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Math Help - Absolute Value Equations

  1. #1
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    Absolute Value Equations

    It's final exam week. Our teacher is reviewing the material given in class this long semester. However, there are questions that he did not have time to go over but that might be on the final.

    Here is a sample:

    Solve for x.

    |x - 3| = |3x + 2| - 1

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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    It's final exam week. Our teacher is reviewing the material given in class this long semester. However, there are questions that he did not have time to go over but that might be on the final.

    Here is a sample:

    Solve for x.

    |x - 3| = |3x + 2| - 1
    Hello Magentarita,

    Case 1:

    x-3=(3x+2)-1

    x=-2

    This solution does not work with the original equation, so throw it out.

    Case 2:

    x-3=-(3x+2)-1

    x=0

    This solution does not work with the original equation, so throw it out.

    Case 3:

    -(x-3)=(3x+2)-1

    \boxed{x=\frac{1}{2}}

    This solution works, so keep it.

    Case 4:

    -(x-3)=-(3x+2)-1

    \boxed{x=-3}

    This solution works, so keep it.


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  3. #3
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    4 cases....

    Quote Originally Posted by masters View Post
    Hello Magentarita,

    Case 1:

    x-3=(3x+2)-1

    x=-2

    This solution does not work with the original equation, so throw it out.

    Case 2:

    x-3=-(3x+2)-1

    x=0

    This solution does not work with the original equation, so throw it out.

    Case 3:

    -(x-3)=(3x+2)-1

    \boxed{x=\frac{1}{2}}

    This solution works, so keep it.

    Case 4:

    -(x-3)=-(3x+2)-1

    \boxed{x=-3}

    This solution works, so keep it.

    I had no idea there were 4 cases.

    Thanks
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