document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209292>Question 1209292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality<BR>\n" );
document.write( "(3 - z)/(z + 1) \ge 2 + 1/(z - 7).<BR>\n" );
document.write( "Write your answer in interval notation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848118 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=848118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem would be far more educational if the answers were not so ugly....<br><BR>\n" );
document.write( "To solve an inequality like this, get everything on the left with 0 on the right and write the expression on the left as a single rational expression.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-z%29%2F%28z%2B1%29-2-1%2F%28z-7%29%3E=0 ALIGN=MIDDLE  ALT=\"%283-z%29%2F%28z%2B1%29-2-1%2F%28z-7%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%283-z%29%28z-7%29-2%28z%2B1%29%28z-7%29-1%28z%2B1%29%29%2F%28%28z%2B1%29%28z-7%29%29%3E=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283z-21-z%5E2%2B7z-2z%5E2%2B12z%2B14-z-1%29%2F%28%28z%2B1%29%28z-7%29%29%3E=0 ALIGN=MIDDLE  ALT=\"%283z-21-z%5E2%2B7z-2z%5E2%2B12z%2B14-z-1%29%2F%28%28z%2B1%29%28z-7%29%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=%28-3z%5E2%2B21z-8%29%2F%28%28z%2B1%29%28z-7%29%29%3E=0 ALIGN=MIDDLE  ALT=\"%28-3z%5E2%2B21z-8%29%2F%28%28z%2B1%29%28z-7%29%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The expression is undefined where the denominator is zero -- at z=-1 and z=7.<br><BR>\n" );
document.write( "The expression value is zero where the numerator is zero.  The quadratic in the numerator has irrational roots, which for simplicity I will represent with A and B.  The values of those roots are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2821-sqrt%28345%29%29%2F6 ALIGN=MIDDLE  ALT=\"A=%2821-sqrt%28345%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = approximately 0.4043041<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%2821%2Bsqrt%28345%29%29%2F6 ALIGN=MIDDLE  ALT=\"B=%2821%2Bsqrt%28345%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = approximately 6.5956959<br><BR>\n" );
document.write( "The four zeros of the numerator and denominator break the number line into 5 intervals.  Use test points or other methods to determine the intervals on which the expression value is greater than or equal to 0.<br><BR>\n" );
document.write( "(1) (-infinity,-1) negative<BR>\n" );
document.write( "(2) (-1,A] positive or zero<BR>\n" );
document.write( "(3) (A,B) negative<BR>\n" );
document.write( "(4) [B,7) zero or positive<BR>\n" );
document.write( "(5) (7,infinity) negative<br><BR>\n" );
document.write( "ANSWER: The inequality is true on the two intervals (-1,A] and [B,7)<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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