document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277460>Question 277460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a non-zero integer n is  chosen such that (2-16/n) is an integer less than 6<BR>\n" );
document.write( "Which of the following must be true of n ?\r<BR>\n" );
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document.write( "A -8   b -6  c -4  d -3  e -1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201994 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=201994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given <BR>\n" );
document.write( "n is a non-zero integer and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%2816%2Fn%29+%3C+6 ALIGN=MIDDLE  ALT=\"2-%2816%2Fn%29+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "find n<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%2816%2Fn%29+%3C+6 ALIGN=MIDDLE  ALT=\"2-%2816%2Fn%29+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > collect like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2816%2Fn%29+%3C+4 ALIGN=MIDDLE  ALT=\"-%2816%2Fn%29+%3C+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Fn+%3C+0+ ALIGN=MIDDLE  ALT=\"-4%2Fn+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now here is the tricky part. In order to isolate n, we need to multiply through by n. If n is positive, then the inequality sign stays 'less than'. However, if n is negative, then the inequalty changes to 'greater than'.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C+n ALIGN=MIDDLE  ALT=\"-4+%3C+n\"   DISABLED_style= \"max-width:90%; height:auto;\" > when n > 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3E+n+ ALIGN=MIDDLE  ALT=\"-4+%3E+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when n < 0\r<BR>\n" );
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document.write( "Every one of the possible answers A through E are negative. So we need to use the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3E+n+ ALIGN=MIDDLE  ALT=\"-4+%3E+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which possible answers are less than -4? Only -8 and -6 (A and B)\r<BR>\n" );
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document.write( "BUT, your problem stated the result had to be < 6 and an integer. You can see that 16/-6 is not an integer, so -6 won't work. 16/-8 is an integer. \r<BR>\n" );
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document.write( "Answer is -8 (A)\r<BR>\n" );
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document.write( "Check that answer by plugging -8 in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-+%2816%2F%28-8%29%29+%3C+6 ALIGN=MIDDLE  ALT=\"2+-+%2816%2F%28-8%29%29+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%2B+2+%3C+6 ALIGN=MIDDLE  ALT=\"2+%2B+2+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%3C+6 ALIGN=MIDDLE  ALT=\"4+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is true. So -8 works<BR>\n" );
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