document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40620>Question 40620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <Could someone please help me to understand how to solve this type of problem? I just cannot seem to get it. I posted another one that is different.<BR>\n" );
document.write( "Solve each rational inequality and state the solution set using interval notation.\r<BR>\n" );
document.write( "\n" );
document.write( "x + 3/x lessthan or eqaul to -2<BR>\n" );
document.write( "           <BR>\n" );
document.write( "(I don't know why this dosen't post right. x + 3 over x is lessthen or eqaul to -2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26019 by </B><A HREF=/tutors/aboutme.mpl?userid=junior403><B>junior403(76)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=junior403><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=26019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the rational inequality and state the solution set using interval notation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28x%29%3C=+-2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%29%3C=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ok, first we need to eliminate the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28x%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by multiplying both sides of the equation by the denominator x. <BR>\n" );
document.write( "This will create an equation that we can work with more easily.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28%28x%2B3%29%2F%28x%29%29%3C=+-2%28x%29 ALIGN=MIDDLE  ALT=\"x%28%28x%2B3%29%2F%28x%29%29%3C=+-2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can simplify by canceling out the x's on the left side and multiplying on the right.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%3C=+-2x ALIGN=MIDDLE  ALT=\"x%2B3%3C=+-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can subtract the x from both sides of the equation...<BR>\n" );
document.write( "x + 3 - x = 3 and -2x -x = -3x<BR>\n" );
document.write( "so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%3C=+-3x ALIGN=MIDDLE  ALT=\"3%3C=+-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, this may get a little tricky...<BR>\n" );
document.write( "We need to isolate the variable x. In order to do that we need to divide both sides by -3.<BR>\n" );
document.write( "However, the rule for inequalities is that when we divide by a NEGATIVE number, we ALWAYS have to chanbge the inequality sign. so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%3C=+-3x ALIGN=MIDDLE  ALT=\"3%3C=+-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > 3/-3 = -1 and 3x/3 = x <BR>\n" );
document.write( "And remember to change the sign.<BR>\n" );
document.write( "So...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3E=+x ALIGN=MIDDLE  ALT=\"-1%3E=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So this tells us that our variable x will always be less than or equal to -1.<BR>\n" );
document.write( "The bracket ] tells us that -1 is included.<BR>\n" );
document.write( "So we show this in interval notation...<BR>\n" );
document.write( "(-~,-1] or (negative infinity, -1]<BR>\n" );
document.write( "I hope this helps.<BR>\n" );
document.write( "Good Luck! <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );