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Math Help - Solve for X - Rearrangement question

  1. #1
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    Solve for X - Rearrangement question

    Hi

    Can someone explain the thought process behind the rearrangement at the end for these two examples?

    <br />
d(a + 9x) = y<br />
    <br />
da + 9dx = y<br />
    <br />
9dx = y - da<br />

    <br />
x = \frac{y-da}{9d}<br />

    I can't see how you get from that to:

    <br />
x = \frac{1}{9}(\frac{y}{d} - a)<br />

    Same with this example:

    <br />
f(a + x) = y<br />
    <br />
fa + fx = y<br />
    <br />
fx = y - fa<br />

    <br />
x = \frac{y - fa}{f}<br />

    To this:

    <br />
x = \frac{y}{f} - a<br />

    Thanks
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by preid View Post
    Hi

    Can someone explain the thought process behind the rearrangement at the end for these two examples?

    <br />
d(a + 9x) = y<br />
    <br />
da + 9dx = y<br />
    <br />
9dx = y - da<br />

    <br />
x = \frac{y-da}{9d}<br />

    I can't see how you get from that to:

    Separate into difference of two fractions:

    {\color{red}x=\frac{y}{9d}-\frac{da}{9d}}

    {\color{red}x=\frac{1}{9}\left(\frac{y}{d}\right)-\frac{1}{9}\left(\frac{da}{d}\right)}

    Factor out 1/9

    {\color{red}\frac{1}{9}\left(\frac{y}{d}-\frac{da}{d}\right)}

    Cancel out the d in the last fraction and you have:

    <br />
x = \frac{1}{9}(\frac{y}{d} - a)<br />

    Same with this example:

    <br />
f(a + x) = y<br />
    <br />
fa + fx = y<br />
    <br />
fx = y - fa<br />

    <br />
x = \frac{y - fa}{f}<br />

    To this:

    <br />
x = \frac{y}{f} - a<br />

    Thanks
    ..
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