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Math Help - Solving inequality with modulus

  1. #1
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    Solving inequality with modulus

    Solve the inequality (x+2)(x-3)>|2x-1|

    (x+2)(x-3)>2x-1 or (x+2)(x-3)<1-2x

    Solving the first inequality: x^2-x-6>2x-1

    x^2-3x-5>0

    x<-1.19 or x>4.19

    Solving the second inequality: x^2-x-6<1-2x

    x^2+x-7<0

    -3.19<x<2.19

    so, x<-1.19 or x>4.19 or -3.19<x<2.19

    But the answer is x<-3.19 or x>4.19

    Where did i go wrong? please advise, thanks!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Punch View Post
    Solve the inequality (x+2)(x-3)>|2x-1|

    (x+2)(x-3)>2x-1 or (x+2)(x-3)<1-2x

    It should be:

    (x+2)(x-3)>|2x-1|\Leftrightarrow

    \begin{Bmatrix} (x+2)(x-3)>2x-1 & \mbox{ if }& x\geq 1/2\\(x+2)(x-3)>1-2x & \mbox{if}& x<1/2\end{matrix}
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  3. #3
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    but how would that change my answer?
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  4. #4
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    You found x= -1.19 as a solution to (x+2)(x-3)> 2x-1 but |2x-1|= 2x-1 only if 2x-1>= 0 or x>= 1/2, as FernandoRevilla said. -1.19 is NOT greater than 1/2.
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