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Math Help - Solve for X

  1. #1
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    Solve for X

    Hello Everyone,

    I'm banging my head against the wall trying to solve this complex fraction. Can anyone point me in the right direction or give any hints / tips?

    1/((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x)) = 10

    I think what's throwing me off most is how to handle the (1-(0.5+x)); should I still multiply by the LCD?

    Thanks!
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  2. #2
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    Hello jello

    Welcome to Math Help Forum!
    Quote Originally Posted by jello View Post
    Hello Everyone,

    I'm banging my head against the wall trying to solve this complex fraction. Can anyone point me in the right direction or give any hints / tips?

    1/((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x)) = 10

    I think what's throwing me off most is how to handle the (1-(0.5+x)); should I still multiply by the LCD?

    Thanks!
    You haven't got this expression quite correct - there's a missing right parenthesis somewhere. If it should come just before the = sign, then what you mean is:

    1/
    ((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x))) = 10

    in which case the equation is:

    \frac{1}{\dfrac{0.25}{30}+ \dfrac{0.25}{20}+\dfrac{x}{15}+ \Big(1-(0.5+x)\Big)}= 10

    Multiply top and bottom of the LHS by 60, and remove the inner pair of brackets from \Big((1-(0.5+x)\Big), noting the minus sign in front of the x:

    \frac{60}{\dfrac{60\times0.25}{30}+ \dfrac{60\times0.25}{20}+\dfrac{60x}{15}+ 60(1-0.5-x)}= 10

    \Rightarrow \frac{6}{0.5+0.75+4x+60(0.5-x)}=1

    \Rightarrow \frac{6}{31.25-56x}=1

    \Rightarrow 6 = 31.25-56x

    \Rightarrow 56x = 25.25

    \Rightarrow x = 0.4509 (to 4 d.p.)

    Grandad
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  3. #3
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    Quote Originally Posted by jello View Post
    Hello Everyone,

    I'm banging my head against the wall trying to solve this complex fraction. Can anyone point me in the right direction or give any hints / tips?

    1/((0.25/30)+(0.25/20)+(x/15)+(1-(0.5+x)) = 10

    I think what's throwing me off most is how to handle the (1-(0.5+x)); should I still multiply by the LCD?

    Thanks!
    The fraction:
     <br />
\dfrac{1}{\dfrac{0.25}{30}+\dfrac{0.25}{20}+\dfrac  {x}{15}+(1-(0.5+x)} = 10<br />

    slight adjustment
     <br />
\dfrac{1}{\dfrac{0.25}{30}+\dfrac{0.25}{20}+\dfrac  {x}{15}+ 0.5 - x } = 10<br />

    common denominator
     <br />
\dfrac{1}{\dfrac{0.25}{30}+\dfrac{1.5 (0.25)}{1.5(20)}+\dfrac{2x}{2(15)}+ \dfrac{30(0.5)}{30} + \dfrac{-30x}{30} } = 10<br />

    some simplification
     <br />
\dfrac{1}{\dfrac{0.25}{30}+\dfrac{0.375}{1.5(20)}+  \dfrac{2x}{2(15)}+ \dfrac{15}{30} + \dfrac{-30x}{30} } = 10<br />

    more
     <br />
\dfrac{1}{\dfrac{0.25 + 0.375 + 2x + 15 - 30x}{30} } = 10<br />

    etc
     <br />
\dfrac{1}{\dfrac{ 15.625 - 28x }{30} } = 10<br />

    big step simplification

     <br />
\dfrac{30}{15.625 - 28x } = 10<br />

    ...
     <br />
30 = 10 (15.625) - 280x<br />

    ...
     <br />
156.25 - 30 = 280x<br />

    to this

     126.25 = 280x

    methodical systematic

    .
    Last edited by aidan; September 9th 2009 at 04:10 AM. Reason: I've gotta learn to type better
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  4. #4
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    You guys rock! Thank you so much for the speedy response and detailed steps.

    When you turned

    (1-(0.5+x)) into (0.5-x)

    does that refer to a special rule? The 1 is meaningless? Why didn't 0.5 become negative as well as x?
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  5. #5
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by jello View Post
    You guys rock! Thank you so much for the speedy response and detailed steps.

    When you turned

    (1-(0.5+x)) into (0.5-x)

    does that refer to a special rule? The 1 is meaningless? Why didn't 0.5 become negative as well as x?
    1-(0.5+x) = 1-0.5-x

    As 1-0.5 = 0.5 that is why it's positive
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  6. #6
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    AAAHHH dunce of the day for me!

    Thanks again everyone.
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