document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109120>Question 109120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving rational inequalities.  I have to solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points.  I have to determine when f(x)=4x/x+1 is less than g(x)= -3x/x-6. \r<BR>\n" );
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document.write( "I have tried to answer the question but my answer doesn't make any sense to me because I can't tell when f(x) is less than g(x) from when I solved the inequalitie algebraically using the method my teacher taught me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79582 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=79582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points.<BR>\n" );
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document.write( "1st: Determine the values x cannot take.<BR>\n" );
document.write( "x=0 because the two fractions would be equal<BR>\n" );
document.write( "x=-1 and x=6 because the denominators cannot be zero.<BR>\n" );
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document.write( "2nd: Draw a number line and mark x=-1, x=0, and x=6<BR>\n" );
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document.write( "3rd: Pick a test point from each of the four intervals defined by these x values. Substitute the test value in 4x/x+1 < -3x/x-6 to see if it is true<BR>\n" );
document.write( "or false.\r<BR>\n" );
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document.write( "In (-inf,-1), pick x=-2, (4*-2)/(-2+1)<(-3*-2)/(-2-6) , false<BR>\n" );
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document.write( "In (-1,0), pick x=-1/2, (-2)/(1/2))<(-3/2)/(-13/2), true<BR>\n" );
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document.write( "In (0,6), pick x=1. (4/2)<(-3/-5), false<BR>\n" );
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document.write( "In (6,inf), pick x=7, (28)/(8)<-21/1, false<BR>\n" );
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document.write( "Solution: -1<x<0<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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