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Math Help - Subject of a linear equation

  1. #1
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    Subject of a linear equation

    Rearrange the formula so that the pronumeral written in square brackets is the subject.

    c = 7 + 2d [d]
    /
    5 - 3d


    Do you need to multiply 5 - 3d to the left side so that, c(5 - 3d) = 7 + 2d?

    If so I ended up with 5c - 3cd = 7 + 2d
    -5c -5c
    -3cd = 7 + 2d - 5c

    I am not sure what to do from here. Could you please help me?

    Thanks a lot.
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  2. #2
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    Quote Originally Posted by stellina_91 View Post
    Rearrange the formula so that the pronumeral written in square brackets is the subject.

    c = 7 + 2d [d]
    /
    5 - 3d


    ...
    I assume that you want to solve for d:

    c = \frac{7+2d}{5-3d} ......... get rid of the denominator by multiplying by (5 - 3d):

    c(5 - 3d) = 7+2d ......... expand the bracket:

    5c - 3cd = 7 + 2d ......... collect all terms containing d at the RHS, the other at the LHS:

    5c - 7 = 2d + 3cd ......... factor out d:

    5c - 7 = (2 + 3c) d ......... divide both sides by the bracket:

    \frac{5c-7}{2+3c} = d ......... that's it!

    I've done this problem extensively so that you have an example to do all similar questions.
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  3. #3
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    Thank you so much for your help, it's greatly appreciated!!!
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