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Math Help - How to solve this inequality?

  1. #1
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    How to solve this inequality?

    abs((2x-1)/(x-1)) = 3.

    I'm trying to figure out what to do and how to finish it since the absolute value is around both (2x+1) and (x-1).
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by AlphaRock View Post
    abs((2x-1)/(x-1)) = 3.

    I'm trying to figure out what to do and how to finish it since the absolute value is around both (2x+1) and (x-1).
    Hi AlphaRock,

    \left|\frac{2x-1}{x-1}\right|=3

    Let's consider case 1.

    \frac{2x-1}{x-1}=3

    2x-1=3(x-1)

    2x-1=3x-3

    \boxed{x=2}

    Check this solution in your original absolute value equation.

    Now consider case 2.

    \frac{2x-1}{x-1}=-3

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

    2x-1=-3x+3

    \boxed{x=\frac{4}{5}}

    Check this solution in your original absolute value equation.
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  3. #3
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    Quote Originally Posted by AlphaRock View Post
    abs((2x-1)/(x-1)) = 3.

    I'm trying to figure out what to do and how to finish it since the absolute value is around both (2x+1) and (x-1).
    Here is a second way.
    Solve: (2x-1)^2=9(x-1)^2
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  4. #4
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    You should, however, note that what you give is NOT an inequality, it is an equation.
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