Results 1 to 4 of 4

Math Help - inequality 3

  1. #1
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    inequality 3

    -x^2+4x>-5 find solution set. I found the answer as (-1,5) but according to book it must be (1,5)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,334
    Thanks
    896

    Re: inequality 3

    Quote Originally Posted by kastamonu View Post
    -x^2+4x>-5 find solution set. I found the answer as (-1,5) but according to book it must be (1,5)
    $-x^2+4x > -5$

    $x^2-4x - 5 < 0$

    $(x-5)(x+1) < 0$

    same thing as the last problem we check signs from $-\infty \to \infty$

    $(-\infty, -1) \rightarrow +$

    $(-1, 5) \rightarrow -$

    $(5, \infty) \rightarrow +$

    and so the solution is

    $(-1,5)$

    and thus you are correct and the book is not!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,492
    Thanks
    1393

    Re: inequality 3

    Or you can solve the inequality more directly by completing the square...

    $\displaystyle \begin{align*} -x^2 + 4x &> -5 \\ 0 &> x^2 - 4x - 5 \\ x^2 - 4x - 5 &< 0 \\ x^2 - 4x + (-2) ^2 - (-2) ^2 - 5 &< 0 \\ \left( x - 2 \right) ^2 - 9 &< 0 \\ \left( x - 2 \right) ^2 &< 9 \\ \left| x - 2 \right| &< 3 \\ -3 < x - 2 &< 3 \\ -1 < x &< 5 \end{align*}$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    181
    Thanks
    1

    Re: inequality 3

    Many Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 26th 2013, 02:10 AM
  2. Replies: 2
    Last Post: January 11th 2011, 08:20 PM
  3. Replies: 3
    Last Post: December 12th 2010, 01:16 PM
  4. Help w/ inequality
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 4th 2010, 07:36 PM
  5. Inequality
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 31st 2008, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum