document.write( "Question 1186615: What is the solution set of x²-4x-12>0 and x²-8x+15<0 \n" ); document.write( "

Algebra.Com's Answer #817547 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "What is the solution set of x²-4x-12 > 0 and x²-8x+15 < 0 ?
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document.write( "First inequaliy   >   in factored form is\r\n" );
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document.write( "     > .\r\n" );
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document.write( "Its solution set is the union of these two semi-infinite intervals  (-oo,-2) U (6,oo)  (see the plot below)\r\n" );
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document.write( "    =============)-------|---------------------------(=========\r\n" );
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document.write( "                -2       0                           6\r\n" );
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document.write( "Second inequaliy   <   in factored form is\r\n" );
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document.write( "     > .\r\n" );
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document.write( "Its solution set is this interval  (3,5)  (see the plot below)\r\n" );
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document.write( "    ---------------------|------------(========)-----------------\r\n" );
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document.write( "                         0            3        5\r\n" );
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document.write( "The problem asks about the intersection of these solution sets (because the service word AND is included to the system).\r\n" );
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document.write( "This intersection is the EMPTY set.  You can see it comparing the plots.\r\n" );
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document.write( "ANSWER.  The solution set of the given system of inequalities is the empty set.\r\n" );
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