document.write( "Question 145277: Textbook Beecher, Penna it is an exercise on polynomials and rational inequalities I think my answer is -4 but I'm not sure. thank you for your help
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Algebra.Com's Answer #105949 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve
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document.write( "x cannot be 0 since we have the term  and\r\n" );
document.write( "we cannot divide by 0. So there are two cases:\r\n" );
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document.write( "Case 1:  (i.e., x is positive)\r\n" );
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document.write( "Since x is in this case a positive number, if we\r\n" );
document.write( "clear of fractions by multiplying through by positive\r\n" );
document.write( "number x, the inequality symbol will NOT be reversed:\r\n" );
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document.write( " AND \r\n" );
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document.write( " AND \r\n" );
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document.write( "Multiply through by -1 to make the first term positive.\r\n" );
document.write( "This DOES reverse the inequality symbol:\r\n" );
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document.write( "Since the square of a real number is never negative,\r\n" );
document.write( "the left side can never be less than 0, so it\r\n" );
document.write( "can only equal 0:\r\n" );
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document.write( "So we get only one solution when ,\r\n" );
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document.write( "namely x = 2\r\n" );
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document.write( "Case 2:  (i.e., x is negative)\r\n" );
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document.write( "Since x is in this case a negative number, if we\r\n" );
document.write( "clear of fractions by multiplying through by positive\r\n" );
document.write( "number x, the inequality symbol WILL be reversed:\r\n" );
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document.write( " AND \r\n" );
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document.write( " AND \r\n" );
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document.write( " AND \r\n" );
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document.write( " AND \r\n" );
document.write( "\r\n" );
document.write( "Multiply through by -1 to make the first term positive.\r\n" );
document.write( "This DOES reverse the inequality symbol:\r\n" );
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document.write( " AND \r\n" );
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document.write( " AND \r\n" );
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document.write( "Since the square of any real number is never negative,\r\n" );
document.write( "the first part  will be true for all\r\n" );
document.write( "values of x, and the second part  is the\r\n" );
document.write( "only thing that must be satisfied.  So the solution is\r\n" );
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document.write( "The graph of this is\r\n" );
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document.write( "<=============o-----@------>\r\n" );
document.write( " -4 -3 -2 -1  0  1  2  3  4 \r\n" );
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document.write( "where \"o\" means \"an open circle\" and where \"@\" means a\r\n" );
document.write( "closed circle.  This is abbreviated in interval \r\n" );
document.write( "notation as\r\n" );
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document.write( "(,0) U {2}\r\n" );
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document.write( "Edwin

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