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Absolute Values

  1. Feb 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Solve the given inequality by interpreting it as a statement about distances in the real line:

    |x-3| < 2|x|

    2. Relevant equations



    3. The attempt at a solution

    I have no clue what to do here and I do not understand the answer in the textbook

    Goes something like this..............
    x^2 - 6x + 9.....................Have no idea how they got that
    = (x-3)^2
    ...............and so forth
     
  2. jcsd
  3. Feb 20, 2014 #2
    There are two possibilities for x: either x is greater than or equal to 3, or x is less than 3.

    If x ≥ 3, what does the inequality look like (i.e. without the absolute value)?
     
  4. Feb 20, 2014 #3

    LCKurtz

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    Science Advisor
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    They used ##|a|<|b| \leftrightarrow a^2<b^2##.
     
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