document.write( "Question 1095251: Hi! I really find this problem difficult. Hoping someone could help me. Thanks!
\n" ); document.write( "(X)/(x-3) is greater than (2x-11)/(2x)
\n" ); document.write( "rational inequality \n" ); document.write( "
Algebra.Com's Answer #709811 by MathTherapy(10557)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Hi! I really find this problem difficult. Hoping someone could help me. Thanks!
\n" ); document.write( "(X)/(x-3) is greater than (2x-11)/(2x)
\n" ); document.write( "rational inequality
\n" ); document.write( "
\"x%2F%28x+-+3%29+%3E+%282x+-+11%29%2F%282x%29\"\r\n" );
document.write( "Based on the DENOMINATORS, \"matrix%281%2C3%2C+x+%3C%3E+3%2C+and%2C+x+%3C%3E+0%29\"\r\n" );
document.write( "Therefore, we already have 2 critical values: 3 and 0\r\n" );
document.write( "\"2x%5E2+%3E+%282x+-+11%29%28x+-+3%29\" ------- Multiplying each side by LCD, (x - 3)(2x)\r\n" );
document.write( "\"2x%5E2+%3E+2x%5E2+-+17x+%2B+33\"\r\n" );
document.write( "\"2x%5E2+-+2x%5E2+%2B+17x+%3E+33\"\r\n" );
document.write( "17x > 33 \r\n" );
document.write( "\"matrix%281%2C3%2C+x+%3E+33%2F17%2C+or%2C+x+%3E+1%2616%2F17%29\"\r\n" );
document.write( "We now have 3 CRITICAL VALUES: \"matrix%281%2C6%2C+%223%2C%22%2C+%220%2C%22%2C+and%2C+33%2F17%2C+or%2C+1%2616%2F17%29\"\r\n" );
document.write( "There now exists the following 4 (FOUR) INTERVALS that need to be tested.  \r\n" );
document.write( "==========
Interval 1: x < 0, or x = - 1\r\n" );
document.write( "\"x%2F%28x+-+3%29+%3E+%282x+-+11%29%2F%282x%29\"\r\n" );
document.write( "\"%28-+1%29%2F%28-+1+-+3%29+%3E+%282%28-+1%29+-+11%29%2F%282%28-+1%29%29\" ------- Substituting - 1 for x\r\n" );
document.write( "\"%28-+1%29%2F%28-+4%29+%3E+%28-+13%29%2F%28-+2%29\"\r\n" );
document.write( "Is \"1%2F4+%3E+13%2F2\"? No!! Therefore, a solution DOES NOT exist in this interval.\r\n" );
document.write( "================
Interval 2: \"0+%3C+x+%3C+1%2616%2F17\", or x = 1\r\n" );
document.write( "\"x%2F%28x+-+3%29+%3E+%282x+-+11%29%2F%282x%29\"\r\n" );
document.write( "\"%281%29%2F%281+-+3%29+%3E+%282%281%29+-+11%29%2F%282%281%29%29\" ------- Substituting 1 for x\r\n" );
document.write( "\"1%2F%28-+2%29+%3E+%28-+9%29%2F2\"\r\n" );
document.write( "Is \"-+1%2F2+%3E+-+9%2F2\"? Yes!! Therefore, a solution DOES exist in this interval.\r\n" );
document.write( "===============
Interval 3: \"1%2616%2F17+%3C+x+%3C+3\", or x = 2\r\n" );
document.write( "\"x%2F%28x+-+3%29+%3E+%282x+-+11%29%2F%282x%29\"\r\n" );
document.write( "\"2%2F%282+-+3%29+%3E+%282%282%29+-+11%29%2F%282%282%29%29\" ------- Substituting 2 for x\r\n" );
document.write( "\"2%2F%28-+1%29+%3E+%28-+7%29%2F4\"\r\n" );
document.write( "Is \"-+2+%3E+-+7%2F4\"? No!! Therefore, a solution DOES NOT exist in this interval.\r\n" );
document.write( "============
Interval 4: x > 3, or x = 4\r\n" );
document.write( "\"x%2F%28x+-+3%29+%3E+%282x+-+11%29%2F%282x%29\"\r\n" );
document.write( "\"4%2F%284+-+3%29+%3E+%282%284%29+-+11%29%2F%282%284%29%29\" ------- Substituting 4 for x\r\n" );
document.write( "\"4%2F1+%3E+%28-+3%29%2F8\"\r\n" );
document.write( "Is \"4+%3E+%28-+3%2F8%29\"? Yes!! Therefore, a solution DOES exist in this interval.
The solution, in INTERVAL NOTATION is:  \n" );
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