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Math Help - inequality

  1. #1
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    inequality

    x+1/3>=4/x

    I got the abswer as (3,+infinite) but according to my book the answer is different.
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  2. #2
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    Re: inequality

    If you multiply both sides by x to get rid of the denominator, you need to take into account 2 cases, one where x > 0 (and the inequality will keep the same sign) and one where x < 0 (and the inequality will reverse its sign).
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    Re: inequality

    It doesn't.It has 2 roots.
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    Re: inequality

    Quote Originally Posted by kastamonu View Post
    x+1/3>=4/x

    I got the abswer as (3,+infinite) but according to my book the answer is different.
    You can be pretty sure anything Prove It tells you is correct.

    $x + \dfrac 1 3 \geq \dfrac 4 x$

    if $x>0$ then

    $x^2+\dfrac x 3 - 4 \geq 0$

    but if $x<0$ then

    $x^2+\dfrac x 3 -4 \leq 0$

    you can go ahead and solve these under the 2 conditions
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  5. #5
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    Re: inequality

    first one is (-inf.,-5/3) u (2/3,+inf.)
    In the question it is asking how many natural numbers are there that satisfy this equation? By this solution it seems to be infinite.
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