Results 1 to 7 of 7

Math Help - Inequality

  1. #1
    Junior Member R3ap3r's Avatar
    Joined
    Apr 2008
    Posts
    58

    Inequality

    Solve for x in the given inequality: 6x - x^2 \ge\;9

    My Work:

    -x^2 + 6x - 9 \ge\; 0

    (-x + 3)(x - 3) \ge\; 0

    -x + 3\ge\; 0\Longrightarrow -x \ge\; -3\Longrightarrow x\le\; 3

    x - 3 \ge\; 0\Longrightarrow x \ge\; 3

    What did I do wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by R3ap3r View Post
    Solve for x in the given inequality: 6x - x^2 \ge\;9

    My Work:

    -x^2 + 6x - 9 \ge\; 0

    {\color{red}(-x + 3)(x - 3) \ge\; 0}

    -x + 3\ge\; 0\Longrightarrow -x \ge\; -3\Longrightarrow x\le\; 3

    x - 3 \ge\; 0\Longrightarrow x \ge\; 3

    What did I do wrong?
    Until the red thing, it's OK

    But you could notice that -x^2+6x-9=-(x^2-6x+9)=-(x-3)^2

    Is it possible that -(x-3)^2 \ge 0 ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member R3ap3r's Avatar
    Joined
    Apr 2008
    Posts
    58
    how exactly is that wrong though? It's how it factors isn't it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by R3ap3r View Post
    how exactly is that wrong though? It's how it factors isn't it?
    No, your working was correct, but there are two problems :

    - there is no solution (but x=3), so that's why you thought you were wrong

    - you forgot a situation : -x+3<0 and x-3<0 (their product is positive ). It'll also yield to an impossibility, but you mustn't forget this case.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member R3ap3r's Avatar
    Joined
    Apr 2008
    Posts
    58
    So the final answer is just x=3? That makes sense.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Yep.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member R3ap3r's Avatar
    Joined
    Apr 2008
    Posts
    58
    hmmm amazing how a simple problem can trick me even when my working is correct
    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