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Math Help - Absolute value equation

  1. #1
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    Post Absolute value equation

    If I have

    |3x-9|=|3-3x|

    I do not see how the solution can be = 2

    I would think the solution would be = {2,6}

    Can someone explain if I am correct or if the given solution was correct, and why? Thanks

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  2. #2
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    Quote Originally Posted by leoslick View Post
    If I have

    |3x-9|=|3-3x|

    I do not see how the solution can be = 2

    I would think the solution would be = {2,6}

    Can someone explain if I am correct or if the given solution was correct, and why? Thanks
    |3x-9| = |3-3x|

    3|x-3| = 3|1-x|

    |x-3| = |1-x|

    square both sides ...

    x^2 - 6x + 9 = 1 - 2x + x^2<br />

    8 = 4x

    2 = x
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  3. #3
    Super Member Bacterius's Avatar
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    Because absolute value turns any negative value into its opposite positive value.

    With 2, it would give :

    |3x - 9| = |3 - 3x|

    |3 \times 2 - 9| = |3 - 3 \times 2|

    |6 - 9| = |3 - 6|

    |-3| = |-3|

    3 = 3

    With 6, it would give :

    |3x - 9| = |3 - 3x|

    |3 \times 6 - 9| = |3 - 3 \times 6|

    |18 - 9| = |3 - 18|

    |-9| = |-15|

    9 \neq 15, so x = 6 is not a solution.
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