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Homework Help: How do you solve -1<2x^2-x<1?

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution

    I can't seem to solve this.. I am in calculus but I get to this point at the end of a long question, and it seems so trivial that I didn't think it would be a good idea to post this in the calculus forum.

    How do you solve this? I know (from wolframalpha) that the answer is -1/2<x<1 but I don't know how it got this.
  2. jcsd
  3. Mar 8, 2012 #2


    Staff: Mentor

    The inequality is equivalent to
    0 < 2x2 - x + 1 < 2,
    which is the same as these two inequalities:
    0 < 2x2 - x + 1 AND 2x2 - x + 1 < 2

    Do you know how to solve these quadratic inequalities?

    Graphically, the solution set to your inequality is the set of x values on the graph of y = 2x2 - x for which -1 < y < 1.
  4. Mar 8, 2012 #3
    OK thanks! Splitting it up into two inequalities really makes it much easier to think about.
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