document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148164>Question 148164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I worked out the inequality and found the possible solutions but do not feel like I am writing the interval notation correctly.  I would appreciate your help and a big thank you in advance.  6x^2+25x+14<=0<BR>\n" );
document.write( "In the end I have -2/3 and -7/2  so far I have ( -7/2]  U [-2/3) with the infinities before the -7/2 and the -2/3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108556 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=108556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B25x%2B14%3C=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B25x%2B14%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B7%29%283x%2B2%29%3C=0 ALIGN=MIDDLE  ALT=\"%282x%2B7%29%283x%2B2%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor the left side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B7%29%283x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B7%29%283x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the left side equal to zero\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set each individual factor equal to zero:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B7=0 ALIGN=MIDDLE  ALT=\"2x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2=0 ALIGN=MIDDLE  ALT=\"3x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve for x in each case:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7%2F2 ALIGN=MIDDLE  ALT=\"x=-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2F3 ALIGN=MIDDLE  ALT=\"x=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our critical values are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7%2F2 ALIGN=MIDDLE  ALT=\"x=-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2F3 ALIGN=MIDDLE  ALT=\"x=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now set up a number line and plot the critical values on the number line\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28+600%2C+-10%2C+10%2C-7%2F2%2C-2%2F3%29 ALIGN=MIDDLE  ALT=\"number_line%28+600%2C+-10%2C+10%2C-7%2F2%2C-2%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's pick some test points that are near the critical values and evaluate them.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's pick a test value that is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F2 ALIGN=MIDDLE  ALT=\"-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how it's to the left of the leftmost endpoint):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's pick <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B25x%2B14%3C=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B25x%2B14%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28-4%29%2B7%29%283%28-4%29%2B2%29%3C=+0 ALIGN=MIDDLE  ALT=\"%282%28-4%29%2B7%29%283%28-4%29%2B2%29%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%3C=+0 ALIGN=MIDDLE  ALT=\"10%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the inequality is false, this means that the interval does <b>not</b> work. So this interval is <b>not</b> in our solution set and we can ignore it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's pick a test value that is in between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F2 ALIGN=MIDDLE  ALT=\"-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's pick <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B25x%2B14%3C=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B25x%2B14%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28-2%29%2B7%29%283%28-2%29%2B2%29%3C=+0 ALIGN=MIDDLE  ALT=\"%282%28-2%29%2B7%29%283%28-2%29%2B2%29%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%3C=+0 ALIGN=MIDDLE  ALT=\"-12%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r<BR>\n" );
document.write( "\n" );
document.write( "   So part our solution in interval notation is <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{7}{2},-\frac{2}{3}\"><font size=\"8\">]</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's pick a test value that is greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how it's to the right of the rightmost endpoint):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's pick <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B25x%2B14%3C=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B25x%2B14%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%281%29%2B7%29%283%281%29%2B2%29%3C=+0 ALIGN=MIDDLE  ALT=\"%282%281%29%2B7%29%283%281%29%2B2%29%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%3C=+0 ALIGN=MIDDLE  ALT=\"45%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the inequality is false, this means that the interval does <b>not</b> work. So this interval is <b>not</b> in our solution set and we can ignore it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Summary:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solution in interval notation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{7}{2},-\frac{2}{3}\"><font size=\"8\">]</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's a graph to prove it\r<BR>\n" );
document.write( "\n" );
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+%282x%2B7%29%283x%2B2%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%282x%2B7%29%283x%2B2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );