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Math Help - unsure on the next step?

  1. #1
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    unsure on the next step?

    Rearrange the following equation to find x in terms of a and b in simplest form (assume that a =/-3b)

    the / should be through the = to show a is not equal to -3b

    Couldnot find the key for it sorry!

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

    3bx+9b^2=a^2-ax

    (3b-a)x=a^2-9b^2

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

    this is where i get unsure.

    I think then it becomes

    (a-3b)(a+3b)
    - ______________

    3b-a

    which then becomes

    x= -(a+b)

    which is x= a-b

    Are my workings out right or am I completley of the mark?

    Apologies for the way i may have presented my workings out still getting to grips with showing my workings out on a computer
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  2. #2
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    Re: unsure on the next step?

    You made some mistakes

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

    3bx+9b^2=a^2-ax

    Add "ax" to both sides

    3bx+ax+9b^2=a^2+ax-ax=a^2

    Subtract "9b^2" from both sides

    x(3b+a)+9b^2-9b^2=a^2-9b^2

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

    Now divide both sides by (3b+a) to get the expression for "x"

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

    and simplify the last line.

    As the denominator cannot be zero,
    the given condition is

    a\ne\ -3b
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  3. #3
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    Re: unsure on the next step?

    so would i be correct in saying x =(a-3b) so x =-a+3b
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  4. #4
    Super Member Quacky's Avatar
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    Re: unsure on the next step?

    Quote Originally Posted by Orlando View Post
    so would i be correct in saying x =(a-3b) so x =-a+3b
    x =(a-3b) does not imply x =-a+3b
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  5. #5
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    Re: unsure on the next step?

    Quote Originally Posted by Orlando View Post
    so would i be correct in saying x =(a-3b) so x =-a+3b
    If you had

    -x=(a-3b)

    then -(-x)=-(a-3b)

    x=-a-(-3b)
    x=3b-a

    But x=(a-3b) so x=a-3b
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