document.write( "Question 151944: x^2 -6x -27<0\r
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Algebra.Com's Answer #111698 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E2+-6x+-27%3C0\"
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document.write( "Find the critical values by\r\n" );
document.write( "setting each factor = 0\r\n" );
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document.write( "\"%28x-9%29=0\" gives critical value \"x=9\"\r\n" );
document.write( "\"%28x%2B3%29=0\" gives critical value \"x=-3\"\r\n" );
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document.write( "Place those critical values on a number line:\r\n" );
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document.write( "-----------o-----------------------------------o---------\r\n" );
document.write( " -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 \r\n" );
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document.write( "Choose a test value for x in the region left of -3.\r\n" );
document.write( "The easiest number to choose is -4.  Substitute this\r\n" );
document.write( "value into either the original inequality or its \r\n" );
document.write( "factored form. I'll choose to substitute in the\r\n" );
document.write( "factored form, but it does not matter which you\r\n" );
document.write( "substitute \"x=-4\" in:\r\n" );
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document.write( "\"%28x-9%29%28x%2B3%29%3C0\"\r\n" );
document.write( "\"%28-4-9%29%28-4%2B3%29%3C0\"\r\n" );
document.write( "\"%28-13%29%28-1%29%3C0\"\r\n" );
document.write( "\"13%3C0\"\r\n" );
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document.write( "This is false so we do not shade the region left of -3.\r\n" );
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document.write( "So we still have only:\r\n" );
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document.write( "-----------o-----------------------------------o---------\r\n" );
document.write( " -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12\r\n" );
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document.write( "Choose a test value for x in the region right of -3 but\r\n" );
document.write( "left of 9. The easiest number to choose is 0.  Substitute \r\n" );
document.write( "this value into either the original inequality or its \r\n" );
document.write( "factored form. I'll choose to substitute in the\r\n" );
document.write( "factored form, but it does not matter which you\r\n" );
document.write( "substitute \"x=0\" in:\r\n" );
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document.write( "\"%28x-9%29%28x%2B3%29%3C0\"\r\n" );
document.write( "\"%280-9%29%280%2B3%29%3C0\"\r\n" );
document.write( "\"%28-9%29%283%29%3C0\"\r\n" );
document.write( "\"-27%3C0\"\r\n" );
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document.write( "This is true so we shade the region right of -3 but left of 9.\r\n" );
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document.write( "-----------o===================================o---------\r\n" );
document.write( " -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12\r\n" );
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document.write( "Choose a test value for x in the region right of 9.\r\n" );
document.write( "The easiest number to choose is 10.  Substitute this\r\n" );
document.write( "value into either the original inequality or its \r\n" );
document.write( "factored form. I'll choose to substitute in the\r\n" );
document.write( "factored form, but it does not matter which you\r\n" );
document.write( "substitute \"x=-4\" in:\r\n" );
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document.write( "\"%28x-9%29%28x%2B3%29%3C0\"\r\n" );
document.write( "\"%2810-9%29%2810%2B3%29%3C0\"\r\n" );
document.write( "\"%281%29%2813%29%3C0\"\r\n" );
document.write( "\"13%3C0\"\r\n" );
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document.write( "This is false so we do not shade the region right of 9.\r\n" );
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document.write( "So we still have:\r\n" );
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document.write( "-----------o===================================o---------\r\n" );
document.write( " -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12\r\n" );
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document.write( "Since the inequality is <, rather than <, neither\r\n" );
document.write( "critical value is itself a solution.\r\n" );
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document.write( "So the final number line graph is:\r\n" );
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document.write( "-----------o===================================o---------\r\n" );
document.write( " -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12\r\n" );
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document.write( "and the interval notation for that is (\"-3\",\"9\").\r\n" );
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document.write( "Edwin
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