![\"\"](\"/images/stars/stars-12.gif\")
You can put this solution on YOUR website!
Solve the inequality:\r\n" );
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document.write( "2/3(3x-9) < 8\r\n" );
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document.write( "Use the distributive law to get rid of the parentheses.\r\n" );
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document.write( " 2/3(3x-9) < 8\r\n" );
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document.write( "(2/3)(3x) + (2/3)(-9) < 8\r\n" );
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document.write( " 2x + (-6) < 8\r\n" );
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document.write( " 2x - 6 < 8\r\n" );
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document.write( "Add 6 to both sides\r\n" );
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document.write( " 2x < 14\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( " x < 7\r\n" );
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document.write( "That may be all your teacher wants. But sometimes \r\n" );
document.write( "they want you to do more.\r\n" );
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document.write( "If you are asked for the solution set than that is \r\n" );
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document.write( " {x|x is real and x < 7}\r\n" );
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document.write( "The way that is read is:\r\n" );
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document.write( "\"The set of all x such that x is a real number which\r\n" );
document.write( "is less than or equal to seven\".\r\n" );
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document.write( "If you are asked for more, i.e., then read the rest. \r\n" );
document.write( "Draw the graph on a number line, and/or give the \r\n" );
document.write( "solution in set-builder notation as well as in interval\r\n" );
document.write( "notation.\r\n" );
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document.write( "The graph on a number line is done this way:\r\n" );
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document.write( "First we draw a number line:\r\n" );
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document.write( "—————————————————————————————————————————————\r\n" );
document.write( "-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11\r\n" );
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document.write( "Then we draw a circle at 7, but we have to go by this rule\r\n" );
document.write( "to determine whether we will use an open circle like this \"o\" \r\n" );
document.write( "or a closed circle like this \"l\". The rule is if it's \" < \" or\r\n" );
document.write( "\" > \" then we use an open circle \"o\" and if its > or <,\r\n" );
document.write( "then we use l. So since this is a case of <, we use \"l\" \r\n" );
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document.write( "———————————————————————————————l—————————————\r\n" );
document.write( "-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11\r\n" );
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document.write( "Now we use this rule:\r\n" );
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document.write( "If it's > or > then you shade to the right because it's\r\n" );
document.write( "\"greater than\" and the greater numbers are to the right.\r\n" );
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document.write( "If it's < or < then you shade to the left because it's\r\n" );
document.write( "\"less than\" and the lesser numbers are to the left.\r\n" );
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document.write( "So we shade to the right:\r\n" );
document.write( " \r\n" );
document.write( "———————————————————————————————lnnnnnnnnnnnnn>\r\n" );
document.write( "-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 \r\n" );
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document.write( "That's the graph. The interval notation is \r\n" );
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document.write( " [7,¥) \r\n" );
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document.write( "If it had been x > 7, then the graph would have been this:\r\n" );
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document.write( "———————————————————————————————onnnnnnnnnnnnn>\r\n" );
document.write( "-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 \r\n" );
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document.write( "and the interval notation would have been \r\n" );
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document.write( " (7,¥)\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com\r\n" );
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