document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199000>Question 1199000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x the inequality equation  (x+9)/(x+1) -2 > 0\r<BR>\n" );
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document.write( "The correct answer is one of the following.  Which one is correct?\r<BR>\n" );
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document.write( "A) -1 < x < 7\r<BR>\n" );
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document.write( "B) x > 7\r<BR>\n" );
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document.write( "C) -1 < x < 8\r<BR>\n" );
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document.write( "D) x > 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832688 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Given the answer choices, by far the quickest path to the answer is to see which one works.  From the given answer choices, the x values -1, 7, and 8 need to be the endpoints of the solution interval(s) -- which means the value of the expression is either 0 or undefined at those values.<br><BR>\n" );
document.write( "The expression is undefined at x=-1 and 0 at x=7; it is neither 0 nor undefined at x=8.  Since the inequality is a strict inequality (endpoints of the intervals not included), the solution set is either (-1,7) or (-infinity,-1) U (7,infinity).  But that second possibility is not one of the answer choices, so<br><BR>\n" );
document.write( "ANSWER: A) (-1,7)<br><BR>\n" );
document.write( "But surely the intended purpose of the problem was for you to learn how to get that answer....<br><BR>\n" );
document.write( "Keep everything on one side of the inequality, with \"0\" on the other side; and combine the terms on the left with a common denominator so the expression is a rational function.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%29%2F%28x%2B1%29+-2+%3E+0 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28x%2B1%29+-2+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%29%2F%28x%2B1%29-%282%28x%2B1%29%29%2F%28x%2B1%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28x%2B1%29-%282%28x%2B1%29%29%2F%28x%2B1%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9-2x-2%29%2F%28x%2B1%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28x%2B9-2x-2%29%2F%28x%2B1%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%2B7%29%2F%28x%2B1%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28-x%2B7%29%2F%28x%2B1%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That rational function is equal to 0 at x = 7 and is undefined at x = -1, so those are endpoints of the interval(s) of the solution set.  And evaluating the expression at x = 0 shows the inequality is satisfied, so the solution set is (-1,7).<br><BR>\n" );
document.write( " </SPAN>\n" );
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