document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134247>Question 134247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality. State the solution set in interval notation and sketch its graph. \r<BR>\n" );
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document.write( "1/6 - 1/3t > 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98178 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=98178\">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=1%2F6-%281%2F3%29t%3E0 ALIGN=MIDDLE  ALT=\"1%2F6-%281%2F3%29t%3E0\"   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=%286%29%281%2Fcross%286%29-%281%2Fcross%283%29%29t%29=%286%29%280%29 ALIGN=MIDDLE  ALT=\"%286%29%281%2Fcross%286%29-%281%2Fcross%283%29%29t%29=%286%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCM of 6. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2t=0 ALIGN=MIDDLE  ALT=\"1-2t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply the LCM to each side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2t%3E0-1 ALIGN=MIDDLE  ALT=\"-2t%3E0-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2t%3E-1 ALIGN=MIDDLE  ALT=\"-2t%3E-1\"   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=t%3C%28-1%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"t%3C%28-1%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2 to isolate t  (note: Remember, dividing both sides by a negative number flips the inequality sign) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C1%2F2 ALIGN=MIDDLE  ALT=\"t%3C1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "--------------------------------------------------------------\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C1%2F2 ALIGN=MIDDLE  ALT=\"t%3C1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (which is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C0.5 ALIGN=MIDDLE  ALT=\"t%3C0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form)\r<BR>\n" );
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document.write( "So the answer in interval notation is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty,\frac{1}{2}\right)\">\r<BR>\n" );
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document.write( "And here's the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C1%2F2 ALIGN=MIDDLE  ALT=\"t%3C1%2F2\"   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=drawing%28500%2C50%2C-9%2C11%2C-10%2C10%2C%0D%0Anumber_line%28500%2C-9%2C11%29%2C%0D%0Acircle%281%2F2%2C-5.8%2C0.35%29%2C%0D%0Acircle%281%2F2%2C-5.8%2C0.4%29%2C%0D%0Acircle%281%2F2%2C-5.8%2C0.45%29%2C%0D%0Ablue%28line%281%2F2%2C-5%2C1%2F2-10%2C-5%29%29%2C%0D%0Ablue%28line%281%2F2%2C-6%2C1%2F2-10%2C-6%29%29%2C%0D%0Ablue%28line%281%2F2%2C-7%2C1%2F2-10%2C-7%29%29%2C%0D%0Ablue%28arrow%281%2F2%2C-5%2C1%2F2-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%281%2F2%2C-5.5%2C1%2F2-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%281%2F2%2C-6%2C1%2F2-10.2%2C-6%29%29%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=t%3C1%2F2 ALIGN=MIDDLE  ALT=\"t%3C1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in blue\r<BR>\n" );
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document.write( "note: at the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1%2F2 ALIGN=MIDDLE  ALT=\"t=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is an <font size=4><b>open</b></font> circle. This means the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1%2F2 ALIGN=MIDDLE  ALT=\"t=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is excluded from the solution set.\r<BR>\n" );
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document.write( "     </SPAN>\n" );
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