document.write( "Question 1137569: Kindly solve this inequality
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Algebra.Com's Answer #755448 by ikleyn(53938) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( " >= \r\n" );
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document.write( "has the domain  x =/= -2  and  x =/= 2  and is equivalent to (moving the right part to the left)\r\n" );
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document.write( " -  >= 0\r\n" );
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document.write( "Write with the common denominator\r\n" );
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document.write( " >= 0.\r\n" );
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document.write( "Simplify step by step\r\n" );
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document.write( " >= 0,\r\n" );
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document.write( " >= 0,\r\n" );
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document.write( " >= 0.      (1)\r\n" );
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document.write( "Simplifying is completed. Next we start analyzing.\r\n" );
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document.write( "The critical points, where the rational function (1) changes its sign, are the points  -2, 0, 2 and 4.\r\n" );
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document.write( "They divide the number line in 5 intervals.\r\n" );
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document.write( "1)  Interval  (,).  \r\n" );
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document.write( "    All four separate factors are negative, hence, the function is POSITIVE.\r\n" );
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document.write( "    Thus this interval IS the part of the solution.\r\n" );
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document.write( "2)  Interval  (,).  \r\n" );
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document.write( "    One factor, (x+2) is positive; the other 3 factors are negative; hence, the function is NEGATIVE.\r\n" );
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document.write( "    Thus this interval is NOT the part of the solution.\r\n" );
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document.write( "3)  Interval  [,).  \r\n" );
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document.write( "    Two factors,  (x+2) and x,  are positive; the other 2 factors are negative; hence, the function is POSITIVE.\r\n" );
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document.write( "    Thus this interval IS the part of the solution.\r\n" );
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document.write( "Moving forward along the number line interval after interval, and analyzing by the similar way, you get the \r\n" );
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document.write( "ANSWER.  The solution is the union of the following intervals:\r\n" );
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document.write( "         (,) U [,) U [,).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Do you understand now why the forum requires one and only one problem per post ?\r
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\n" ); document.write( "\n" ); document.write( "Because otherwise you will get a mess.\r
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