Results 1 to 3 of 3

Math Help - Inequalities with a variable in the denominator

  1. #1
    Member Chokfull's Avatar
    Joined
    May 2009
    From
    Neverland
    Posts
    108
    Thanks
    1

    Inequalities with a variable in the denominator

    I'm past this, but couldn't remember the rule....I have
    <br />
        \frac {5} {(x+1)^3} < N<br />
    Then there is a rule for solving this.... You can't multiply both sides by (x+1)^3,because you don't know if x is negative or positive. The book says you should get
    <br />
       {\sqrt [3]{5/|N|}}<br />
    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by Chokfull View Post
    I'm past this, but couldn't remember the rule....I have
    <br />
        \frac {5} {(x+1)^3} < N<br />
    Then there is a rule for solving this.... You can't multiply both sides by (x+1)^3,because you don't know if x is negative or positive. The book says you should get
    <br />
       {\sqrt [3]{5/|N|}}<br />
    Thanks!
    With these types of equalities you have a couple of chouces.

    As you said you cannot multiply both sides by (x+1)^3, however you can multiply both by (x+1)^6, as you know this is a positive number.

    You can also make both sides into fractions and add or subtract to rearrange.

    For example,  \frac {5} {(x+1)^3} <\frac{N(x+1)^3}{(x+1)^3}, leading to \frac {5} {(x+1)^3} - \frac{N(x+1)^3}{(x+1)^3}<0

    Can you solve this from here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Chokfull's Avatar
    Joined
    May 2009
    From
    Neverland
    Posts
    108
    Thanks
    1
    Quote Originally Posted by craig View Post
    With these types of equalities you have a couple of chouces.

    As you said you cannot multiply both sides by (x+1)^3, however you can multiply both by (x+1)^6, as you know this is a positive number.

    You can also make both sides into fractions and add or subtract to rearrange.

    For example,  \frac {5} {(x+1)^3} <\frac{N(x+1)^3}{(x+1)^3}, leading to \frac {5} {(x+1)^3} - \frac{N(x+1)^3}{(x+1)^3}<0

    Can you solve this from here?
    OK, but how does that get an absolute value? I'll fiddle with it for now but don't see how it gets {\sqrt [3]{5/|N|}}<br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: July 16th 2009, 03:45 PM
  2. Replies: 2
    Last Post: December 17th 2008, 02:10 PM
  3. Inequalities with variable in denominator
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 25th 2008, 12:07 PM
  4. variable in denominator
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 10th 2007, 02:21 PM
  5. variable in the numerator and denominator
    Posted in the Math Topics Forum
    Replies: 8
    Last Post: October 18th 2006, 10:29 AM

Search Tags


/mathhelpforum @mathhelpforum