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Math Help - Inequalities Problem

  1. #1
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    Wink Inequalities Problem

    I can't do this homework!

    How can i solve this?
    |2x-1| < 3-x

    Thank you for helping...
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Inequalities Problem

    Express |2x-1|=\begin{Bmatrix} 2x-1 & \mbox{ if }& x\geq 1/2\\-2x+1 & \mbox{ if }& x<1/2\end{matrix}

    Let us see what do you obtain (work your homework).
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  3. #3
    MHF Contributor
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    Re: Inequalities Problem

    Quote Originally Posted by chumchumy View Post
    I can't do this homework!

    How can i solve this?
    |2x-1| < 3-x

    Thank you for helping...
    You should know that if \displaystyle |X| < a then \displaystyle -a < X < a.

    So in your case \displaystyle |2x-1| < 3-x \implies -(3-x) < 2x-1 < 3-x
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