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March 30, 2017

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Solve the following inequality and write answer using interval notation. Please show all of your work.
2x-5/3x^4-x^3+275x-125>=0

  • algebra - ,

    Your casual use of parentheses makes me assume you mean

    (2x-5)/(3x^4 - x^3 + 275x - 125) >= 0
    let's try to factor the denominator. We get not much help.

    You sure you don't mean

    3x^4 - x^3 + 375x - 125?

    That would be

    x^3 (3x-1) + 125(3x-1)
    (x^3+125)(3x-1)
    (x+5)(x^2 - 25x + 25)(3x-1)

    Anyway, working with your original function, the denominator is positive when x < -4.54 or x > 0.45

    The numerator is positive when x > 2.5

    If you plot the points -4.54, 0.45, 2.5 on the number line, you will see

    on (-oo,4.54) we have +/- so y < 0
    on (-4.54,0.45) we have -/- so y > 0
    on (0.45,2.5) we have +/- so y < 0
    on (2.5,oo) we have +/+ so y > 0

    y>0 on [-4.54,0.45] U [2.5,oo)

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