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Math Help - Isolating a value

  1. #1
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    Isolating a value

    Hi, maths is a long time ago for me and I need to solve this equation (if its possible). I've read where to post but its been so long I'm still not sure so if this isnt the right area then I apologise.

    I have a formula where,

    x = a - b + (((a+b)/2) * e) * f

    is it possible to rearrange this formula so I could isolate b i.e. b = ?

    Any help would be greatly appreciated
    Many thanks
    Steve
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  2. #2
    A Plied Mathematician
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    I believe you can:

    x = a - b + ef\,\dfrac{a+b}{2}\quad\to

    x-a=-b+ef\,\dfrac{a+b}{2}=-b+\dfrac{efa}{2}+\dfrac{efb}{2}\quad\to

    Can you continue?
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  3. #3
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    Thank you Adrian, very much appreciated.

    I've tried to complete it from here but I'm getting stuck. It's for a work assignment which i hope can be solved this way but I just wish I continued with Maths at school. I'm getting stuck removing the division to isolate the b? am I on completely the wrong track?

    Thanks again
    Steve
    Last edited by Stevekuk; January 18th 2011 at 03:38 AM. Reason: typo
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  4. #4
    A Plied Mathematician
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    Well, can you show me what you've done?
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  5. #5
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    by all means but please be kind this is my first attempt at trying to remember how to do this. I've just ordered some books from Amazon.

    Following your last line

    x - a - efa/2 = -b + efb/2

    x- a - efa/2 = -b + b(ef/2)

    from there I feel I want to square both sides to get rid of the divide but then I just get lost?

    Thanks Adrian
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  6. #6
    A Plied Mathematician
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    Great so far! I wouldn't square both sides. Instead, I would factor the b out of both terms on the RHS.
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  7. #7
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    would that make the RHS -b(1-ef/2)? is that allowed?

    I am enjoying this, breaking out of the norm
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  8. #8
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    is this correct?

    - ( x - a) - efa/2 = b
    1 - ef/2

    if the format is off I'll repost, if this is correct is this the neatest solution?
    Thanks again
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  9. #9
    A Plied Mathematician
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    You're close, but I think your factorization of -b instead of b got you into sign trouble. I do this:

    x- a - efa/2 = -b + b(ef/2)

    x- a - efa/2 = b(ef/2-1)

    b=\dfrac{x-a-efa/2}{ef/2-1}.

    But you definitely have the right idea.
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  10. #10
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    Fantastic, many many thanks Adrian, you're a lifesaver.
    Kind regards
    Steve
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  11. #11
    A Plied Mathematician
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    You're welcome. Have a good one!
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