Results 1 to 5 of 5

Math Help - Absolute Value

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    3

    Absolute Value

    solve
    |x-1|=1-x.

    i got it down to x=1 but it the solution can also be any number between 0 and 1. help???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    First of all we have the condition 1-x\geq 0 (because the left side is \geq 0). So, x\leq 1.
    But, for x\leq 1 we have |x-1|=1-x.
    So, the inequality stands for all x\in(-\infty,1].
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Quote Originally Posted by scheuerman View Post
    solve
    |x-1|=1-x.

    i got it down to x=1 but it the solution can also be any number between 0 and 1. help???
    You have only to understand this concept:

    If x >= 0, then |x| = x -- The absolute value does nothing to a nonnegative value.

    If x < 0, then |x| = -x -- Example, |-3| = -(-3) = 3

    So, you have

    |x-1|

    For x-1 >= 0, or x >= 1, |x-1| = x-1. Solve x-1 = 1-x, but ONLY for x >= 1

    For x-1 < 0, or x < 1, |x-1| = -(x-1) = 1-x. Solve 1-x = 1-x, but ONLY for x < 1

    Let's see what you get.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2007
    Posts
    3
    Thank you guys soo much... but i still really dont get it...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by scheuerman View Post
    Thank you guys soo much... but i still really dont get it...
    |x|=x if x\geq 0 and |x|=-x is x<0 by definition.

    Given |x-1| = |y| where y=x-1. We have |y| = y if y\geq 0 meaning |x-1| = x-1 if x-1\geq 0 so this means |x-1|=x-1 if x\geq 1.

    Similaryl |x-1|=1-x if x<1.
    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. Replies: 8
    Last Post: May 23rd 2010, 11:59 PM
  3. finding absolute maximum and absolute minimum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2009, 05:22 PM
  4. Replies: 2
    Last Post: November 8th 2009, 02:52 PM
  5. Find the absolute maximum and absolute minimum
    Posted in the Calculus Forum
    Replies: 5
    Last Post: December 12th 2008, 10:46 AM

Search Tags


/mathhelpforum @mathhelpforum