document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114832>Question 114832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x/3 - 2 &#8804; 8 - x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83600 by </B><A HREF=/tutors/aboutme.mpl?userid=jgr45><B>jgr45(31)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jgr45><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=jgr45><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83600\">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=2x%2F3 ALIGN=MIDDLE  ALT=\"2x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-2 &#8804; 8-x\r<BR>\n" );
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document.write( "First off, remember that inequalities are solved exactly the same way as equations.  The only difference is when you multiply/divide by a negative number, the sign has to change to the opposite.\r<BR>\n" );
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document.write( "Start by multiplying each term by 3 to eliminate the fraction:\r<BR>\n" );
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document.write( "2x - 6 &#8804; 24 - 3x\r<BR>\n" );
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document.write( "Now get the variables on one side and constants on the other:\r<BR>\n" );
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document.write( "2x &#8804; 30 - 3x (adding 6)<BR>\n" );
document.write( "5x &#8804; 30 (adding 3x)\r<BR>\n" );
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document.write( "x &#8804; 6\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F3 ALIGN=MIDDLE  ALT=\"2x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-2 =? 8-x\r<BR>\n" );
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document.write( "To check your answer, treat the expression as an equation, because we're only concerned with the boundary, or endpoint, of the graph.  Subbing 6 for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%286%29%2F3 ALIGN=MIDDLE  ALT=\"2%286%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-2 =? 8-6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F3 ALIGN=MIDDLE  ALT=\"12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-2 =? 2<BR>\n" );
document.write( "4-2 =? 2<BR>\n" );
document.write( "2 = 2, Check.\r<BR>\n" );
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document.write( "Now to check to see if the graph is going in the correct direction, often a good number to try is 0 (the origin).  So--plug in 0 for x, and this time keep the original sign:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%29%2F3 ALIGN=MIDDLE  ALT=\"2%280%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-2 &#8804;? 8-0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F3 ALIGN=MIDDLE  ALT=\"0%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-2 &#8804;? 8<BR>\n" );
document.write( "Please note that it is permissible for a dividend/numerator to be 0.  It is the DIVISOR, or DENOMINATOR, that cannot be 0.<BR>\n" );
document.write( "0-2 &#8804;? 8<BR>\n" );
document.write( "-2 &#8804; 8 -- A true statement, so 0 should be included in the solution and should be part of the graph.  Therefore the arrow should be drawn in the direction from 6 that includes 0, namely the left side.\r<BR>\n" );
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document.write( "If you were asked to graph the solution, it would be a closed point at 6 and everything to the left. </SPAN>\n" );
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