document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93536>Question 93536</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013062568X/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> solve and graph the solution:<BR>\n" );
document.write( "2(m-3) + 7 < 21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68109 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=68109\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28m-3%29+%2B+7+%3C+21 ALIGN=MIDDLE  ALT=\"2%28m-3%29+%2B+7+%3C+21\"   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=2m-6+%2B+7+%3C+21 ALIGN=MIDDLE  ALT=\"2m-6+%2B+7+%3C+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%2B7%3C21%2B6 ALIGN=MIDDLE  ALT=\"2m%2B7%3C21%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 6 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%2B7%3C27 ALIGN=MIDDLE  ALT=\"2m%2B7%3C27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3C%2827%29%2F%282%29 ALIGN=MIDDLE  ALT=\"m%3C%2827%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2 to isolate m\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3C%2827%29%2F%282%29 ALIGN=MIDDLE  ALT=\"m%3C%2827%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3C13.5 ALIGN=MIDDLE  ALT=\"m%3C13.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form\r<BR>\n" );
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document.write( "Now lets graph the solution set of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3C13.5 ALIGN=MIDDLE  ALT=\"m%3C13.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set up a number line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28500%2C3.5%2C23.5%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C3.5%2C23.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > note: just replace the x with the variable you are working with\r<BR>\n" );
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document.write( "Now plot the point m=13.5 on the number line\r<BR>\n" );
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document.write( "Now pick any test point you want, I'm going to choose m=0, and test the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3C13.5 ALIGN=MIDDLE  ALT=\"m%3C13.5\"   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=0%3C13.5 ALIGN=MIDDLE  ALT=\"0%3C13.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0 ALIGN=MIDDLE  ALT=\"m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since this inequality is true, we simply shade the entire portion in which contains the point m=0 using the point m=13.5 as the boundary.This means we shade everything to the left of the point m=13.5 like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C50%2C3.5%2C23.5%2C-10%2C10%2C%0D%0Anumber_line%28500%2C3.5%2C23.5%29%2C%0D%0Acircle%2813.5%2C-5.8%2C0.35%29%2C%0D%0Acircle%2813.5%2C-5.8%2C0.4%29%2C%0D%0Acircle%2813.5%2C-5.8%2C0.45%29%2C%0D%0Ablue%28line%2813.5%2C-5%2C13.5-10%2C-5%29%29%2C%0D%0Ablue%28line%2813.5%2C-6%2C13.5-10%2C-6%29%29%2C%0D%0Ablue%28line%2813.5%2C-7%2C13.5-10%2C-7%29%29%2C%0D%0Ablue%28arrow%2813.5%2C-5%2C13.5-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%2813.5%2C-5.5%2C13.5-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%2813.5%2C-6%2C13.5-10.2%2C-6%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3C13.5 ALIGN=MIDDLE  ALT=\"m%3C13.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in blue\r<BR>\n" );
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document.write( "note: at the point m=13.5, there is an <b>open</b> circle. This means the point m=13.5 is excluded from the solution set.\r<BR>\n" );
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