document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148204>Question 148204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the inequality 6+3y<4(3-x) for y and graph the solution. Please show me this step by step because I think I went wrong somewhere down the line, and I need to see where. Thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108601 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=108601\">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=6%2B3y%3C4%283-x%29 ALIGN=MIDDLE  ALT=\"6%2B3y%3C4%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B3y%3C12-4x ALIGN=MIDDLE  ALT=\"6%2B3y%3C12-4x\"   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=3y%3C12-4x-6 ALIGN=MIDDLE  ALT=\"3y%3C12-4x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%3C-4x%2B6 ALIGN=MIDDLE  ALT=\"3y%3C-4x%2B6\"   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=y%3C%28-4x%2B6%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y%3C%28-4x%2B6%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y%3C%28-4x%29%2F%283%29%2B%286%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y%3C%28-4x%29%2F%283%29%2B%286%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y%3C-%284%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y%3C-%284%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=-%284%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (replace the inequality sign with an equals sign)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=-%284%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in a test point (0,0) into the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y%3C-%284%2F3%29x%2B2\"   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=y%3C-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y%3C-%284%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C-%284%2F3%29%2A%280%29%2B2 ALIGN=MIDDLE  ALT=\"0%3C-%284%2F3%29%2A%280%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   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%3C2 ALIGN=MIDDLE  ALT=\"0%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify.\r<BR>\n" );
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document.write( "Since the inequality is true, this means that we shade the entire region that contains the point (0,0)\r<BR>\n" );
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document.write( "In other words, we simply shade the <b>entire</b> region that is below the line.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-0%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-2.66666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-5.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-8%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-10.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-13.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-16%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-18.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-21.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-26.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-29.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-32%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-34.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-37.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-40%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-42.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F3%29x%2B2%2C-%284%2F3%29x%2B2-45.3333333333333%29%0D%0A%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=y%3C-%284%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y%3C-%284%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in green\r<BR>\n" );
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document.write( "note: the boundary should be a dotted line.<BR>\n" );
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