and write a description (try to make your game amazing and not obvious).
Test site: mixed operation of algebraic expressions.
Special topic: opening up.
Analysis: suppose the number written at the beginning is n, 2 plus n gets n+2, n+2 times 5 gets 5(n+2), minus 10 gets 5(n+2)- 10, and divide by 5 to get $ \ frac {5 (n+2)-65438.
( 1)$ \ frac { 5(n+2)- 10 } { 5 } $；
(2) $ \ frac {5 (n+2)-10} {5} $ = $ \ frac {5n+10-10} {5} $ = n, because the simplification result is n, the game is arbitrary.
(3) The answer is not unique. As long as the game is reasonable, score as appropriate.
For example, according to the following calculation:
,
The result is 1.
Reason: (x2+x) ÷ x-x = x+1-x =1.