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If points A,B and C lie on a coordinate line and points A and B have\r\n" );
document.write( "coordinates of 15 and 7 respectively, then which of the possible \r\n" );
document.write( "coordinates for point C satisfy(ies) d(A,C)< d(B,C)?\r\n" );
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document.write( "This is when C is closer to A than it is to B \r\n" );
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document.write( " |C - A| < {C - B|\r\n" );
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document.write( "|C - 15| < |C - 7|\r\n" );
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document.write( "The boundary equation is\r\n" );
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document.write( "|C - 15| = |C - 7|\r\n" );
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document.write( "This breaks into two equations:\r\n" );
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document.write( "C - 15 = C - 7 OR C - 15 = -(C - 7}\r\n" );
document.write( " -15 = -7 OR C - 15 = -C + 7\r\n" );
document.write( " 2C = 22\r\n" );
document.write( " C = 11\r\n" );
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document.write( "So we set up a number line:\r\n" );
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document.write( " B A\r\n" );
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document.write( "-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 \r\n" );
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document.write( "Then we test a point on either side of 11 in the original\r\n" );
document.write( "inequality:\r\n" );
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document.write( "|C - 15| < |C - 7|\r\n" );
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document.write( "Say we pick test point less than 11, say 10\r\n" );
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document.write( "|10 - 15| < |10 - 7|\r\n" );
document.write( " |-5| < |3|\r\n" );
document.write( " 5 < 3\r\n" );
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document.write( "That's false, so we DO NOT shade the line to the left of 11.\r\n" );
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document.write( "Now we pick test point greater than 11, say 12\r\n" );
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document.write( "|12 - 15| < |12 - 7|\r\n" );
document.write( " |-3| < |5|\r\n" );
document.write( " 3 < 5\r\n" );
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document.write( "That's true, so we DO shade the line to the right of 11.\r\n" );
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document.write( "So the answer is C Î (11,¥).\r\n" );
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document.write( " B A\r\n" );
document.write( " | |\r\n" );
document.write( "-------------------------------------oCCCCCCCCCCCCCCCCCCCCC>\r\n" );
document.write( "-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17\r\n" );
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document.write( "Edwin \n" );
document.write( "