document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168704>Question 168704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given x-1(less then or equal to)3x + 1(less than or equal to) x + 5. Solve for x and show your answer on the number line and in interval notaion.  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124360 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=124360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%3C=3x%2B1%3C=x%2B5 ALIGN=MIDDLE  ALT=\"x-1%3C=3x%2B1%3C=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given compound inequality.\r<BR>\n" );
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document.write( "Break up the compound inequality to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%3C=3x%2B1 ALIGN=MIDDLE  ALT=\"x-1%3C=3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B1%3C=x%2B5 ALIGN=MIDDLE  ALT=\"3x%2B1%3C=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So let's solve the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%3C=3x%2B1 ALIGN=MIDDLE  ALT=\"x-1%3C=3x%2B1\"   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=x-1%3C=3x%2B1 ALIGN=MIDDLE  ALT=\"x-1%3C=3x%2B1\"   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=x%3C=3x%2B1%2B1 ALIGN=MIDDLE  ALT=\"x%3C=3x%2B1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3x%3C=1%2B1 ALIGN=MIDDLE  ALT=\"x-3x%3C=1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   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=-2x%3C=1%2B1 ALIGN=MIDDLE  ALT=\"-2x%3C=1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%3C=2 ALIGN=MIDDLE  ALT=\"-2x%3C=2\"   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=x%3E=%282%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x%3E=%282%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. note: Remember, the inequality sign flips when we divide both sides by a negative number. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=-1 ALIGN=MIDDLE  ALT=\"x%3E=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Now let's solve the second inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B1%3C=x%2B5 ALIGN=MIDDLE  ALT=\"3x%2B1%3C=x%2B5\"   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=3x%2B1%3C=x%2B5 ALIGN=MIDDLE  ALT=\"3x%2B1%3C=x%2B5\"   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=3x%3C=x%2B5-1 ALIGN=MIDDLE  ALT=\"3x%3C=x%2B5-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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=3x-x%3C=5-1 ALIGN=MIDDLE  ALT=\"3x-x%3C=5-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=2x%3C=5-1 ALIGN=MIDDLE  ALT=\"2x%3C=5-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3C=4 ALIGN=MIDDLE  ALT=\"2x%3C=4\"   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=x%3C=%284%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x%3C=%284%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=x%3C=2 ALIGN=MIDDLE  ALT=\"x%3C=2\"   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 solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=-1 ALIGN=MIDDLE  ALT=\"x%3E=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <b>and</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=2 ALIGN=MIDDLE  ALT=\"x%3C=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Our answer also looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=x%3C=2 ALIGN=MIDDLE  ALT=\"-1%3C=x%3C=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the answer in interval notation is   <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{-1,2}\"><font size=\"8\">]</font>\r<BR>\n" );
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document.write( "Also, the answer in set-builder notation is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|-1 \le x \le 2\right\}\">\r<BR>\n" );
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document.write( "Here's the graph of the solution set\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C80%2C-6%2C+7%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-6%2C+7+%2C-1%2C2%29%2C%0D%0A%0D%0Ablue%28line%28-1%2C0%2C2%2C0%29%29%2C%0D%0Ablue%28line%28-1%2C0.30%2C2%2C0.30%29%29%2C%0D%0Ablue%28line%28-1%2C0.15%2C2%2C0.15%29%29%2C%0D%0Ablue%28line%28-1%2C-0.15%2C2%2C-0.15%29%29%2C%0D%0Ablue%28line%28-1%2C-0.30%2C2%2C-0.30%29%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the solution set\r<BR>\n" );
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document.write( "Note:\r<BR>\n" );
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document.write( "There is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including this value in the solution set\r<BR>\n" );
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document.write( "Also, there is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including this value in the solution set.<BR>\n" );
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