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Math Help - solving this linear equation

  1. #1
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    solving this linear equation

    Solve for x in terms of a and b

    2a + 3(x-2) = ax + b
    ---
    3

    ^^( that's 2a over 3)

    I know it's probably simple but I can't get it!
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Larianne View Post
    Solve for x in terms of a and b

    2a + 3(x-2) = ax + b
    ---
    3

    ^^( that's 2a over 3)

    I know it's probably simple but I can't get it!
    Hi Larianne,

    It's only simple for those who already know how to do it.

    \frac{2a}{3}+3(x-2)=ax+b

    \frac{2a}{3}+3x-6=ax+b

    Multiply through by 3.

    2a+9x-18=3ax+3b

    Group x terms together.

    9x-3ax=3b-2a+18

    Factor out a 3x on the left.

    3x(3-a)=3b-2a+18

    Divide both sides by 3(3-a).

    x=\frac{3b-2a+18}{3(3-a)}
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  3. #3
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    Thank Masters!

    So I can't get x as a 'whole' number? That's what I was having trouble with.

    Larianne.
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by Larianne View Post
    Thank Masters!

    So I can't get x as a 'whole' number? That's what I was having trouble with.

    Larianne.
    You're dealing with 'literals' here. This means your answer will not be a number. Both a and b are unknown variables at this time, so we just solve for whichever variable is required. It's like converting formulas like this:

    d=rt Distance = rate X time

    r=\frac{d}{t} Rate = distance divided by time

    t=\frac{d}{r} Time = distance divided by rate.
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