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# word problems and turning them into algebraic equation to slove

Show algebraically why the following Number Trick always works?
Choose any number; add 5; double the result; subtract 4;divide by 2;subtract the original number. the result is always 3.

### 2 Answers by Expert Tutors

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
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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
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...

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Nancy;
{{[2(x+5)]-4}/2} -x
[(2x+10-4)/2]-x
x+5-2-x
3