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Math Help - Solve the following inequality

  1. #1
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    Post Solve the following inequality

    (3a+7)/(a+4) >= 0

    I forgot the step to solve the problem , please help me !!!
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  2. #2
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    Quote Originally Posted by hoanghai549 View Post
    (3a+7)/(a+4) >= 0
    You want to insure that both of 3a+7\ge0~\&~a+4>0 are true
    or both 3a+7\le0~\&~a+4<0 are true.
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  3. #3
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    So It means I have to solve the two above conditions or just use the one thing ?
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  4. #4
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    Quote Originally Posted by hoanghai549 View Post
    So It means I have to solve the two above conditions or just use the one thing ?
    There will be two different intervals in the solution set.
    So solve both and unite.
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  5. #5
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    nice thanks for your help
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  6. #6
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    deleted
    Last edited by Archie Meade; February 20th 2011 at 04:07 PM.
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  7. #7
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    Quote Originally Posted by hoanghai549 View Post
    (3a+7)/(a+4) >= 0
    Look at the numerator and the denominator.
    If both have the same sign then the inequality is true.
    It is easy to see that if a<-4 then both are negative.
    If a\ge -\frac{7}{3} then both are non-negative.

    Write the solution set as  (-\infty,-4)\cup\left[-\frac{7}{3},\infty\right).

    There is no complicated calculation necessary.
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