*+ 6*

*your number(x)+3:*(2x+6)/2=x+3

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.

Tutors, sign in to answer this question.

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...

Hi Nancy;

{{[2(x+5)]-4}/2} -x

[(2x+10-4)/2]-x

x+5-2-x

3

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

MaryLynne W.

Positive, patient tutor, focused on your getting results easily

$11.50 per 15 min

View Profile >

Michael D.

Math/Accounting/Business/Social Studies and Test Prep Tutor

$11.25 per 15 min

View Profile >

Bradley C.

Experienced Math and Programming Tutor

$11.25 per 15 min

View Profile >