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Infinate Value Problems

  1. Apr 11, 2005 #1
    Hi,

    I was wondering if anyone could help me with these infinate value questions that I really dont get... :uhh:

    stuff like this:

    |2x+4| = 16

    or

    |10x| + 5 = 40

    (i made these questions off the top of my head, so they might not work out properly and nicely)

    Thanks :smile:
     
  2. jcsd
  3. Apr 11, 2005 #2

    matt grime

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    Are you only looking for answers where x is a real number? Since there are only at most two answers.

    |y|= r if and only if y=r or y=-r.

    If you're talking abuot C or some other space, just say so and someone will explain what to do there.
     
  4. Apr 11, 2005 #3

    arildno

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    Dearly Missed

    You do mean "absolute value", right?
    The way to solve these questions is:
    1) Determine the different x-intervals in which the expression inside a given absolute value signs are positive or negative.
    For example, for your second case we have:
    [tex]10x<0\to{x}<0, 10x\geq0\to{x}\geq0[/tex]
    Hence, you have two distinct regions two consider: x less than 0 and x greater than (or equal to) zero.

    2) See what solutions exist, if any, on each region:
    In your second case:
    a)[tex]10x<0:[/tex]
    Here, 10x<0, so |10x|=-10x.
    Thus, we must check if we have actual solutions satisfying: -10x+5=40
    Rearranging terms, we get [tex]x=-3.5[/tex]
    Since -3.5<0, this represents a true solution, since x must be negative in this region.

    b)[tex]10x\geq0[/tex]
    Here, |10x|=10x, thus we must check if we have solutions of: 10x+5=40
    and we see that x=3.5 works.
    Get it?
    EDIT:
    If you are to find solutions where you have nummerous addends in the form of absolute values, just split up your analysis in the appropriate manner.
     
    Last edited: Apr 11, 2005
  5. Apr 11, 2005 #4
    thanks a bunch
     
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