document.write( "Question 43104: Can anyone solve the following?\r
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document.write( "27< 4|y + 9|-9\r
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document.write( "Thanks so much \n" );
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Algebra.Com's Answer #28131 by AnlytcPhil(1807) You can put this solution on YOUR website! Can anyone solve the following?\r\n" ); document.write( "\r\n" ); document.write( " 27 < 4|y + 9| - 9\r\n" ); document.write( "\r\n" ); document.write( "You must learn two principles for \r\n" ); document.write( "inequalities to remove the absolute\r\n" ); document.write( "value bars:\r\n" ); document.write( "-----------------------------------\r\n" ); document.write( "1. If C > 0\r\n" ); document.write( " |Ax + B| < C\r\n" ); document.write( "\r\n" ); document.write( " can be rewritten as\r\n" ); document.write( "\r\n" ); document.write( " \" -C < Ax + B < C \" \r\n" ); document.write( "-----------------------------------\r\n" ); document.write( "2. If C > 0\r\n" ); document.write( "\r\n" ); document.write( " |Ax + B| > C\r\n" ); document.write( "\r\n" ); document.write( " can be rewritten as\r\n" ); document.write( "\r\n" ); document.write( " \" Ax + B < -C OR Ax + B > C \"\r\n" ); document.write( "\r\n" ); document.write( "------------------------------------ \r\n" ); document.write( "Note the above two principles also \r\n" ); document.write( "hold for < and > \r\n" ); document.write( "\r\n" ); document.write( " -4|y + 9| + 27 < -9\r\n" ); document.write( "\r\n" ); document.write( " -4|y + 9| < -9 - 27\r\n" ); document.write( "\r\n" ); document.write( " -4|y + 9| < -36\r\n" ); document.write( "\r\n" ); document.write( "Divide both sides by -4, which reverses\r\n" ); document.write( "the inequality:\r\n" ); document.write( "\r\n" ); document.write( " |y + 9| > 9 \r\n" ); document.write( "\r\n" ); document.write( "This is principle 2 above\r\n" ); document.write( "\r\n" ); document.write( " y + 9 < -9 OR y + 9 > 9\r\n" ); document.write( "\r\n" ); document.write( " y < -18 OR y > 0\r\n" ); document.write( "\r\n" ); document.write( "Plot on a numberline:\r\n" ); document.write( "\r\n" ); document.write( " <======o-----------o======> \r\n" ); document.write( " -18 0\r\n" ); document.write( "\r\n" ); document.write( "Interval notation:\r\n" ); document.write( "\r\n" ); document.write( " (-¥, -18) È (0, ¥) \r\n" ); document.write( "\r\n" ); document.write( "Edwin\r\n" ); document.write( "AnlytcPhil@aol.com\n" ); document.write( " |