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General question, inequalities and graphing

  1. Dec 19, 2007 #1
    [tex]x+|x|=y+|y|[/tex]

    so for x which in a sense will be the same for y

    x if x > 0
    -x if x < 0

    now does that only apply to my absolute x? or does it apply to both x and |x|?
     
  2. jcsd
  3. Dec 19, 2007 #2

    symbolipoint

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    You should consider four sets of conditions: both less than zero, both greater than zero, one less and other greater; the other greater and the one less. An obvious solution is in case x=y=0, but you should check the other four conditions.
     
  4. Dec 19, 2007 #3
    no i meant if x < 0, then does it become

    (-x) + (-x) or x + (-x)

    does the condition only apply to the absolute value? but i checked my SM, i couldn't resist any longer :p
     
  5. Dec 19, 2007 #4

    symbolipoint

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    Use a number line to justify this: but if x<0, then
    [tex] \[
    x + \left| x \right| = x + ( - x)
    \]
    [/tex]
     
  6. Dec 19, 2007 #5

    HallsofIvy

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    The trouble is you don't say what those two lines are EQUAL to. You should say "for x

    |x|= x if [itex]x\ge 0[/itex]
    |x|= -x if x< 0.

    Yes, of course, that applies only to the absolute value of x- it wouldn't make sense to say that x= -x! As symbolipoint said, you will have 4 cases to consider- the four quadrants- [itex]x\ge 0[/itex] and [itex]y\ge 0[/itex]; [itex]x\ge 0[/itex] and y< 0; x< 0 and [itex]y\ge 0[/itex]; x< 0 and y< 0.
     
  7. Dec 19, 2007 #6
    Thanks! Unfortunately, I have another :p
     
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