document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158239>Question 158239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each inequality. Graph the solutions.\r<BR>\n" );
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document.write( "5|2b+1|-3< 7<BR>\n" );
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document.write( "the <  is like 7 is greater than or equal to<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 #116609 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=116609\">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=5%2Aabs%282b%2B1%29-3%3C=7 ALIGN=MIDDLE  ALT=\"5%2Aabs%282b%2B1%29-3%3C=7\"   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=5%2Aabs%282b%2B1%29%3C=10 ALIGN=MIDDLE  ALT=\"5%2Aabs%282b%2B1%29%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282b%2B1%29%3C=2 ALIGN=MIDDLE  ALT=\"abs%282b%2B1%29%3C=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5\r<BR>\n" );
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document.write( "Break up the absolute value (remember, if you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29%3C=+a ALIGN=MIDDLE  ALT=\"abs%28x%29%3C=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+-a ALIGN=MIDDLE  ALT=\"x+%3E=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C=+a ALIGN=MIDDLE  ALT=\"x+%3C=+a\"   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=2b%2B1+%3E=+-2 ALIGN=MIDDLE  ALT=\"2b%2B1+%3E=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B1+%3C=+2 ALIGN=MIDDLE  ALT=\"2b%2B1+%3C=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the absolute value inequality using the given rule\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+%3C=+2b%2B1+%3C=+2 ALIGN=MIDDLE  ALT=\"-2+%3C=+2b%2B1+%3C=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the two inequalities to get a compound inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3+%3C=+2b+%3C=+1 ALIGN=MIDDLE  ALT=\"-3+%3C=+2b+%3C=+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=-3%2F2+%3C=+b+%3C=+1%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2+%3C=+b+%3C=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Divide all sides by 2 to isolate b\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is\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{-\frac{3}{2},\frac{1}{2}}\"><font size=\"8\">]</font>\r<BR>\n" );
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document.write( "and the answer in set-builder notation is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{b\|-\frac{3}{2} \le b \le \frac{1}{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-8%2C+6%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-8%2C+6+%2C-3%2F2+%2C+1%2F2%29%2C%0D%0A%0D%0Ablue%28line%28-3%2F2+%2C0%2C+1%2F2%2C0%29%29%2C%0D%0Ablue%28line%28-3%2F2+%2C0.30%2C+1%2F2%2C0.30%29%29%2C%0D%0Ablue%28line%28-3%2F2+%2C0.15%2C+1%2F2%2C0.15%29%29%2C%0D%0Ablue%28line%28-3%2F2+%2C-0.15%2C+1%2F2%2C-0.15%29%29%2C%0D%0Ablue%28line%28-3%2F2+%2C-0.30%2C+1%2F2%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=b=-3%2F2+ ALIGN=MIDDLE  ALT=\"b=-3%2F2+\"   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=b=+1%2F2 ALIGN=MIDDLE  ALT=\"b=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including this value in the solution set. </SPAN>\n" );
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