document.write( "Question 751237: Solve the following rational inequalties for the given variable\r
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Algebra.Com's Answer #457081 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28x%2B3%29%2F2x\" < 2\r\n" );
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document.write( "Subtract 2 from both sides to get 0 on the right:\r\n" );
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document.write( "\"%28x%2B3%29%2F2x\" - 2 < 0\r\n" );
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document.write( "Get a common denominator of 2x.  Multiply the 2 by \"2x%2F%282x%29\"\r\n" );
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document.write( "\"%28x%2B3%29%2F%282x%29\" - 2·\"2x%2F%282x%29\" < 0\r\n" );
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document.write( "\"%28x%2B3%29%2F%282x%29\" - \"4x%2F%282x%29\" < 0\r\n" );
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document.write( "\"%28%28x%2B3%29-4x%29%2F%282x%29\" < 0\r\n" );
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document.write( "\"%28x%2B3-4x%29%2F%282x%29\" < 0\r\n" );
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document.write( "\"%283-3x%29%2F%282x%29\" < 0\r\n" );
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document.write( "Factor the numerator\r\n" );
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document.write( "\"%283%281-x%29%29%2F%282x%29\" < 0\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "\"%281-x%29%2F%282x%29\" < 0\r\n" );
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document.write( "Multiply both sides by 2\r\n" );
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document.write( "\"%281-x%29%2Fx\" < 0\r\n" );
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document.write( "Find all critical values by setting numerator and denominator = 0\r\n" );
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document.write( " 1-x=0        x=0\r\n" );
document.write( "  -x=-1       \r\n" );
document.write( "   x=1  \r\n" );
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document.write( "So the critical values are 0 and 1\r\n" );
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document.write( "Put these on a number line:\r\n" );
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document.write( "----------o--o---------\r\n" );
document.write( "-3 -2 -1  0  1  2  3  4\r\n" );
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document.write( "test a value to the left of 0, say x=-1\r\n" );
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document.write( "Substitute it in\r\n" );
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document.write( "\"%281-x%29%2Fx\" < 0\r\n" );
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document.write( "\"%281-%28-1%29%29%2F%28-1%29\" < 0\r\n" );
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document.write( "\"%281%2B1%29%2F%28-1%29\" < 0\r\n" );
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document.write( "\"2%2F%28-1%29\" < 0\r\n" );
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document.write( "-2 < 0\r\n" );
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document.write( "This is true so we shade the portion of the\r\n" );
document.write( "number line left of 0\r\n" );
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document.write( "< ==========o--o---------\r\n" );
document.write( "  -3 -2 -1  0  1  2  3  4\r\n" );
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document.write( "test a value between 0 and 1 say x=0.5\r\n" );
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document.write( "Substitute it in\r\n" );
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document.write( "\"%281-0.5%29%2F0.5\" < 0\r\n" );
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document.write( "\"0.5%2F0.5\" < 0\r\n" );
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document.write( "1 < 0\r\n" );
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document.write( "That is false so we do not shade the portion of the\r\n" );
document.write( "number line between 0 and 1.  So we still have\r\n" );
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document.write( "< ==========o--o---------\r\n" );
document.write( "  -3 -2 -1  0  1  2  3  4\r\n" );
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document.write( "We test a value to the right of 1, say x=2\r\n" );
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document.write( "Substitute it in\r\n" );
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document.write( "\"%281-x%29%2Fx\" < 0\r\n" );
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document.write( "\"%281-%282%29%29%2F2\" < 0\r\n" );
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document.write( "\"%28-1%29%2F2\" < 0\r\n" );
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document.write( "\"-1%2F2\" < 0\r\n" );
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document.write( "This is true so we shade the portion of the\r\n" );
document.write( "number line right of 1\r\n" );
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document.write( "<  =========o--o======== >\r\n" );
document.write( "  -3 -2 -1  0  1  2  3  4\r\n" );
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document.write( "That's the graph of the solution set, in interval notation\r\n" );
document.write( "that is\r\n" );
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document.write( "\"%28matrix%281%2C3%2C%0D%0A%0D%0A-infinity%2C%22%2C%22%2C0%29%29\"\"U\"\"%28matrix%281%2C3%2C%0D%0A%0D%0A1%2C%22%2C%22%2Cinfinity%29%29\"\r\n" );
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document.write( "Edwin
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