Results 1 to 4 of 4

Math Help - Absolute Value Equations

  1. #1
    Banned
    Joined
    Sep 2008
    Posts
    47

    Absolute Value Equations

    Could someone please tell me how to solve the following without graphing?

    (1) |x+4|+|x-7|=|2x-1|

    (2) |x-|x-1||=\lfloor x \rfloor (Greatest integer function of x)

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2008
    Posts
    3
    Quote Originally Posted by Winding Function View Post
    Could someone please tell me how to solve the following without graphing?

    (1) |x+4|+|x-7|=|2x-1|

    (2) |x-|x-1||=\lfloor x \rfloor (Greatest integer function of x)

    Thanks in advance!
    For number (1) if you state the boundaries for what the absolute value signs would do to the terms you can solve it as a simple algebraic equation.

    For example: |x-7| take away the absolute value signs and state that it is only true for positive real numbers x-7 > or equal to 0

    |x+4| is just x+4 because the absolute value sign doesn't affect positive real numbers.

    I hope this was helpful
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Sep 2008
    Posts
    47
    Um, the problem didn't specify any boundaries. Could someone please show me how to solve the equations? Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    For x \geq 7:

    |x + 4| + |x - 7| = |2x - 1| is equivalent to

    x + 4 + x - 7 = 2x - 1
    2x - 3 = 2x - 1
    which is impossible.

    For 0.5 \leq x < 7:

    |x + 4| + |x - 7| = |2x - 1| is equivalent to

    x + 4 + 7 - x = 2x - 1
    11 = 2x - 1
    12 = 2x
    x = 6
    and that's one solution.

    For -4 \leq x < 0.5:

    |x + 4| + |x - 7| = |2x - 1| is equivalent to

    x + 4 + 7 - x = 1 - 2x
    11 = 1 - 2x
    10 = -2x
    x = -5
    but this solution is not in the correct domain.

    For x < -4:

    |x + 4| + |x - 7| = |2x - 1| is equivalent to

    -x - 4 + 7 - x = 1 - 2x
    -2x + 3 = -2x + 1
    which is impossible.

    Hence, the one solution to this equation is x = 6.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: September 15th 2011, 04:34 AM
  2. Absolute Value Equations
    Posted in the Algebra Forum
    Replies: 8
    Last Post: September 5th 2011, 12:10 PM
  3. absolute value equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 31st 2009, 10:42 PM
  4. Absolute Value Equations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 21st 2008, 08:06 PM
  5. Absolute Value Equations
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 5th 2008, 02:45 PM

Search Tags


/mathhelpforum @mathhelpforum