document.write( "Question 1051852: Solve the inequality \"%28x%5E4%283x-5%29%5E2%28x%2B1%29%5E2%29%2F%28x%5E2-3x%2B2%29%3E=0\" \n" ); document.write( "
Algebra.Com's Answer #667317 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\"%28x%5E4%283x-5%29%5E2%28x%2B1%29%5E2%29%2F%28x%5E2-3x%2B2%29%3E=0\"\r\n" );
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document.write( "The denominator is the only thing not factored,\r\n" );
document.write( "so factor it\r\n" );
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document.write( "\"%28x%5E4%283x-5%29%5E2%28x%2B1%29%5E2%29%2F%28%28x-1%29%28x-2%29%29%3E=0\"\r\n" );
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document.write( "The critical numbers are the zeros of all the factors:\r\n" );
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document.write( "0, \"5%2F3\", -1, 1, 2\r\n" );
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document.write( "Arrange them in numerical order:\r\n" );
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document.write( "-1, 0, 1, \"5%2F3\", 2\r\n" );
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document.write( "-1, 0, 1, \"1%262%2F3\", 2\r\n" );
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document.write( "and put them on a number line:\r\n" );
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document.write( "-----------o----o----o--o-o------\r\n" );
document.write( "-3   -2   -1    0    1    2    3 \r\n" );
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document.write( "Choose test values less than the least, in between\r\n" );
document.write( "them, and greater than the greatest:\r\n" );
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document.write( "Test values: -2, -0.5, 0.5, 1.5, 1.9, 3\r\n" );
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document.write( "If the test value gives \"%22%22%3E=0\" when substituted\r\n" );
document.write( "in the open interval which the test value is in is \r\n" );
document.write( "part of the solution; otherwise it's not.\r\n" );
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document.write( "Substituting -2 gives 161.333... which is \"%22%22%3E=0\",\r\n" );
document.write( "so \"%28matrix%281%2C3%2C-infinity%2C%22%2C%22%2C1%29%29\" is part of\r\n" );
document.write( "the solution.\r\n" );
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document.write( "Substituting -0.5 gives 0.176... which is \"%22%22%3E=0\",\r\n" );
document.write( "so \"%28matrix%281%2C3%2C-1%2C%22%2C%22%2C0%29%29\" is part of\r\n" );
document.write( "the solution.\r\n" );
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document.write( "Substituting 0.5 gives 2.296... which is \"%22%22%3E=0\",\r\n" );
document.write( "so \"%28matrix%281%2C3%2C0%2C%22%2C%22%2C1%29%29\" is part of\r\n" );
document.write( "the solution.\r\n" );
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document.write( "Substituting 1.5 gives -31.64... which is \"%22%22%3C0\",\r\n" );
document.write( "so \"%28matrix%281%2C3%2C1%2C%22%2C%22%2C5%2F3%29%29\" is NOT part of\r\n" );
document.write( "the solution.\r\n" );
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document.write( "Substituting 1.9 gives -596.71... which is \"%22%22%3C0\",\r\n" );
document.write( "so \"%28matrix%281%2C3%2C5%2F3%2C%22%2C%22%2C2%29%29\" is NOT part of\r\n" );
document.write( "the solution.\r\n" );
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document.write( "Substituting 3 gives 10368 which is \"%22%22%3E=0\",\r\n" );
document.write( "so \"%28matrix%281%2C3%2C1%2C%22%2C%22%2C2%29%29\" is part of\r\n" );
document.write( "the solution.\r\n" );
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document.write( "The critical numbers from the numerator 0,5/3, and -1\r\n" );
document.write( "satisfy the given inequality since \"equal to 0\" is allowed.  \r\n" );
document.write( "However the critical numbers from the denominator, 1 and 2, \r\n" );
document.write( "do not.\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "Edwin
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