document.write( "Question 309805: How do I write the solution set of {x| } for (x+20)(x -10)(x+11)>0. \n" ); document.write( "
Algebra.Com's Answer #221594 by Edwin McCravy(20060)\"\" \"About 
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How do I write the solution set of {x| } for \"%28x%2B20%29%28x-10%29%28x%2B11%29%3E0\"
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document.write( "Find all the critical values by setting each of the factors on the\r\n" );
document.write( "left = 0\r\n" );
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document.write( "x + 20 = 0 gives critical value x = -20\r\n" );
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document.write( "x - 10 = 0 gives critical value x = 10\r\n" );
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document.write( "x + 11 = 0 gives critical value x = -11\r\n" );
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document.write( "Mark them on a number line:\r\n" );
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document.write( "----------o-----------------------------------o-----------------------------------------------------------------------------------o---------\r\n" );
document.write( "-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 11 12 13\r\n" );
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document.write( "Choose a value left of -20, the left-most critical value,\r\n" );
document.write( "say x = -21.  Test it by substituting in the inequality:\r\n" );
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document.write( "\"%28x%2B20%29%28x-10%29%28x%2B11%29%3E0\"\r\n" );
document.write( "\"%28-21%2B20%29%28-21-10%29%28-21%2B11%29%3E0\"\r\n" );
document.write( "\"%28-1%29%28-21%29%28-10%29%3E0\"\r\n" );
document.write( "\"-210%3E0\"\r\n" );
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document.write( "That is false so we DO NOT shade the part of the number line\r\n" );
document.write( "left of -20.  So we still have the unshaded number line\r\n" );
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document.write( "----------o-----------------------------------o-----------------------------------------------------------------------------------o---------\r\n" );
document.write( "-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 11 12 13\r\n" );
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document.write( "Choose a value between -20 and -11, say x = -12.  Test it by substituting in the inequality:\r\n" );
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document.write( "\"%28x%2B20%29%28x-10%29%28x%2B11%29%3E0\"\r\n" );
document.write( "\"%28-12%2B20%29%28-12-10%29%28-12%2B11%29%3E0\"\r\n" );
document.write( "\"%288%29%28-22%29%28-1%29%3E0\"\r\n" );
document.write( "\"176%3E0\"\r\n" );
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document.write( "That is true so we DO shade the part of the number line between -20 and\r\n" );
document.write( "-11.  So we have:\r\n" );
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document.write( "----------o===================================o-----------------------------------------------------------------------------------o--------->\r\n" );
document.write( "-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 11 12 13\r\n" );
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document.write( "Choose a value between -11 and 10, say x = 0.  Test it by substituting in the inequality:\r\n" );
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document.write( "\"%28x%2B20%29%28x-10%29%28x%2B11%29%3E0\"\r\n" );
document.write( "\"%280%2B20%29%280-10%29%280%2B11%29%3E0\"\r\n" );
document.write( "\"%2820%29%28-10%29%2811%29%3E0\"\r\n" );
document.write( "\"-2200%3E0\"\r\n" );
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document.write( "That is false so we DO NOT shade the part of the number line between -20 and\r\n" );
document.write( "-11.  So we still have:\r\n" );
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document.write( "----------o===================================o-----------------------------------------------------------------------------------o--------->\r\n" );
document.write( "-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 11 12 13\r\n" );
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document.write( "Choose a value right of 10, the right-most critical value,\r\n" );
document.write( "say x = 11.  Test it by substituting in the inequality:\r\n" );
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document.write( "\"%28x%2B20%29%28x-10%29%28x%2B11%29%3E0\"\r\n" );
document.write( "\"%2811%2B20%29%2811-10%29%2811%2B11%29%3E0\"\r\n" );
document.write( "\"%2821%29%281%29%2822%29%3E0\"\r\n" );
document.write( "\"462%3E0\"\r\n" );
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document.write( "That is true so we DO shade the part of the number line to the right of\r\n" );
document.write( "10.  So we have:\r\n" );
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document.write( "----------o===================================o-----------------------------------------------------------------------------------o=========>\r\n" );
document.write( "-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 11 12 13\r\n" );
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document.write( "In set-builder notation the solution set is written:\r\n" );
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document.write( "{x | -20 < x < -11 OR x > 10}\r\n" );
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document.write( "In interval notation the solution set is written:\r\n" );
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document.write( "(-20,-11) U (10,\"infinity\")\r\n" );
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