document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208859>Question 1208859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality. Express your answer using set notation and interval notation.  Graph the solution set.\r<BR>\n" );
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document.write( "(1/3) < [(x + 1)/2] <= (2/3)\r<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 #847352 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3+%3C+%28x%2B1%29%2F2+%3C=+2%2F3 ALIGN=MIDDLE  ALT=\"1%2F3+%3C+%28x%2B1%29%2F2+%3C=+2%2F3\"   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=2%2A%281%2F3%29+%3C+2%2A%28x%2B1%29%2F2+%3C=+2%2A%282%2F3%29 ALIGN=MIDDLE  ALT=\"2%2A%281%2F3%29+%3C+2%2A%28x%2B1%29%2F2+%3C=+2%2A%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply all sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+%3C+x%2B1+%3C=+4%2F3 ALIGN=MIDDLE  ALT=\"2%2F3+%3C+x%2B1+%3C=+4%2F3\"   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=2%2F3+-+1+%3C+x%2B1-1+%3C=+4%2F3+-+1 ALIGN=MIDDLE  ALT=\"2%2F3+-+1+%3C+x%2B1-1+%3C=+4%2F3+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from all sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+-+3%2F3+%3C+x+%3C=+4%2F3+-+3%2F3 ALIGN=MIDDLE  ALT=\"2%2F3+-+3%2F3+%3C+x+%3C=+4%2F3+-+3%2F3\"   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=-1%2F3+%3C+x+%3C=+1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3+%3C+x+%3C=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The answer in set builder notation would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left{\text{x} | \text{x}\in\mathbb{R}, \ -\frac{1}{3} < \text{x} \le \frac{1}{3}\right}\"><BR>\n" );
document.write( "That translates to \"x is any real number between -1/3 and 1/3; excluding -1/3 but including 1/3\".\r<BR>\n" );
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document.write( "The interval notation would be (-1/3, 1/3]<BR>\n" );
document.write( "A curved parenthesis means we exclude the endpoint -1/3.<BR>\n" );
document.write( "A square bracket is there to include the endpoint 1/3.\r<BR>\n" );
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document.write( "Here's the graph on a number line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C200%2C-6%2C6%2C-3%2C3%2C%0D%0Aline%28-10%2C0%2C10%2C0%29%2Cline%28-5%2C0.04%2C-5%2C-0.04%29%2Cline%28-2.5%2C0.04%2C-2.5%2C-0.04%29%2Cline%280%2C0.04%2C0%2C-0.04%29%2Cline%282.5%2C0.04%2C2.5%2C-0.04%29%2Cline%285%2C0.04%2C5%2C-0.04%29%2Clocate%28-5.1%2C-0.25%2C%22-2%22%29%2Clocate%28-2.6%2C-0.25%2C%22-1%22%29%2Clocate%28-0.05%2C-0.25%2C%220%22%29%2Clocate%282.45%2C-0.25%2C%221%22%29%2Clocate%284.95%2C-0.25%2C%222%22%29%2C%0D%0Ared%28%0D%0Acircle%28-5%2F6%2C0%2C0.18%29%2Ccircle%28-5%2F6%2C0%2C0.20%29%2Ccircle%28-5%2F6%2C0%2C0.22%29%2Ccircle%28-5%2F6%2C0%2C0.24%29%2C%0D%0Acircle%285%2F6%2C0%2C0.06%29%2Ccircle%285%2F6%2C0%2C0.08%29%2Ccircle%285%2F6%2C0%2C0.10%29%2Ccircle%285%2F6%2C0%2C0.12%29%2Ccircle%285%2F6%2C0%2C0.14%29%2Ccircle%285%2F6%2C0%2C0.16%29%2Ccircle%285%2F6%2C0%2C0.18%29%2Ccircle%285%2F6%2C0%2C0.20%29%2Ccircle%285%2F6%2C0%2C0.22%29%2Ccircle%285%2F6%2C0%2C0.24%29%2C%0D%0Aline%28-5%2F6%2B0.2%2C0%2B0.08%2C5%2F6%2C0%2B0.08%29%2C%0D%0Aline%28-5%2F6%2B0.2%2C0%2B0.06%2C5%2F6%2C0%2B0.06%29%2C%0D%0Aline%28-5%2F6%2B0.2%2C0%2C5%2F6%2C0%29%2C%0D%0Aline%28-5%2F6%2B0.2%2C0-0.08%2C5%2F6%2C0-0.08%29%2C%0D%0Aline%28-5%2F6%2B0.2%2C0-0.06%2C5%2F6%2C0-0.06%29%2C%0D%0Alocate%28-5%2F6-0.5%2C0.2%2B0.5%2C%22-1%2F3%22%29%2C%0D%0Alocate%285%2F6-0.2%2C0.2%2B0.5%2C%221%2F3%22%29%0D%0A%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Described in words: plot an open hole at -1/3 and a closed filled in circle at 1/3. Shade in between. \r<BR>\n" );
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document.write( "Another way to express the diagram could be like this<BR>\n" );
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document.write( "              -1/3     1/3\r\n" );
document.write( "--|--------|-----O==|==●-----|--------|--\r\n" );
document.write( " -2       -1        0        1        2 \r\n" );
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