document.write( "Question 895479: Problem regarding \"%282x%2B1%29%2F%283x-1%29+%3E+1\"\r
\n" ); document.write( "\n" ); document.write( "I actually know how to solve it. I solved in many ways because I wanted to be an expert of it.\r
\n" ); document.write( "\n" ); document.write( "I plotted a graph taking \"y+=+%282x%2B1%29%2F%283x-1%29\" and highlighted the area. I got the answer 1/3 < x < 2\r
\n" ); document.write( "\n" ); document.write( "I solved it in this way too..\r
\n" ); document.write( "\n" ); document.write( "\"%282x%2B1%29%2F%283x-1%29+-+1+%3E+0\" and got the same solution.\r
\n" ); document.write( "\n" ); document.write( "But my problem is... WHY CAN'T I CROSS MULTIPLY LIKE THIS???\r
\n" ); document.write( "\n" ); document.write( "\"2x%2B1+%3E+3x-1\" \r
\n" ); document.write( "\n" ); document.write( "Please don't tell \"Because we don't know whether 'x' is plus or minus which changes > to < I want a better explanation. Thank you so much.
\n" ); document.write( "

Algebra.Com's Answer #542860 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
Problem regarding \"%282x%2B1%29%2F%283x-1%29+%3E+1\"\r
\n" ); document.write( "\n" ); document.write( "I actually know how to solve it. I solved in many ways because I wanted to be an expert of it.\r
\n" ); document.write( "\n" ); document.write( "I plotted a graph taking \"y+=+%282x%2B1%29%2F%283x-1%29\" and highlighted the area. I got the answer 1/3 < x < 2\r
\n" ); document.write( "\n" ); document.write( "I solved it in this way too..\r
\n" ); document.write( "\n" ); document.write( "\"%282x%2B1%29%2F%283x-1%29+-+1+%3E+0\" and got the same solution.\r
\n" ); document.write( "\n" ); document.write( "But my problem is... WHY CAN'T I CROSS MULTIPLY LIKE THIS???\r
\n" ); document.write( "\n" ); document.write( "\"2x+%2B+1+%3E+3x+-+1\" \r
\n" ); document.write( "\n" ); document.write( "Please don't tell \"Because we don't know whether 'x' is plus or minus which changes > to < I want a better explanation. Thank you so much.
\n" ); document.write( "

\n" ); document.write( "\"%282x+%2B+1%29%2F%283x+-+1%29+%3E+1\", with \"x+%3C%3E+1%2F3\", since this value would render the inequality UNDEFINED
\n" ); document.write( "In this case, you certainly CAN cross-multiply \"%282x+%2B+1%29%2F%283x+-+1%29+%3E+1\" to get: \"2x+%2B+1+%3E+3x+-+1\"
\n" ); document.write( "\"2x+-+3x+%3E+-+1+-+1\"
\n" ); document.write( "\"-+x+%3E+-+2\"
\n" ); document.write( "\"x+%3C+%28-+2%29%2F-+1\" ------ Note that the INEQUALITY sign changed, since DIVISION by a negative value (- 1) dictates such
\n" ); document.write( "Therefore, \"x+%3C+2\"
\n" ); document.write( "We now have 2 CRITICAL POINTS: \"1%2F3\", and \"2\"
\n" ); document.write( "The intervals to test for values to make the inequality TRUE would then be:
\n" ); document.write( "1) \"x+%3C+1%2F3\", and
\n" ); document.write( "2) \"1%2F3+%3C+x+%3C+2\"\r
\n" ); document.write( "\n" ); document.write( "For \"x+%3C+1%2F3\", we can use 0 for x
\n" ); document.write( "Does the INEQUALITY PROVE TRUE when this occurs? Let's see!!
\n" ); document.write( "With x = 0, \"%282x+%2B+1%29%2F%283x+-+1%29+%3E+1\" becomes: \"%282%280%29+%2B+1%29%2F%283%280%29+-+1%29+%3E+1\"
\n" ); document.write( "\"%280+%2B+1%29%2F%280+-+1%29+%3E+1\"____\"1%2F-1+%3E+1\"____\"-+1+%3E+1\" (FALSE)\r
\n" ); document.write( "\n" ); document.write( "For \"1%2F3+%3C+x+%3C+2\", we can use 1 for x
\n" ); document.write( "Does the INEQUALITY PROVE TRUE when this occurs? Let's see!!
\n" ); document.write( "With x = 1, \"%282x+%2B+1%29%2F%283x+-+1%29+%3E+1\" becomes: \"%282%281%29+%2B+1%29%2F%283%281%29+-+1%29+%3E+1\"
\n" ); document.write( "\"%282+%2B+1%29%2F%283+-+1%29+%3E+1\"____\"3%2F2+%3E+1\" (TRUE)
\n" ); document.write( "As seen from the 2 tested intervals, the only solution is: \"highlight_green%28highlight_green%281%2F3+%3C+x+%3C+2%29%29\"
\n" ); document.write( "***Another test interval is: \"x+%3E+2\", but I knew that this interval would render the INEQUALITY, false.
\n" ); document.write( "So, your answer is CORRECT!! Good job!!
\n" ); document.write( "You can do the check!! \r
\n" ); document.write( "\n" ); document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
\n" ); document.write( "Further help is available, online or in-person, for a fee, obviously. \r
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