Results 1 to 4 of 4

Math Help - Module Equations.

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    1

    Module Equations.

    Greetings,

    I'm new to this forum and I require urgent help. I was gone from my country for 2 weeks and meanwhile my class revised the math stuff from previous year. Can anyone help?

    |x-3|=-1

    |x+4|=2

    |x|=2+x

    ||x|-2|=2

    Sorry if my english isn't pleasing, it's not my first language. Thanks indeed.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2011
    Posts
    13

    Re: Module Equations.

    Sure. I'll refer to these "modules" as "absolute values".

    The key thing to remember is that, for instance,

    |3| = 3 and
    |-3| = 3

    In other words, if the number inside the lines is negative, it becomes positive, but if it's positive, it stays positive. So each of these is two problems in one.

    Your first problem is a trick question; an absolute value cannot be negative.

    Your second problem, |x+4|=2, can be solved. If x+4 is positive, then its absolute value remains x+4, so we have:
    x+4=2

    x=-2

    However, if x+4 is negative, then its absolute value will become positive. This means that it is multiplied by -1. So we have

    -(x+4)=

    -x-4=2

    -x=6

    x=-6

    Thus the two solutions for the second problem are -2 and -6.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2011
    Posts
    13

    Re: Module Equations.

    The third problem works in the same way, but with a twist.

    |x|=2+x

    If x is positive, then its absolute value is also positive. So we have:

    x=2+x, and by subtracting x from both sides we get
    0=2, which is absurd. Thus there is no answer that makes the equation true if x is positive.

    Suppose x was negative. Then its absolute value would be positive, which means it would be -x. In that case,

    -x=2+x

    -2x=2

    x=-1

    So there is only one solution in this case: -1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2011
    Posts
    13

    Re: Module Equations.

    The fourth problem involves this process used twice (an absolute value within an absolute value)

    ----

    Firstly, we take the innermost absolute value. If x is positive, then we have:

    |x-2|=2

    From here, if x-2 is positive, we have:

    x-2=2

    x=4

    And if x-2 is negative, then -(x-2)=-x+2 is positive, so

    -x+2=2

    x=0.
    ---------

    Now suppose x is negative. Then -x is positive. In that case,

    |-x-2|=2

    If -x-2 is positive, we have:

    -x-2=2

    -x=4

    x=-4

    If -x-2 is negative, then -(-x-2)=x+2 is positive, and we have:

    x+2=2

    x=0

    This gets us through all the possibilities. Thus the possible answers are -4, 0, and 4.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: November 30th 2011, 02:50 AM
  2. Module Help
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 5th 2011, 03:13 PM
  3. About some module over a DVR
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 13th 2011, 12:48 AM
  4. k[x]-module
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 20th 2010, 03:03 PM
  5. R-module
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 20th 2009, 10:14 AM

Search Tags


/mathhelpforum @mathhelpforum