Algebra.Com's Answer #854039 by ikleyn(53750)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "solve. x-2/x+1 greater or equal to 3
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document.write( " The solution in the post by @jai_kos in incorrect.\r
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document.write( " It is incorrect methodologically and gives incorrect answer.\r
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document.write( " See my correct solution below.\r
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document.write( "They want you solve this inequality\r\n" );
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document.write( "  >= 3. (1)\r\n" );
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document.write( "Transform it equivalently this way\r\n" );
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document.write( " - 3 >= 0 <<<---=== moving 3 from right side to left side with changing the sign\r\n" );
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document.write( " -  >= 0 <<<---=== writing '3' with the common denominator\r\n" );
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document.write( "  >= 0 <<<---=== simplifying\r\n" );
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document.write( "  >= 0 <<<---=== simplifying further\r\n" );
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document.write( "Now, the left side rational function can be non-negative if and only if\r\n" );
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document.write( " EITHER the numerator is non-negative and denominator is positive\r\n" );
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document.write( " -2x - 5 >= 0 and x + 1 > 0 (2)\r\n" );
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document.write( " OR the numerator is non-positive and denominator is negative\r\n" );
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document.write( " -2x - 5 <= 0 and x + 1 < 0. (3)\r\n" );
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document.write( "In case (2), -2x >= 5 and x > -1, which is the same as \r\n" );
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document.write( " x <= -5/2 and x > -1.\r\n" );
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document.write( " These both inequalities, taken together, has no solution.\r\n" );
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document.write( "In case (3), -2x <= 5 and x < -1, which is the same as \r\n" );
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document.write( " x >= -5/2 and x < -1.\r\n" );
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document.write( "Thus the final solution to the given inequality is this set of real numbers -5/2 <= x < -1,\r\n" );
document.write( "or, in the interval notation, the set [ , ).\r\n" );
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document.write( "Solved.\r
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document.write( "The error made by @jai_kos is that when he multiplies both sides of the original inequality by (x+1),
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document.write( "he misses the case when (x+1) is negative, which requires different treatment.\r
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document.write( "This error, which jai_kos makes solving the problem, is a typical error, which beginners make
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document.write( "when trying to solve such inequalities,
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document.write( "until the more experienced teachers/tutors will explain their error and will show a right way solving.\r
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