document.write( "Question 147744: solve the absolute calue inequality. other than 0, use interval notation to express the solution set and graph the solution set on a number line
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Algebra.Com's Answer #108144 by Edwin McCravy(20054)\"\" \"About 
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solve the absolute calue inequality. other than 0, use interval notation to express the solution set and graph the solution set on a number line
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document.write( "Here are the rules for removing the absolute value bars in an\r\n" );
document.write( "absolute value inequality of the form \r\n" );
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document.write( "1.  For cases of the form \"abs%28expression%29%3CA\" where A is \r\n" );
document.write( "    a positive number, write this:\r\n" );
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document.write( "                      \"-A%3Cexpression%3CA\"     \r\n" );
document.write( "                      \r\n" );
document.write( "    \r\n" );
document.write( "2.  For cases of the form \"abs%28expression%29%3C=A\" where A is a\r\n" );
document.write( "    positive number, write this:\r\n" );
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document.write( "                      \"-A%3C=expression%3C=A\"     \r\n" );
document.write( "                      \r\n" );
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document.write( "3.  For cases of the form \"abs%28expression%29%3EA\" where A is a \r\n" );
document.write( "    positive number, write this:\r\n" );
document.write( "             \r\n" );
document.write( "               \"-A%3Cexpression\"\"OR\"\"expression%3EA\"  \r\n" );
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document.write( "4.  For cases of the form \"abs%28expression%29%3E=A\" where A is a\r\n" );
document.write( "    positive number, write this:\r\n" );
document.write( "             \r\n" );
document.write( "               \"-A%3C=expression\"\"OR\"\"expression%3E=A\" \r\n" );
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document.write( "Your problem:\r\n" );
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document.write( "\"abs%28%282y%2B6%29%2F3%29%3C2\" is case 1, so to remove the absolute value symbols,\r\n" );
document.write( "we write:\r\n" );
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document.write( "\"-2%3C%282y%2B6%29%2F3%3C2\"\r\n" );
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document.write( "Now we multiply all three sides by 3 to clear of the fraction:\r\n" );
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document.write( "\"-2%2A3%3C3%2A%282y%2B6%29%2F3%3C2%2A3\"\r\n" );
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document.write( "\"-2%2A3%3Ccross%283%29%2A%282y%2B6%29%2Fcross%283%29%3C2%2A3\"\r\n" );
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document.write( "\"-6%3C2y%2B6%3C6\"\r\n" );
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document.write( "Subtract \"6\" from all three sides:\r\n" );
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document.write( "\"-6-6%3C2y%2B6-6%3C6-6\"\r\n" );
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document.write( "\"-12%3C2y%3C0\"\r\n" );
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document.write( "Divide all three sides by 2 to solve for y\r\n" );
document.write( "in the middle:\r\n" );
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document.write( "\"%28-12%29%2F2%3C%282y%29%2F2%3C0%2F2\"\r\n" );
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document.write( "\"%28-12%29%2F2%3C%28cross%282%29y%29%2Fcross%282%29%3C0%2F2\"\r\n" );
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document.write( "\"-6%3Cy%3C0\"\r\n" );
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document.write( "Mark -6 and 0 with open circles\r\n" );
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document.write( "<--------------o-----------------o------------>\r\n" );
document.write( " -10 -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  \r\n" );
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document.write( "Now shade between them:\r\n" );
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document.write( "<--------------o=================o------------>\r\n" );
document.write( " -10 -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4\r\n" );
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document.write( "In interval notation that is written (-6,0)\r\n" );
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document.write( "Edwin
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