Results 1 to 2 of 2

Math Help - Inequality with absolute values

  1. #1
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Smile Inequality with absolute values

    Solve for
    |x(x+1)| < |x +4|

    [x(x+1)] 2 < (x+4)2
    [x(x+1)] 2 (x+4)2 < 0
    [x (x+1)
    (x+4)] [x (x+1) + (x+4)] < 0
    (
    x2 + x – x – 4) (x2 + x + x + 4) < 0
    (x2 4) (x2 + 2x + 4) < 0

    the product of two factors is negative since it is less than (<) zero (0).

    and
    x2 + 2x + 4 = x2 + 2x + 1 + 3
    =
    (x + 1)2 + 3 then it is positive.

    then (x2 4) is negative.
    Finally:
    x2 4 < 0
    x2 < 4
    take the sq. root on both sides, then
    |x| < 2 Q.E.D





    Follow Math Help Forum on Facebook and Google+

  2. #2
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2
    [x(x+1)] ^2 < (x+4)^2 this has to be like this... i don't know how to make or raise the 2 as exponent. please understand please help me rewrite the posted and solved problem

    [x(x+1)]^ 2 < (x+4)^2
    [x(x+1)] ^2 – (x+4)^2 < 0
    [x (x+1) – (x+4)] [x (x+1) + (x+4)] < 0
    (x^2 + x – x – 4) (x^2 + x + x + 4) < 0
    (x^2 – 4) (x^2 + 2x + 4) < 0

    the product of two factors is negative since it is less than (<) zero (0).

    and x^2 + 2x + 4 = x^2 + 2x + 1 + 3
    = (x + 1)^2 + 3 then it is positive.

    then (x^2 – 4) is negative.
    Finally:
    x^2 – 4 < 0
    x^2 < 4
    take the sq. root on both sides, then
    |x| < 2 Q.E.D
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 7th 2011, 08:11 AM
  2. Inequality with absolute values
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 15th 2010, 09:35 AM
  3. sketch an inequality with absolute values?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 23rd 2009, 07:02 PM
  4. inequality with absolute values
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 7th 2009, 07:39 AM
  5. Replies: 5
    Last Post: September 6th 2008, 09:38 PM

/mathhelpforum @mathhelpforum