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Homework Help: Factoring something with absolute value

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to find where these intersect:
    y = |x|
    3y - x = 8

    2. Relevant equations



    3. The attempt at a solution

    I equate them:
    |x| = (1/3)x + (8/3)
    |x| - (1/3)x - (8/3) = 0
    |3x| - x - 8 = 0
    |2x| - 8 = 0
    |x| = 4

    Is that right?
    How do I get the other solution?
     
  2. jcsd
  3. Feb 1, 2010 #2

    Mark44

    Staff: Mentor

    The line below is wrong. |3x| - x = 2x if x >=0, but is equal to -4x if x < 0.
    Rewrite the line above as
    |3x| = x + 8

    Now get rid of the absolute values by writing two equations, one for x >= 0 and the other for x < 0. For example, if |a| = 2, then a = 2 or -a = 2.

    Look at the section in your book that defines absolute values.

     
  4. Feb 1, 2010 #3
    Are there some general rules I should know? About when to do a case?
     
  5. Feb 1, 2010 #4

    Mark44

    Staff: Mentor

    Just this,
    |a| = b ==> a = b or -a = b
     
  6. Feb 1, 2010 #5
    Okay great thank you I understand now
     
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