Results 1 to 8 of 8

Math Help - [SOLVED] help with this inequality

  1. #1
    Member
    Joined
    Jan 2009
    From
    USA
    Posts
    123

    [SOLVED] help with this inequality

    Solve the following inequality. Write the answer in interval notation.



    I got:

    (-inifinity, 23/5)U(4,infinity)

    && got it wrong
    does anyone know how to figure this out
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    How did you arrive at your answer? You added the 6 to the left-hand side, converted to the common denominator, combined the two fractions into one, found the zeroes of the numerator and denominator, tested the sign on each interval, and... then what?

    Please be complete. Thank you!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    From
    USA
    Posts
    123
    huh?

    i was left with

    (-5x-23)/(x-4)

    which was where i got my answer that is wrong
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Feb 2009
    Posts
    92
    is it all real numbers?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2009
    From
    USA
    Posts
    123
    no it is not all real numbers

    because i kno by (-5x-23)/x-4

    that the x in the denominator is 4.

    but i am not sure if that fraction is right at all though
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2009
    Posts
    92
    Quote Originally Posted by lsnyder View Post
    no it is not all real numbers

    because i kno by (-5x-23)/x-4

    that the x in the denominator is 4.

    but i am not sure if that fraction is right at all though
    oops, isnt it
    25/7<=x<4

    x-1/x-4 <= -6
    =x-1<= -6x+24
    =7x-1<=24
    =7x<=25
    x<=25/7

    and

    x-1/x-4 <= -6
    x-4<=-6x+24
    7x<=28
    x<=4
    (i'm not sure why it's not equal to 4. When I worked it out on a calculator, it came up as x<4)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, lsnyder!

    Solve the following inequality. Write the answer in interval notation.
    . . . \frac{x-1}{x-4} \:\leq\:-6

    I got: . \left(-\infty, \tfrac{23}{5}\right) \cup (4, \infty) . . . and got it wrong.

    Does anyone know how to figure this out ?

    After several false starts, I was forced to graph the function.


    We have: . y \:=\:\frac{x-1}{x-4}

    . . When is it below y = -6 ?
    Code:
              |
              |         :*
              |         :
              |         : *
              |         :   *
              |         :       *
              |         :               *
       - - - 1+ - - - - : - - - - - - - - -
        *     |         :
              *         :4
      --------+---*-----+-------------------- 
              |      *  :
              |       o :
              |         :
              |        o:
              |         :

    The function has a vertical asymptote x = 4 and horizontal asymptote y = 1.


    We see that for values of x slightly below 4, the graph is below  y = -6

    If the function equals -6, we have: . \frac{x-1}{x-4} \:=\:-6 \quad\Rightarrow\quad x \:=\:\frac{25}{7}

    Therefore, the interval is: . \left[\frac{25}{7},\,4\right)

    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Feb 2009
    Posts
    92
    why is it not equal to 4?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Simple inequality.
    Posted in the Algebra Forum
    Replies: 0
    Last Post: April 6th 2010, 11:36 PM
  2. [SOLVED] Triangle Inequality
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 10th 2010, 02:24 PM
  3. [SOLVED] Inequality
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 16th 2009, 02:57 PM
  4. [SOLVED] Inequality
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 30th 2009, 01:46 AM
  5. [SOLVED] Inequality
    Posted in the Calculus Forum
    Replies: 10
    Last Post: August 9th 2008, 07:03 AM

Search Tags


/mathhelpforum @mathhelpforum