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Math Help - Solving inequalities

  1. #1
    Junior Member
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    Solving inequalities

    How would I go about solving
    (1/x) + 4 < 2/x?


    Any help would be greatly appreciated!!
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  2. #2
    Super Member
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    Quote Originally Posted by Random-Hero- View Post
    How would I go about solving
    (1/x) + 4 < 2/x?


    Any help would be greatly appreciated!!
     \frac{1}{x} + 4 < \frac{2}{x}

    Subtract  \frac{2}{x} from both sides!

     \frac{1}{x} + 4 - \frac{2}{x} < 0

    Subtract 4 from both sides!

     \frac{1}{x}  - \frac{2}{x} < -4

    Now you have to re-write the LHS as a single fraction, which is easy since they have the same denominator!

     \frac{1-2}{x}   < -4

     \frac{-1}{x}   < -4

    Now if you multiply through by negative 1, you'll get a nicer expression, but remember that when you multiply through by negative 1, the direction of the inequality changes!

     \frac{1}{x}   > 4

    Can you draw any conclusions from this?
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  3. #3
    Member Last_Singularity's Avatar
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    Quote Originally Posted by Random-Hero- View Post
    How would I go about solving
    (1/x) + 4 < 2/x?


    Any help would be greatly appreciated!!
    I recommend these steps:

    1. Rewrite 4 as 4x/x
    2. Combine the two terms on the left hand side
    3. Cancel out the x terms in the denominator
    4. Subtract 1 from both sides
    5. Divide by 4 on both sides

    Assuming that x is nonzero, of course.
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