document.write( "Question 693272: (3x - 10) / (x - 4) >2 \n" ); document.write( "

Algebra.Com's Answer #802905 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
(3x - 10) / (x - 4) > 2
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\n" ); document.write( "\n" ); document.write( " The solution in the post by @CubeyThePenguin is ABSOLUTELY WRONG.\r
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document.write( "Transform the inequality, using equivalent transformations\r\n" );
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document.write( "     > 2\r\n" );
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document.write( "     - 2 > 0\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\r\n" );
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document.write( "     > 0    (*)\r\n" );
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document.write( "Inequality (*) is equivalent to the given inequality.\r\n" );
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document.write( "There are two critical points x= 2 and x= 4, that divide the number line in three non-intersecting intervals\r\n" );
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document.write( "          (-oo,2), (2,4) and (4,oo).\r\n" );
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document.write( "In the first interval, both the numerator and denominator of (*) are negative;  so the inequality (*) is valid; \r\n" );
document.write( "so the interval (-oo,2)  is the part of the solution set.\r\n" );
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document.write( "In the second interval, the numerator of (*) is positive, while the denominator of (*) is negative;  \r\n" );
document.write( "so the inequality (*) is not valid; thus the interval (2,4)  is NOT the part of the solution set.\r\n" );
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document.write( "In the third interval, both the numerator and denominator of (*) are positive;  so the inequality (*) is valid; \r\n" );
document.write( "so the interval (4,oo)  is the part of the solution set.\r\n" );
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document.write( "ANSWER.  The solution set to the given inequality is the union of two intervals  (-oo,2) U (4,oo).\r\n" );
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