document.write( "Question 172028: |2x-5|/|2x-1|<1/2 I need you to list solution in interval notation pls. Tnx \n" ); document.write( "
Algebra.Com's Answer #129095 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "|2x-5|/|2x-1|<1/2 I need you to list solution in interval notation pls. Tnx\r\n" );
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document.write( "We get 0 on the right by subtracting 2 from both sides:\r\n" );
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document.write( "\"abs%282x-5%29%2Fabs%282x-1%29%3C1%2F2\"\r\n" );
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document.write( "We first find the endpoints by solving the equation:\r\n" );
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document.write( "\"abs%282x-5%29%2Fabs%282x-1%29=1%2F2\"\r\n" );
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document.write( "Which involves solving two equations:\r\n" );
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document.write( "\"%282x-5%29%2F%282x-1%29=1%2F2\" and \"%282x-5%29%2F%282x-1%29=-1%2F2\" \r\n" );
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document.write( "The first gives solution \"x=9%2F2\" and the second gives\r\n" );
document.write( "solution 11/6\r\n" );
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document.write( "\"9%2F2\" is about 4.5 and {{11/6}}} is about 1.8333···\r\n" );
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document.write( "Mark those on a number line:\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( "Test a value to the left of \"11%2F6\". The easiest\r\n" );
document.write( "value is 0.  Substitute it into the original\r\n" );
document.write( "inequality:\r\n" );
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document.write( "\"abs%282x-5%29%2Fabs%282x-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%282%280%29-5%29%2Fabs%282%280%29-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%28-5%29%2Fabs%28-1%29%3C1%2F2\"\r\n" );
document.write( "\"5%2F1%3C1%2F2\"\r\n" );
document.write( "\"5%3C1%2F2\"\r\n" );
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document.write( "That is clearly false so do not shade the part to the\r\n" );
document.write( "left of \"11%2F2\".  So we still have just:\r\n" );
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document.write( "-2     -1     0     1     2     3     4     5     6 \r\n" );
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document.write( "Now test a value between \"11%2F6\" and \"9%2F2\".\r\n" );
document.write( "The easiest value is 2.  Substitute it into the original\r\n" );
document.write( "inequality:\r\n" );
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document.write( "\"abs%282x-5%29%2Fabs%282x-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%282%282%29-5%29%2Fabs%282%282%29-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%284-5%29%2Fabs%284-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%28-1%29%2Fabs%283%29%3C1%2F2\"\r\n" );
document.write( "\"1%2F3%3C1%2F2\"\r\n" );
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document.write( "That is true so we do shade the part between\r\n" );
document.write( "\"11%2F6\" and \"9%2F2\".  Now we have this:\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( "Now we test a value to the right of \"9%2F2\". The easiest\r\n" );
document.write( "value is 5.  Substitute it into the original\r\n" );
document.write( "inequality:\r\n" );
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document.write( "\"abs%282x-5%29%2Fabs%282x-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%282%285%29-5%29%2Fabs%282%285%29-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%2810-5%29%2Fabs%2810-1%29%3C1%2F2\"\r\n" );
document.write( "\"abs%285%29%2Fabs%289%29%3C1%2F2\"\r\n" );
document.write( "\"5%2F9%3C1%2F2\"\r\n" );
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document.write( "That is clearly false so do not shade the part to the\r\n" );
document.write( "rightt of \"9%2F2\".\r\n" );
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document.write( "So the graph of the solution is\r\n" );
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document.write( "-2     -1     0     1     2     3     4     5     6\r\n" );
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document.write( "and the interval notation is\r\n" );
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document.write( "\"%28matrix%281%2C3%2C+11%2F6%2C++%22%2C%22%2C+9%2F2%29%29\"\r\n" );
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document.write( "Edwin
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