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Question:


catlover
Student
High School - 10th Grade

What does the variable x equal for the following proportion?

The equation is:

x-2/x+6 = x/2

Remember, you need to cross multiply and the dashes equal fraction bars. Please help!

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Posted by catlover on Tuesday May 26, 2009 at 4:07 PM and tagged with algebra, math.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    x-2/x+6=x/2 .  Multiplying by 2x both sides, we get

    2x^2-4+ 12x=x^2. Subtract x^2 from both sides to get,

    2x^2-x^2 -4 +12x =0 =>

    [x^2+12x]-4 =0=>

    [(x+6)^2-36] -4 = 0=>

    (x+6)^2 -40=0=>

    (x+6)^2 = 40=>

    x+6 = +sqrt(40)=2sqrt(10) or  x=-sqrt(40) = -2sqrt(10)

    Therefore,

    x= -6+2srt(10) =0.3246 nearly

    or

    x=-6-2sqrt(10) = -12.3246 nearly'


    NB:

    I do not recommend this which is wrong . But many people have a tendency to do this way by voluntarily imposing brackets as below:

    (x-2)/(x+6)  = x/2 . Mutiplying  by  2(x+6)

    2(x-2) = x(x+6)=>

    2x-4=x^2+6x=>

    0=x^2+6x-2x+4 =>

    0=x^2+4x+4   or  0 = (x+2)^2 =>

    x+2 = 0  or

    x=-2 is a double root.

    Looks nice and simple. But volunteering to impose a bracket like this change the given expression.

     

     

     

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    Posted by neela on Tuesday May 26, 2009 at 10:53 PM