let me explain what is actually happening
let x be the number you choose
add 5, which gives you x+5
double the result which gives you 2(x+5)=2x+10
subtract 4 which gives you 2x+10-4=2x+6
no matter what number you choose you always end up with 2 times your number
+ 6
now when you divide by 2 you get your number(x)+3:(2x+6)/2=x+3
your number(x)+3 minus the original number(x) gives you 3 all the time
examples:choose 4
4+5=9
2*9=18
18-4=14 which is 8+6=2(4)+6; see! you get 2 times your number +6
divide by 2
[2(4)+6]/2=4+3;your number + 3
now subtract your number and you get 3
choose 5
5+5=10
2*10=20
20-4=16 which is 10+6=2(5)+6
divide by 2 to get 5+3
subtract 5 to get 3 again
choose 6
6+5=11
2*11=22
22-4=18 which is 2(6)+6
divide by 2 to get 6+3 (divide each term by 2 !)
subtract 6 and you end up with 3 again
choose 15
15+5=20
2*20=40
40-4=36=2(15)+6
divide by 2 to get 15+3
subtract 15 to get 3 again and again and again...