document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123204>Question 123204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x+y<9 ,     the < or > signs means equal to or greater or lesser than.<BR>\n" );
document.write( "x-y<7,       the > has a line under it.  Didn't know how to make it on here.<BR>\n" );
document.write( "x>0,\r<BR>\n" );
document.write( "\n" );
document.write( "Which of the following points satisfy the inequalities?<BR>\n" );
document.write( "      (2,5),  ( 0,9),  (3,-2) or  (-1,0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90407 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=90407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The best way is to plot these<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+y+%3C+9 ALIGN=MIDDLE  ALT=\"3x+%2B+y+%3C+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+y+%3C+7 ALIGN=MIDDLE  ALT=\"x+-+y+%3C+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+0 ALIGN=MIDDLE  ALT=\"x+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+y+%3C+9 ALIGN=MIDDLE  ALT=\"3x+%2B+y+%3C+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+-3x+%2B+9 ALIGN=MIDDLE  ALT=\"y+%3C+-3x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+y+%3C+7 ALIGN=MIDDLE  ALT=\"x+-+y+%3C+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+%3C+-x+%2B+7 ALIGN=MIDDLE  ALT=\"-y+%3C+-x+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and reverse the < sign<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E+x+-+7 ALIGN=MIDDLE  ALT=\"y+%3E+x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E0 ALIGN=MIDDLE  ALT=\"x+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > No <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > involved here. This is saying that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "can never be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or negative. It's domain is the right half of<BR>\n" );
document.write( "the graph<BR>\n" );
document.write( "I'll do a plot of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+-3x+%2B+9 ALIGN=MIDDLE  ALT=\"y+%3C+-3x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E+x+-+7 ALIGN=MIDDLE  ALT=\"y+%3E+x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-2%2C+30%2C+-15%2C+15%2C+-3x+%2B+9%2Cx+-+7%29 ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-2%2C+30%2C+-15%2C+15%2C+-3x+%2B+9%2Cx+-+7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution is the little triangular area bounded by the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > axis<BR>\n" );
document.write( "and the lines. Now see which points are in that area<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(2,5) looks to be just outside, and it fails (1) because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+-3x+%2B+9 ALIGN=MIDDLE  ALT=\"y+%3C+-3x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%3C+%28-3%29%2A2+%2B+9 ALIGN=MIDDLE  ALT=\"5+%3C+%28-3%29%2A2+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%3C+-6+%2B+9 ALIGN=MIDDLE  ALT=\"5+%3C+-6+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%3C+3 ALIGN=MIDDLE  ALT=\"5+%3C+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is clearly not true<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(0,9) This looks like it might be in the area, but it fails (1) also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+-3x+%2B+9 ALIGN=MIDDLE  ALT=\"y+%3C+-3x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%3C+%28-3%29%2A0+%2B+9 ALIGN=MIDDLE  ALT=\"9+%3C+%28-3%29%2A0+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%3C+9 ALIGN=MIDDLE  ALT=\"9+%3C+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is clearly not true also<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(3,-2) This fails in the area<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(-1,0) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > can't be negative, as I said, and it is<BR>\n" );
document.write( "also clearly outside the area<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "So, only (3,-2) satisfies the inequalities answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );