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March 17th, 2011, 09:28 AM   #1
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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?
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March 17th, 2011, 09:44 AM   #2
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Re: Inequality





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March 17th, 2011, 10:29 AM   #3
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Re: Inequality

Thank you!
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March 18th, 2011, 02:39 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
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March 18th, 2011, 04:07 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
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March 18th, 2011, 04:22 AM   #6
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Your solution is much easier. Thanks, daniel_an!
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March 18th, 2011, 05:30 AM   #7
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Re: Inequality

Wow! Nice solution.
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