document.write( "Question 1162206: solve the following inequality[1/x-2> or =1] and graph the solution on the real number line \n" ); document.write( "
Algebra.Com's Answer #785953 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "Get 0 on the right:\r\n" );
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document.write( "Get LCD\r\n" );
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document.write( "The critical values are when the numerator or\r\n" );
document.write( "the denominator equals 0:\r\n" );
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document.write( "The numerator is 0 when x = 3\r\n" );
document.write( "The denominator is 0 when x = 2\r\n" );
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document.write( "So we draw a number line and mark the critical \r\n" );
document.write( "numbers\r\n" );
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document.write( "-----------------o---o- ---------\r\n" );
document.write( "-2  -1   0   1   2   3   4   5  6\r\n" );
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document.write( "This divides the number line into three intervals\r\n" );
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document.write( "We pick a test value in the left-most interval.\r\n" );
document.write( "The easiest number there to pick for a test value\r\n" );
document.write( "is 0, so we substitute it in the inequality:\r\n" );
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document.write( "That's false so we do not shade the numbers in the\r\n" );
document.write( "left most region, so we still have\r\n" );
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document.write( "-----------------o---o-----------\r\n" );
document.write( "-2  -1   0   1   2   3   4   5  6\r\n" );
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document.write( "We pick a test value in the middle interval, between\r\n" );
document.write( "2 and 3. The easiest number there to pick for a test value\r\n" );
document.write( "is 2.5, so we substitute it in the inequality:\r\n" );
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document.write( "That's true so we shade the numbers in the\r\n" );
document.write( "middle region, so we now have\r\n" );
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document.write( "-----------------o===o---------- \r\n" );
document.write( "-2  -1   0   1   2   3   4   5  6\r\n" );
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document.write( "We pick a test value in the right-most interval, greater\r\n" );
document.write( "than 3. The easiest number there to pick for a test value\r\n" );
document.write( "is 4, so we substitute it in the inequality:\r\n" );
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document.write( "That's false so we do not shade the numbers in the\r\n" );
document.write( "right-most region, so we have\r\n" );
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document.write( "-----------------o===o----------- \r\n" );
document.write( "-2  -1   0   1   2   3   4   5  6\r\n" );
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document.write( "Finally we test the critical numbers themselves:\r\n" );
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document.write( "We test 2\r\n" );
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document.write( "1/0 is not defined, so we do not shade at 2\r\n" );
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document.write( "We test 3\r\n" );
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document.write( "That's true so we do shade at 3\r\n" );
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document.write( "-----------------o===☻----------- \r\n" );
document.write( "-2  -1   0   1   2   3   4   5  6\r\n" );
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document.write( "Interval notation:\r\n" );
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document.write( "Edwin
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