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> 1\r\n" );
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document.write( "Multiply both sides by 24 to clear the fraction.\r\n" );
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document.write( " 8x + 6y > 24\r\n" );
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document.write( "Divide both sides by 2 to simplify\r\n" );
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document.write( " 4x + 3y > 12\r\n" );
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document.write( "First we draw the graph of the boundary line which has\r\n" );
document.write( "equation like the inequality except that we replace the > with =\r\n" );
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document.write( "Boundary line's equation is\r\n" );
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document.write( " 4x + 3y = 12\r\n" );
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document.write( "Get the intercepts of (3,0) and (0,4)\r\n" );
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document.write( "Draw the line dotted, not solid, because the inequality symbol is\r\n" );
document.write( "> and not >, which means that the points on the boundary line\r\n" );
document.write( "are NOT solutions to the inequality. \r\n" );
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document.write( "All the solutions to the inequality are on one side or the other \r\n" );
document.write( "of that dotted boundary line.\r\n" );
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document.write( "To determine which side of that dotted line we shade, we pick\r\n" );
document.write( "a test point on each side of the line, which can be any arbitrary \r\n" );
document.write( "points as long as they are not on the boundary line. \r\n" );
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document.write( "Suppose we pick the test point (4,5) on the upper side of the\r\n" );
document.write( "line and (1,1) on the lower side of the line.\r\n" );
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document.write( "We substitute both points in the inequality 4x + 3y > 12\r\n" );
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document.write( "For test pt. (4,5) For test pt. (1,1)\r\n" );
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document.write( " 4x + 3y > 12 4x + 3y > 12\r\n" );
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document.write( "4(4) + 3(5) > 12 4(1) + 3(1) > 12\r\n" );
document.write( " 16 + 15 > 12 4 + 3 > 12\r\n" );
document.write( " 31 > 12 7 > 12\r\n" );
document.write( " TRUE FALSE\r\n" );
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document.write( "So we shade the side of the dotted line for which the \r\n" );
document.write( "test point is a solution, which is the side that (4,5)\r\n" );
document.write( "is on, or the upper side, like the green region above\r\n" );
document.write( "the dotted line:\r\n" );
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document.write( "Shortcuts: \r\n" );
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document.write( "1. You don't really need to get a test point\r\n" );
document.write( "on but one side of the line, because if it tests TRUE,\r\n" );
document.write( "it is a solution, so you shade that side. If it tests\r\n" );
document.write( "FALSE, it is NOT a solution so the solutions are all on\r\n" );
document.write( "the other side of the line. (The reason I used two\r\n" );
document.write( "test points was to show you what would happen if you\r\n" );
document.write( "picked one on either side).\r\n" );
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document.write( "2. If the line does not go through the origin then you\r\n" );
document.write( "can pick the origin (0,0) as a test point, since 0 is\r\n" );
document.write( "so easy to work with you can probably substitute it in \r\n" );
document.write( "your head.\r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-07.gif\")
