algebra

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Solve the following inequality and write your answer using interval notation . Please show all your work
10^3 + 6x^2 - 90x - 54 < 0

  • algebra -

    I think you meant
    10x^3 + 6x^2 - 90x - 54 < 0 , divide by 2
    5x^3 + 3x^2 - 45x - 27 < 0
    x^2(5x+3) - 9(5x+3) < 0
    (5x+3)(x^2-9) < 0
    (5x+3)(x+3)(x-3) < 0
    critical values are x = -5/3, -3, and 3

    Test the expression for different values, one in each part of the domain.
    We don't have to find the actual value, just the sign of the answer
    let x = -5 , for x < -5/3
    - - - < 0 , that works
    let x = -2 , for between -5/3 and -3
    - + - > 0 , no good
    let x = 0 , for between -3 and 3
    + + - < 0 , that works
    let x = 10, for x > 3
    +++ > 0 , no good

    so x < -5/3 OR -3 < x < 3

    I will let you change that to the interval notation that you were taught. Personally I prefer the above notation.

  • algebra -

    Me too but it gets counted wrong in this format.

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