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Solving an absolut-valued function

  1. Dec 12, 2011 #1
    1. The problem statement, all variables and given/known data

    I have an abs-function |x-4|*x -x = 0

    which I need to solve.


    3. The attempt at a solution

    Do I need to re-arrange so I get

    |x-4| = x/x = 1


    thus we have x-4 = -1 or x-4 = 1.

    Hence x = 3 or x = 5 ?
     
  2. jcsd
  3. Dec 12, 2011 #2

    Dick

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    You unwisely divided by x. You can only do that if x is nonzero. You are missing a possible value for x.
     
  4. Dec 12, 2011 #3
    well in the assigment x belongs to R.

    But how do I obtain the final value of x? I am lost here. Any way to remove the abs value ?
     
  5. Dec 12, 2011 #4
    And doesn't R contain 0?
     
  6. Dec 12, 2011 #5
    it most certainly does, but what do I do with the equation to obtain the final and third solution?
     
  7. Dec 12, 2011 #6

    Dick

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    The cleanest way is to factor it into x*(|x-4|-1)=0. How can the product of two numbers be zero?
     
  8. Dec 12, 2011 #7
    split x*(l x-4 l -1)=0 into two equations. That should help you even more.
     
  9. Dec 12, 2011 #8
    I know then x is either zero or x is found by solving |x-4|-1 = 0

    cool, thanks !
     
  10. Dec 12, 2011 #9
    Great !! And what are the values?
     
  11. Dec 12, 2011 #10
    x = 0 or x = 3 og x = 5?
     
  12. Dec 12, 2011 #11
    Nice job!
     
  13. Dec 12, 2011 #12

    HallsofIvy

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    Why the question mark? (In both this and your original post.)

    What do you get if you put one of those numbers into the original equation?
     
  14. Dec 13, 2011 #13
    They mean nothing. Simply placed them in the wrong place.
     
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