Results 1 to 4 of 4

Math Help - Help Inequalities with absolute

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Help Inequalities with absolute

    8.) /(3-2x) divided by (2+x)/ < 4

    / means absolute value
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123

    graph solution only

    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    8.) /(3-2x) divided by (2+x)/ < 4

    / means absolute value
    Hi,

    I haven't much time, therefore I attach a diagram so you can get graphically a solution. (I only guess: x < (-11)/2 or x > (-5)/6 )

    If I find some time today the algebraic solution will follow.

    tschüss

    EB
    Attached Thumbnails Attached Thumbnails Help Inequalities with absolute-abs_glg1.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    8.) /(3-2x) divided by (2+x)/ < 4

    / means absolute value

    |(3-2x)/(2+x)|<4,

    means:

    -4 < (3-2x)/(2+x) < 4

    Now its a good idea to sketch (3-2x)/(2+x), (see attachment)

    Now solving (3-2x)/(2+x) = -4, gives x=-11/2 and so

    -4 < (3-2x)/(2+x)

    when x<-11/2, and alsowhen x>-2 (where the vertical asymtote is).

    Now solve (3-2x)/(2+x) = 4, gives x=-5/6 and so:

    (3-2x)/(2+x) < 4 for x>-5/6m and also when x<-2.

    Combining these we see that both inequalities are satisfied when

    x<-11/2 or x>-5/6.

    RonL
    Attached Thumbnails Attached Thumbnails Help Inequalities with absolute-gash.jpg  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    8.) /(3-2x) divided by (2+x)/ < 4

    / means absolute value
    Hi,

    here I am again. You already know the solution of your problem, because CaptBlack has done it. I promised to come back with a solution. So here are my two cents:

    abs((3-2x)/(2+x)) < 4 , x ≠ -2

    First remove the absolute value:

    A) (3-2x)/(2+x) > -4 and B) (3-2x)/(2+x) < 4

    A) Multiply by the denominator. There are 2 possibilities:

    A1) 3-2x > -4*(2+x) and x > -2
    3 - 2x > -8 - 4x
    11 > -2x
    x < (-11)/2 and x > -2 that means: no solution

    A2) 3-2x < -4*(2+x) and x < - 2
    3 - 2x < -8 - 4x
    11 < -2x
    x < (-11)/2 and x < -2 that means: this set belongs to the solution


    B) Multiply by the denominator. There are 2 possibilities:

    B1) 3-2x < 4*(2+x) and x > -2
    3 - 2x < 8 + 4x
    -5 < 6x
    x > (-5)/6 and x > -2 that means: this set belongs to the solution

    B2) 3-2x < 4*(2+x) and x < -2
    3 - 2x < 8 + 4x
    -5 < 6x
    x > (-5)/6 and x < -2 that means: no solution

    tschüss

    EB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Absolute value Inequalities 2
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 17th 2011, 03:24 PM
  2. Absolute Value Inequalities
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 22nd 2011, 06:55 AM
  3. Absolute Inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 29th 2008, 05:35 PM
  4. Absolute Value Inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 19th 2008, 03:46 PM
  5. Absolute Inequalities
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 12th 2007, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum