document.write( "Question 1016566: How would I solve the following rational inequality:
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Algebra.Com's Answer #632956 by ikleyn(52864) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( " < 3.   (1)\r\n" );
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document.write( "1. Assume that x > 0.\r\n" );
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document.write( "   Multiply both sides of (1) by 3x, which is positive in this case. You will get an inequality\r\n" );
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document.write( "  x - 5 < 9x  --->  -5 < 8x  --->  x > .\r\n" );
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document.write( "  Thus he solution in this case is the set of real {x | x > 0}, i.e the interval (,).\r\n" );
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document.write( "2. Assume that x < 0.\r\n" );
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document.write( "   Multiply both sides of (1) by 3x, which is negative in this case. You will get an inequality\r\n" );
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document.write( "  x -5 > 9x  --->  -5 > 8x  --->  x < .   <----  Notice that I changed the inequality sign when multiplied by negative number!\r\n" );
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document.write( "  Thus he solution in this case is the set of real {x | x <  }, i.e the semi-infinite interval (,).\r\n" );
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document.write( "Answer. The solution is the union of two intervals: (,) U (,).\r\n" );
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\n" ); document.write( "\n" ); document.write( "The plot of the function f(x) = $\"%28x-5%29%2F%283x%29\"$ is shown below.\r
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\n" ); document.write( "\n" ); document.write( "Figure. Plot y = $\"%28x-5%29%2F%283x%29\"$ \r
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