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 March 17th, 2011, 08:28 AM #1 Newbie   Joined: Mar 2011 Posts: 2 Thanks: 0 Inequality I'm having trouble with this inequality: 1/(x-5) < 4/5x I'm pretty sure the first step is to do this: 1/(x-5) - 4/5x < 0 But I'm stuck here. Could anyone nudge me in the right direction? March 17th, 2011, 08:44 AM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1140 Math Focus: Elementary mathematics and beyond Re: Inequality March 17th, 2011, 09:29 AM #3 Newbie   Joined: Mar 2011 Posts: 2 Thanks: 0 Re: Inequality Thank you! March 18th, 2011, 01:39 AM   #4
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Quote:
 Originally Posted by greg1313
x ? 0, x ? 5
x + 20 > 0, 5x(x - 5) < 0 or x + 20 < 0, 5x(x - 5) > 0
For 5x(x - 5) < 0: 5x > 0, x - 5 < 0 or 5x < 0, x - 5 > 0
x > 0, x < -5 or x < 0, x > -5
For 5x(x - 5) > 0: 5x > 0, x - 5 > 0 or 5x < 0, x - 5 < 0
x > 0, x > -5 or x < 0, x < -5
For x + 20 > 0 and x + 20 < 0: x > -20 and x < -20, respectively
x > -20, x > 0, x < -5 or x < 0, x > -5 OR x < -20, x > 0, x > -5 or x < 0, x < -5
x < 0, x > -5 is equivalent to -5 < x < 0
x > 0, x > -5 is equivalent to x > 0
x < 0, x < -5 is equivalent to x < -5
x > -20, x > 0, x < -5 or -5 < x < 0 OR x < -20, x > 0 or x < -5
x > -20 and -5 < x < 0 is equivalent to -5 < x < 0
x = 1 does not satisfy x > 0, x < -5
-5 < x < 0 OR x < -20, x > 0 or x < -5
x = 1 does not satisfy x < -20 and x > 0
x < -20 and x < -5 is equivalent to x < -20
? -5 < x < 0 or x < -20 March 18th, 2011, 03:07 AM   #5
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Re:

Quote:
Originally Posted by johnny
Quote:
 Originally Posted by greg1313
x ? 0, x ? 5
x + 20 > 0, 5x(x - 5) < 0 or x + 20 < 0, 5x(x - 5) > 0
For 5x(x - 5) < 0: 5x > 0, x - 5 < 0 or 5x < 0, x - 5 > 0
x > 0, x < -5 or x < 0, x > -5
For 5x(x - 5) > 0: 5x > 0, x - 5 > 0 or 5x < 0, x - 5 < 0
x > 0, x > -5 or x < 0, x < -5
For x + 20 > 0 and x + 20 < 0: x > -20 and x < -20, respectively
x > -20, x > 0, x < -5 or x < 0, x > -5 OR x < -20, x > 0, x > -5 or x < 0, x < -5
x < 0, x > -5 is equivalent to -5 < x < 0
x > 0, x > -5 is equivalent to x > 0
x < 0, x < -5 is equivalent to x < -5
x > -20, x > 0, x < -5 or -5 < x < 0 OR x < -20, x > 0 or x < -5
x > -20 and -5 < x < 0 is equivalent to -5 < x < 0
x = 1 does not satisfy x > 0, x < -5
-5 < x < 0 OR x < -20, x > 0 or x < -5
x = 1 does not satisfy x < -20 and x > 0
x < -20 and x < -5 is equivalent to x < -20
? -5 < x < 0 or x < -20
i think it would have been easier to multiply
the whole equation by the square of the denominator
giving u:

then just draw it and determine negative domains March 18th, 2011, 03:22 AM #6 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Your solution is much easier. Thanks, daniel_an! March 18th, 2011, 04:30 AM #7 Newbie   Joined: Mar 2011 Posts: 4 Thanks: 0 Re: Inequality Wow! Nice solution. Tags inequality Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post amirmath Calculus 1 May 18th, 2013 10:38 AM jatt-rockz Algebra 2 November 5th, 2011 08:21 PM martexel Applied Math 4 July 16th, 2010 04:27 PM yehoram Algebra 2 June 27th, 2010 05:52 PM Razzvy Algebra 5 October 18th, 2009 10:40 AM

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