Which are solutions of the equation 4×2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4

Question

Which are solutions of the equation 4×2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4

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    0
    2021-09-06T07:46:30+00:00

    Answer:

    Given the equation: 4x^2-7x = 3x+24

    rewrite the above equation as: 4x^2-7x-3x-24=0

    Like terms are those whose variables are same.

    Combine like terms :

    4x^2-10x-24=0 ….[1]

    Now, to solve the above quadratic equation:

    For quadratic equation: ax^2+bx+c=0 where a,b, and c are constant.

    then the solutions are:  

    x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}              …[2]

    in equation [1], the values of a= 4, b=-10 and c= -24.

    then, by putting these in the [2] we get,

    x_{1,2}=\frac{-(-10)\pm\sqrt{(-10)^2-4(4)(-24)}}{2\cdot 4}

    On solving we get,  the solutions are:

    x_{1}=-1.5=-\frac{3}{2} and x_{2}=4

    Check :

    By substituting the values of x= -1.5 and x=4 in equation  4x^2-7x = 3x+24 we have;

    for x=-1.5

    4x^2-7x=3x+24

    4(-1.5)^2-7(-1.5)=3(-1.5)+24

    4(2.25)+10.5=-4.5+24

    9+10.5=19.5

    19.5=19.

    Similarly, for x=4

    4x^2-7x=3x+24

    4(4)^2-7(4)=3(4)+24

    4(16)-28=12+24

    64-28=36

    36=36

    Therefore, the only solution of the equation  4x^2-7x = 3x+24  is, x= -1.5 and x=4

    0
    2021-09-06T07:46:53+00:00

    4×2 – 7x = 3x + 24
     First we rewrite the quadratic equation:
     4×2 – 7x – 3x – 24 = 0
     4×2 – 10x – 24 = 0
     The solutions to the quadratic equation in this case are:
     x1 = 4
     x2 = -1.5
     Answer:
     x = -3/2
     x = 4

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