document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121697>Question 121697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please assisyt me in the following:<BR>\n" );
document.write( "Graph the following inequalities:<BR>\n" );
document.write( "2x-2>5\r<BR>\n" );
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document.write( "7x-3>_16\r<BR>\n" );
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document.write( "Trying to help my daughter with her homework.<BR>\n" );
document.write( "Randy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89389 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It looks like you may have forgotten part of these equations when you wrote them.\r<BR>\n" );
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document.write( "In their current state, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2%3E5 ALIGN=MIDDLE  ALT=\"2x-2%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > needs to be solved for x, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2%3E5 ALIGN=MIDDLE  ALT=\"2x-2%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3E5%2B2 ALIGN=MIDDLE  ALT=\"2x%3E5%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3E7 ALIGN=MIDDLE  ALT=\"2x%3E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E7%2F2 ALIGN=MIDDLE  ALT=\"x%3E7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On the number line, this would graph by putting a circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to indicate that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > itself is NOT an element of the solution set, and then making a heavy line to the right of your circle to indicate that everything larger than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > IS an element of the solution set.\r<BR>\n" );
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document.write( "The second problem comes out to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=19%2F7 ALIGN=MIDDLE  ALT=\"x%3E=19%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since you have \"or equal,\" you would make a solid dot at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F7 ALIGN=MIDDLE  ALT=\"19%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F7 ALIGN=MIDDLE  ALT=\"19%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > IS included in the solution set.\r<BR>\n" );
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document.write( "If you are trying to graph these on a coordinate plane, you would either have a dashed vertical line at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with everything to the right shaded for the first problem, or a solid vertical line at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F7 ALIGN=MIDDLE  ALT=\"19%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > with everything to the right shaded for the second problem.\r<BR>\n" );
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document.write( "On the other hand, if you really meant to write\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2y%3E5 ALIGN=MIDDLE  ALT=\"2x-2y%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-3y%3E=16 ALIGN=MIDDLE  ALT=\"7x-3y%3E=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That is another story altogether.\r<BR>\n" );
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document.write( "In this case, solve the inequality for y.  Then graph the analogous equation. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2y%3E5 ALIGN=MIDDLE  ALT=\"2x-2y%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y%3E-2x%2B5 ALIGN=MIDDLE  ALT=\"-2y%3E-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by -2 (remember, since you are dividing by a negative, reverse the sense of the inequality)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3Cx-%285%2F2%29 ALIGN=MIDDLE  ALT=\"y%3Cx-%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The analogous equation would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-%285%2F2%29 ALIGN=MIDDLE  ALT=\"y=x-%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a line with a slope of 1 and a y-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%285%2F2%29 ALIGN=MIDDLE  ALT=\"-%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Go ahead and plot this line on the graph, but you need to make it a dashed line because the original inequality did not include equality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx-%285%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx-%285%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The last thing is to determine which half-plane to shade.  Select a convenient point that is NOT on the line.  Let's pick (1,1) which is above and to the left of the line, and substitute these coordinate values into the original equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%29-2%281%29%3E5 ALIGN=MIDDLE  ALT=\"2%281%29-2%281%29%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E5 ALIGN=MIDDLE  ALT=\"0%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This statement is clearly false, therefore the selected point is on the wrong side of the line -- so shade in the other side.  Your final result should be a dashed line where the line on the graph above is, with everything below and to the right of the line shaded.\r<BR>\n" );
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document.write( "The dashed line means that points ON the line are NOT included in the solution set.  For example, the point (1,-3/2) is on the line but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%29-2%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"2%281%29-2%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals 5, but is not greater than 5.\r<BR>\n" );
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document.write( "The other equation will work out pretty much the same way, except that you will have a solid line because the inequality includes equals.\r<BR>\n" );
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document.write( "Write back if you are still having trouble.\r<BR>\n" );
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document.write( "John </SPAN>\n" );
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