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The Rule of False to solve linear equations

Discussion in 'Mathematics' started by dydx, Dec 11, 2011.

  1. Suppose we want to solve:

    x + x/7 = 24

    1. We make a guess, say x = 7
    2. Substitute x = 7 into LHS of equation. This gives 8
    3. Now divide the RHS by 8 and multiply by the guess 7 and voila, you have x.

    x = 24/8 x 7 = 21.
     
  2. Suppose we want to solve:

    x + x/7 = 24

    1. We make a guess, say x = 7
    2. Substitute x = 7 into LHS of equation. This gives 8
    3. Now divide the RHS by 8 and multiply by the guess 7 and voila, you have x.

    x = 24/8 x 7 = 21.
     
  3. DM

    DM New commenter

    I choose x = 0 as my first guess.
     
  4. Nice one DM.

    Anyway, generalising this method...

    ax+bx=n

    x=nx/[(a+b)x]

    x=n/[a+b]

    Not too surprising.
     

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