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Math Help - Multiple absolute value inequality

  1. #1
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    Multiple absolute value inequality

    Hello, I was asked to solve this inequality analytically.

    |x^2 - x| - |x| < 1

    However, I do not know how to start it....
    I'm not sure how to solve inequalities with more than one
    absolute value in it. How would I solve this?
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  2. #2
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    You use the what's called known as triangle inequalities:

    |a+b|\le|a|+|b|

    |a|-|b|\le |a-b|

    | |a| +|b| |\le |a-b|

    So you can do:

    |x^2-x|-|x| \le |x^2-x -x|

    which:

    |x^2-x-x|=|x^2-2x|


    so your last line would be:

    |x^2-2x|<1

    Are you supposed to solve for x?
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  3. #3
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    I guess I am supposed to find the intervals of x which satisfies the inequality. Thank you for your help, it's looking good so far. I hadn't learned about the triangle inequalities before.
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  4. #4
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    no problem, so you can take it from there? if you run into any more trouble i'm glad to help
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  5. #5
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    I'll give it a try for now. Thank you for the help, I'll see if i run into any problems.
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  6. #6
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    Krizalid's Avatar
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