document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90385>Question 90385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sole each inequality. State the solution set interval notation and sketch its graph!\r<BR>\n" );
document.write( "\n" );
document.write( "1/6 - 1/3 t > 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Please Help :( </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65976 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=65976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The goal in this problem is to solve for t. You can do this by basically using the same rules<BR>\n" );
document.write( "and procedures as you would for solving an equation with two exceptions. First, you replace <BR>\n" );
document.write( "the equal sign of an equation with the inequality sign, and Second if you divide or multiply<BR>\n" );
document.write( "the inequality by a minus quantity, then you reverse the direction of the inequality<BR>\n" );
document.write( "sign. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "That being said, let's do the problem:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6+-+%281%2F3%29+t+%3E+0 ALIGN=MIDDLE  ALT=\"1%2F6+-+%281%2F3%29+t+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "As you would do with an equation, get rid of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side by subtracting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.  When you do that the inequality becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F3%29t+%3E+-%281%2F6%29 ALIGN=MIDDLE  ALT=\"-%281%2F3%29t+%3E+-%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the denominators by multiplying both sides of the equation by +6. When you<BR>\n" );
document.write( "do that the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%286%2F3%29t+%3E+-%286%2F6%29 ALIGN=MIDDLE  ALT=\"-%286%2F3%29t+%3E+-%286%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "By dividing the denominators into the numerators on both sides, you simplify the equation to:<BR>\n" );
document.write( ".<BR>\n" );
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;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally, you can now solve for t by dividing both sides of the inequality by -2. However,<BR>\n" );
document.write( "don't forget the rule about multiplying or dividing both sides by a NEGATIVE quantity. <BR>\n" );
document.write( "Because of this rule, when we divide both sides by -2, we need to reverse the direction of<BR>\n" );
document.write( "the inequality sign. Dividing by -2 results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29t%2F%28-2%29+%3E+%28-1%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"%28-2%29t%2F%28-2%29+%3E+%28-1%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and reversing the direction of the inequality sign makes it:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29t%2F%28-2%29+%3C+%28-1%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"%28-2%29t%2F%28-2%29+%3C+%28-1%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now doing the actual division by -2 simplifies the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+%3C+1%2F2 ALIGN=MIDDLE  ALT=\"t+%3C+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This tells us that for the original problem, as long as t is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > the inequality<BR>\n" );
document.write( "will be true. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can verify this by going to the original inequality and substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for t. You get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29+-+%281%2F3%29%2A%281%2F2%29+%3E0 ALIGN=MIDDLE  ALT=\"%281%2F6%29+-+%281%2F3%29%2A%281%2F2%29+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Doing the multiplication results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29+-+%281%2F6%29+%3E0 ALIGN=MIDDLE  ALT=\"%281%2F6%29+-+%281%2F6%29+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this reduces to<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3E+0 ALIGN=MIDDLE  ALT=\"0+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This is obviously not true. But suppose we make t less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Will the inequality then<BR>\n" );
document.write( "be true? Let's set t = 0 which is obviously less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When t is 0 the inequality <BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6+-+%281%2F3%29%2A0+%3E+0 ALIGN=MIDDLE  ALT=\"1%2F6+-+%281%2F3%29%2A0+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6+%3E+0 ALIGN=MIDDLE  ALT=\"1%2F6+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This is obviously true. So it lends support to our answer that if t is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > the<BR>\n" );
document.write( "original inequality will be true.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem a little more.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );