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Double Inequality

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  • 16-01-2016 1:15pm
    #1
    Stanford
    Registered Users Posts: 1,178 ✭✭✭


    Could someone please help me with solving double inequalities such as this one.

    3x+4 < x2-6 < 9-2x

    Note that x2 means x squared.


    Any help appreciated

    G


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    #2
    pointywalnut
    Registered Users Posts: 63 ✭✭pointywalnut


    3x+4 <x^2-6 <9-2x

    Solve the first inequality 3x+4 <x^2-6 by setting both sides as being equal
    3x+4 =x^2-6
    x^2-3x-10=0
    Using the formula for a quadratic equation x=(-b±√(b^2-4ac))/2a
    Gives us x = -2 and x = 5.
    By inspection the first inequality 3x+4 <x^2-6 is not true for the range -2 =< x <= 5

    Solve the second inequality x^2-6 <9-2x by setting both sides as being equal
    x^2-6 <9-2x
    x^2 + 2x-15=0
    Gives us x = -5 and x = 3.

    By inspection the second inequality is true in the range -5 < x < 3
    By removing the range where the first inequality is not true, from the range where the second inequality is true, leaves us with the range where both inequalities are true -5 < x < -2


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