document.write( "Question 1086390: Solve the inequality. (Enter your answer using interval notation.)
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Algebra.Com's Answer #700623 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "We get 0 on the right:\r\n" );
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document.write( "After getting LCD and simplifying, we have:\r\n" );
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document.write( "To find all critical values, we set the numerator and denominator\r\n" );
document.write( "equal to 0 and solve for x:\r\n" );
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document.write( "We set the numerator = 0 and solve for x:\r\n" );
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document.write( ", which we solve by the quadratic formula \r\n" );
document.write( "and get \r\n" );
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document.write( " which are critical numbers \r\n" );
document.write( "approximately -11.8 and -6.2.\r\n" );
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document.write( "We set the denominator = 0,  and solve for \r\n" );
document.write( "x and get -1,-8, and -9.\r\n" );
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document.write( "So we place all the critical numbers on a number line, guessing\r\n" );
document.write( "about where -11.8 and -6.2 should go between integers.\r\n" );
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document.write( "-----------o----------o---o------o--------------------o--------\r\n" );
document.write( "-14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1\r\n" );
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document.write( "We pick the most convenient test value in each interval, and\r\n" );
document.write( "substitute it into \r\n" );
document.write( "and if we get a non-positive number, we include that interval\r\n" );
document.write( "in the solution.  If we get a positive number we do not.\r\n" );
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document.write( "For interval \r\n" );
document.write( "we choose test value -12, substitute it, and get a negative\r\n" );
document.write( "number, so we include that interval.\r\n" );
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document.write( "For interval \r\n" );
document.write( "we choose test value -10, substitute it, and get a positive\r\n" );
document.write( "number, so we do not include that interval.\r\n" );
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document.write( "For interval \r\n" );
document.write( "we choose test value -8.5, substitute it, and get a negative\r\n" );
document.write( "number, so we include that interval.\r\n" );
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document.write( "For interval \r\n" );
document.write( "we choose test value -7, substitute it, and get a positive\r\n" );
document.write( "number, so we do not include that interval.\r\n" );
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document.write( "For interval \r\n" );
document.write( "we choose test value -2, substitute it, and get a negative\r\n" );
document.write( "number, so we include that interval.\r\n" );
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document.write( "For interval \r\n" );
document.write( "we choose test value 0, substitute it, and get a positive\r\n" );
document.write( "number, so we do not include that interval.\r\n" );
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document.write( "Next, we include the critical values which cause the numerator\r\n" );
document.write( "to be 0, which are .\r\n" );
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document.write( "Thus the solution is \r\n" );
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document.write( "Edwin

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