Results 1 to 4 of 4

Math Help - inequality

  1. #1
    Newbie
    Joined
    Jan 2007
    Posts
    3

    inequality

    x+x>1 in equality i cnat figure out how to factor it it does not make sense to me how you can have a single x and a negative 1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by msdonnelly View Post
    x+x>1 in equality i cnat figure out how to factor it it does not make sense to me how you can have a single x and a negative 1
    Hello,

    x^2+x > 1 \Longleftrightarrow x^2+x-1 > 0

    Now factor the LHS of this inequality:

    x^2+x-1 > 0 \Longleftrightarrow x^2+x+\frac{1}{4}-\frac{1}{4}-1>0 \Longleftrightarrow \left(x+\frac{1}{2} \right)^2-\frac{5}{4}>0

    \left(x+\frac{1}{2} \right)^2-\frac{5}{4}>0 \Longleftrightarrow \left(x+\frac{1}{2} +\frac{1}{2} \cdot \sqrt{5} \right) \cdot \left(x+\frac{1}{2}-\frac{1}{2} \cdot \sqrt{5} \right)>0

    A product of 2 factors is positive (that means it is greater than zero) if both factors have the same sign. Therefore you get 2 sets of 2 inequalities:

    \left(x+\frac{1}{2} +\frac{1}{2} \cdot \sqrt{5} \right)>0\ \wedge \  \left(x+\frac{1}{2}-\frac{1}{2} \cdot \sqrt{5} \right)>0 \vee
    \left(x+\frac{1}{2} +\frac{1}{2} \cdot \sqrt{5} \right)<0\ \wedge \  \left(x+\frac{1}{2}-\frac{1}{2} \cdot \sqrt{5} \right)<0

    Solve each inequality for x. Simplify. YOU'll get:

     x>-\frac{1}{2}+\frac{1}{2} \cdot \sqrt{5} \ \ \vee \ \ x< -\frac{1}{2} -\frac{1}{2} \cdot \sqrt{5}

    I've attached a diagram to show you how to solve such inequalities by graphing.

    EB
    Attached Thumbnails Attached Thumbnails inequality-unglg_quad1.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by msdonnelly View Post
    x+x>1 in equality i cnat figure out how to factor it it does not make sense to me how you can have a single x and a negative 1
    Wow, three posts for the same question? ... You think it'll get answered that much quicker?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by msdonnelly View Post
    x+x>1 in equality i cnat figure out how to factor it it does not make sense to me how you can have a single x and a negative 1
    How much of the helper time do you think you have a right to waste!

    One question one post.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 11th 2011, 08:20 PM
  2. Replies: 3
    Last Post: December 12th 2010, 01:16 PM
  3. inequality
    Posted in the Math Challenge Problems Forum
    Replies: 7
    Last Post: July 25th 2010, 06:11 PM
  4. Inequality help
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 8th 2010, 06:24 AM
  5. Inequality :\
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 12th 2009, 01:57 PM

Search Tags


/mathhelpforum @mathhelpforum