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Solving an Inequality problem

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Solve the inequality

    (2x-3)(4x+5)>(x+6)(x+6)


    2. Relevant equations
    factoring?


    3. The attempt at a solution

    I got to the point where

    (7x)^2-14x-51>0 I can't solve this, because it can't be factored out. So am I doing something wrong????
     
  2. jcsd
  3. Sep 17, 2011 #2

    symbolipoint

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    Good work reaching that quadratic inequality. It would be related to a parabola opening upward. Look for the critical points. Does this have no roots, one root, or two roots? Which intervals make the quadratic inequality true?

    For critical points, remember the general solution to a quadratic equation, or can you factor the expression?
    EDIT: In fact, you're right. 7x^2-14x-51 is not factorable. Use either completing the square, or the solution to a quadratic equation.
     
  4. Sep 17, 2011 #3

    HallsofIvy

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    Well, first, it is NOT (7x)^2, it is 7x^2. As symbolipoint suggested, complete the square or use the quadratic formula to determine the values of x at which 7x^2- 14x- 51= 0. Since the graph of this function is a parabola opening upward, the values of x satisfying the inequality will be less than the lower of the two zeros and larger than the larger. The values of x between the zeros satify "< 0".
     
  5. Sep 17, 2011 #4
    okay, using quadratic formula I got

    x=7+/- sq root of 406 all over 7

    (sorry I'm not sure how to write this to make since any other way.)

    is this correct?
     
    Last edited: Sep 17, 2011
  6. Sep 17, 2011 #5

    HallsofIvy

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    Yes, those are the solutions to the quadratic equation. Now, what are the solutions to the inequality?
     
  7. Sep 17, 2011 #6
    how do i do that?

    is it
    .00000004? one of them? we haven't had this in class. i'm thinking she wrote this problem wrong.
     
  8. Sep 17, 2011 #7

    symbolipoint

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    You may be more successful in fully managing the solution if you just study the parts from the book to fill-in the topics that your teacher has not yet shown you in class.
     
  9. Sep 18, 2011 #8

    HallsofIvy

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    I already told you how to do that:
    No, this problem is perfectly solvable. You have already done most of the work. Do you understand that inequalities typically have not a single solution, but a range of solutions?
     
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