document.write( "Question 63264: solve. x-2/x+1 greater or equal to 3
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Algebra.Com's Answer #854047 by n2(79) $\"\"$ $\"About$

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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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