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Math Help - How do you solve this inequality?

  1. #1
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    How do you solve this inequality?

    |1-x|<|2x-5|
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  2. #2
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    Re: How do you solve this inequality?

    Follow the same procedure I outlined in your last question.
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  3. #3
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    Re: How do you solve this inequality?

    Quote Originally Posted by Prove It View Post
    Follow the same procedure I outlined in your last question.
    I did. It got me more confused. Can you explain this one too? Maybe I'll get it. I'm not used to the way you handled it. BTW the answer I get is x<2 or x>4.
    Last edited by aroe; November 24th 2012 at 12:44 AM.
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  4. #4
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    Re: How do you solve this inequality?

    using MarkFL2's clever approach, note that |a| = √(a2).

    so |1-x| < |2x-5| is the same as:

    √(1-x)2 < √(2x-5)2

    squaring both sides:

    (1-x)2 < (2x-5)2

    1-2x+x2 < 4x2-20x+25

    0 < 3x2-18x+24

    0 < x2-6x+8

    0 < (x-2)(x-4) <---for this to be true, both factors must be either both positive, or both negative.
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  5. #5
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    Re: How do you solve this inequality?

    Quote Originally Posted by Deveno View Post
    using MarkFL2's clever approach, note that |a| = √(a2).

    so |1-x| < |2x-5| is the same as:

    √(1-x)2 < √(2x-5)2

    squaring both sides:

    (1-x)2 < (2x-5)2

    1-2x+x2 < 4x2-20x+25

    0 < 3x2-18x+24

    0 < x2-6x+8

    0 < (x-2)(x-4) <---for this to be true, both factors must be either both positive, or both negative.
    That would mean the answer is x>4 or x<2 which is the same answer I get.
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  6. #6
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    Re: How do you solve this inequality?

    I still like the other method Proveit used. If he can solve it again that way that would be great.
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  7. #7
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    Re: How do you solve this inequality?

    I'm not going to do your work for you. You know the procedure, you can try it!
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  8. #8
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    Re: How do you solve this inequality?

    Sorry I miswrote the question it's actually
    |1-x|>|2x-5|

    And I can't find an answer for it.
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  9. #9
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    Re: How do you solve this inequality?

    Since you found:

    |1-x|<|2x-5|

    gives the solution (-\infty,2)\,\cup\,(4,\infty)

    then you may state:

    |1-x|>|2x-5|

    gives the solution (2,4)
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