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Math Help - What am I doing wrong?

  1. #1
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    What am I doing wrong?

    What am I doing wrong?

    |2x+1|<|x+3| Solve for x.

    So the correct answer is -4/3<x<2 based on my deductions. But my problem is my solution generates more answers.

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

    1) 2x+1<x+3 => x<2
    2) 2x+1<-(x+3) => x<-4/3
    3) -(2x+1)<(x+3) =>x>-4/3
    4) -(2x+1)<-(x+3) => x>2


    What am I doing wrong in the solution to get 2), 4) as wrong answers. I know I am probably having a brain fart and missing something obvious.

    Thanks in advance for your help.
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  2. #2
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    Re: What am I doing wrong?

    Do not double post!
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  3. #3
    Senior Member MacstersUndead's Avatar
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    Re: What am I doing wrong?

    For this problem, find the critical points of this equation and drop the signs for the particular ranges.

    In this case, it's when 2x+1 = 0 and x+3 = 0, so x= -1/2 and -3

    When x< -3, 2x+1 is negative and so is x+3
    Hence on the condition that x< -3, -(2x+1) < -(x+3) if and only if 2x+1 > x+3 if and only if x>2

    Does there exist solutions with x<-3 and x>2?

    Repeat the same process for intervals (-3,-1/2), (-1/2, positive infinity). When solving the inequality the possible solution set intersected the interval in which the inequality is valid, will give you your solution
    Last edited by MacstersUndead; November 24th 2012 at 12:06 AM.
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  4. #4
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    Re: What am I doing wrong?

    First time post. Thought I posted in the wrong area.
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  5. #5
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    Re: What am I doing wrong?

    If that's the case, you just report your post and tell them what happened, the mods will move it for you.
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