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Math Help - IM stuck on algebra!

  1. #1
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    Exclamation IM stuck on algebra!

    I have homework due tomorrow which I as usual forgot about and left till the last minute...its algebra which im hopeless at, any help would be much appreciated.

    1) -x < 4

    2) 12x > 2x^2

    3) x - 3 2x - 1
    ____ = _____

    x - 1 4x + 5

    4) 3(2x + 5)
    _________ = 6x + 1
    4

    5) find the x coordinates of the points of intersection of the two parabolas
    y = 3x^2 + 5x - 6 and y = -2x^2 - 3x + 18



    Any help wud be much appreciated
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  2. #2
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    Quote Originally Posted by Brownhash View Post
    I have homework due tomorrow which I as usual forgot about and left till the last minute...its algebra which im hopeless at, any help would be much appreciated.

    1) -x < 4

    2) 12x > 2x^2

    3) x - 3 2x - 1
    ____ = _____

    x - 1 4x + 5

    4) 3(2x + 5)
    _________ = 6x + 1
    4

    5) find the x coordinates of the points of intersection of the two parabolas
    y = 3x^2 + 5x - 6 and y = -2x^2 - 3x + 18



    Any help wud be much appreciated
    I'll post the solutions. If you can't follow them, say which steps don't make sense and I'll explain them...

    1. -x<4 gives 0<x+4 which means -4<x or x>-4

    2. 12x > 2x^2
    6x > x^2
    6>x if x\geq 0 else 6<x if x<0

    3. \frac{x-3}{x-1}=\frac{2x-1}{4x+5}
    (x-3)(4x+5)=(2x-1)(x-1)
    4x^2+5x-12x-15=2x^2-2x-x+1
    4x^2-7x-15=2x^2-3x+1
    2x^2-4x-16=0
    2(x^2-2x-8)=0
    x^2-2x-8=0
    (x-4)(x+2)=0
    x-4 = 0 or x+2=0
    x=4 or x=-2

    4. \frac{3(2x+5)}{4}=6x+1
    3(2x+5)=4(6x+1)
    6x+30=24x+4
    30-4=24x-6x
    26=18x
    \frac{26}{18}=x
    \frac{13}{9}=x

    5. Intersection points between functions occur when the functions are equal. Since they are both equal to y, they are equal to each other...

    3x^2 + 5x - 6 = -2x^2 - 3x + 18
    5x^2+8x-24=0

    x=\frac{-8\pm\sqrt{8^2-4\times5\times(-24)}}{2\times5} using the Quadratic Formula
    =\frac{-8\pm\sqrt{64+480}}{10}=\frac{-8\pm\sqrt{544}}{10}=\frac{-8\pm4\sqrt{34}}{10}=\frac{-4\pm2\sqrt{34}}{5}

    So x=\frac{-4+2\sqrt{34}}{5} or x=\frac{-4-2\sqrt{34}}{5}
    Last edited by Prove It; August 19th 2008 at 03:04 AM.
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  3. #3
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    Thankyou

    I understand them now thanks for the help.
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