4=3 Math Problem. Can you figure it out?

Discussion in 'Community Discussion' started by sjjordan, Nov 8, 2006.

  1. sjjordan macrumors 6502

    Joined:
    Jun 10, 2003
    Location:
    United States
    #1
    I ran into this math problem earlier today and it took me a while, but I figured out what's wrong with it. Thought I'd pass it on for fun. Enjoy!

    Suppose:
    a + b = c
    This can also be written as:
    4a - 3a + 4b - 3b = 4c - 3c
    After reorganising:
    4a + 4b - 4c = 3a + 3b - 3c
    Take the constants out of the brackets:
    4 * (a+b-c) = 3 * (a+b-c)
    Remove the same term left and right:
    4 = 3
     
  2. bearbo macrumors 68000

    bearbo

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    Jul 20, 2006
    #2
    4*0 = 3*0 does not mean 4 = 3
     
  3. Kolind macrumors regular

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    Nov 2, 2006
    Location:
    Denmark
    #3
    a+b-c does not necessarily give zero... the problem is that you can't remove the same term on both sides as it's being multiplied with the two constants.
     
  4. bearbo macrumors 68000

    bearbo

    Joined:
    Jul 20, 2006
    #4
    a+b=c therefore a+b-c = 0

    you most certainly can remove the same term from both side if they're being multiplied both side, by constant or variable... but you cannot remove term if there's , for instant, an addition...

    i.e. a*b+c = e*b+f, you cannot then remove the b to make it a+c = e+f...
     
  5. atszyman macrumors 68020

    atszyman

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    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #5
    a+b = c

    c=c

    c-c = 0

    a+b-c = 0

    4*0=3*0

    does not mean 4=3

    the removal of the term is legitimate, sort of.

    for x*y = z*y you can divide both sides by y and determine x=z.

    However if y=0 you cannot do this since you are dividing by zero which is undefined....

    I guess you're both right.

    if a+b were not equal to c then you could remove the (a+b-c) by dividing both sides by (a+b-c). But when you do this the following equation is no longer true:

    4a - 3a + 4b - 3b = 4c - 3c

    That equation is only true when a+b = c which means (a+b-c) = 0 and you cannot factor it out because it requires dividing by zero.
     
  6. Kolind macrumors regular

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    Nov 2, 2006
    Location:
    Denmark
    #6
    Looks like I was a bit too fast there ;)

    In this case a+b-c=0 - not sure what I was thinking :confused:

    I second whatever Bearbo said... and will stop trying to write anything about math in English :p
     
  7. MongoTheGeek macrumors 68040

    MongoTheGeek

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    Its not so much where you are as when you are.
    #7
    Most times when you get problem like this the answer is you can't divide by 0.
     
  8. bemylover macrumors regular

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    Jun 20, 2005
    #8
    That's probably "always", rather than "most times".
     
  9. fradac macrumors regular

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    Oct 24, 2003
    Location:
    Atlanta, GA
    #9
    yup its another one of those "cant cancel 0 on both side of equation"

    here is another example

    a = b = 1

    a*a = a*b

    a*a - b*b = a*b - b*b

    (a+b)(a-b) = b(a-b)

    a+b = b

    1+1 = 1

    2 = 1
     
  10. Rodimus Prime macrumors G4

    Rodimus Prime

    Joined:
    Oct 9, 2006
    #10
    umm again you have a bunch of zeros in there.

    a=b=1
    a-b=0
    So most of you work falls apart when almost all the proof = zero. You just removed. oh and 0/0 is undefined so it falls apart there as well

    I going to show you exactly where it fails.
    (a+b)(a-b)=b(a-b)
    You divided out the a-b. Only one problem a-b=0 and and 0/0=undefined. that makes the next step invalided.
     
  11. sassyk431 macrumors newbie

    Joined:
    Mar 10, 2014
    #11
    –(4+3a)=9(3–a)

    Can some one explain how to do this problem?

    –(4+3a)=9(3–a)
     
  12. BenTrovato macrumors 68000

    BenTrovato

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    Jun 29, 2012
    Location:
    Canada
    #12
    -4 - 3a = 27 - 9a
    6a = 31
    a = 31/6
     
  13. ideal.dreams macrumors 68020

    ideal.dreams

    Joined:
    Jul 19, 2010
    Location:
    OH
    #13
    You joined a MACRumors website and dug up a thread that is 8 years old for help with your math homework. Cool :cool:

    Distribute. -4-3a=27-9a
    Combine like terms. 6a=31
    Isolate variable. a=31/6
     
  14. The Doctor11 macrumors 603

    The Doctor11

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    Dec 15, 2013
    Location:
    New York
    #14
    I can get homework help on here? This site just got better :D
     

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