document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=895479>Question 895479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem regarding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%2F%283x-1%29+%3E+1 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%2F%283x-1%29+%3E+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I actually know how to solve it. I solved in many ways because I wanted to be an expert of it.\r<BR>\n" );
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document.write( "I plotted a graph taking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282x%2B1%29%2F%283x-1%29 ALIGN=MIDDLE  ALT=\"y+=+%282x%2B1%29%2F%283x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and highlighted the area. I got the answer 1/3 < x < 2\r<BR>\n" );
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document.write( "I solved it in this way too..\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%2F%283x-1%29+-+1+%3E+0 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%2F%283x-1%29+-+1+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and got the same solution.\r<BR>\n" );
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document.write( "But my problem is... WHY CAN'T I CROSS MULTIPLY LIKE THIS???\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1+%3E+3x-1 ALIGN=MIDDLE  ALT=\"2x%2B1+%3E+3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542843 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=542843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can solve it this way too.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%2F%283x-1%29=1 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%2F%283x-1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=3x-1 ALIGN=MIDDLE  ALT=\"2x%2B1=3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=-2 ALIGN=MIDDLE  ALT=\"-x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So this is one of the critical values.<BR>\n" );
document.write( "The other is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > since the denominator goes to zero.<BR>\n" );
document.write( "Now split the number line into three regions and test the inequality in those three regions.<BR>\n" );
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document.write( "A better way to say it is that by multiplying, you're losing information that's included when the value of the denominator crosses from one sign to the other and it's irretrievable because the assumption you make is that the denominator doesn't go to zero (but in fact it does).<BR>\n" );
document.write( "If the denominator never goes to or through zero, you can solve it this way. <BR>\n" );
document.write( "Additionally, allowing for division by zero leads to contradictions. <BR>\n" );
document.write( "Hope that helps. </SPAN>\n" );
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