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March 25, 2017

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For this inequality

3x^(2) - 2x -1 > or equal 0

I get x=1 , x=-1/3

would the solution set become
{x|1 < x < -1/3}

I wasn't sure about the sign, if it should be greater than or equal to .

  • Math - ,

    3x^2 - 2x - 1 >= 0,

    Factor using the A*C Method:
    A * C = 3 * -1 = -3 = 1 * -3,
    3x^2 + (x -3x) - 1 >= 0,
    (3x^2 - 3x) + (x - 1) >= 0,
    3x(x - 1) + (x - 1) >= 0,
    (x - 1) (3x + 1) >= 0,

    x - 1 >= 0,
    x >= 1.

    3x + 1 >= 0,
    3x >= -1,
    x >= -1/3.

    Solution Set: x >= 1, and x >= -1/3.


    This is not a compound inequality; therefore, your last step does
    not apply.

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