document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=706327>Question 706327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you do multiplication property of inequalities to solve the inequality and show me how to graph the solution set.\r<BR>\n" );
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document.write( "-1/4t>_4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435092 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=435092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F4%29t%3E=4 ALIGN=MIDDLE  ALT=\"%28-1%2F4%29t%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying everything (both sides of the inequality sign) times as positive number<BR>\n" );
document.write( "results in an equivalent inequality, so multiplying times 4 we would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%3E=16 ALIGN=MIDDLE  ALT=\"-t%3E=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Changing the sign of the expressions on both sides<BR>\n" );
document.write( "(it is exactly the same as multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "flips everything to the other side of zero,<BR>\n" );
document.write( "so to get an equivalent inequality, you also have to flip the inequality sign, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%3E=16 ALIGN=MIDDLE  ALT=\"-t%3E=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t%3C=-16%29 ALIGN=MIDDLE  ALT=\"highlight%28t%3C=-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I could have done both steps in one by multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29 ALIGN=MIDDLE  ALT=\"%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "It's the same thing, but harder to visualize.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The \"properties\" are what common sense tells you.<BR>\n" );
document.write( "It's what makes sense in real world situations.<BR>\n" );
document.write( "Math does not require to memorize much.<BR>\n" );
document.write( "You just have know meaning of some symbols and definitions,<BR>\n" );
document.write( "and think of what it means,<BR>\n" );
document.write( "not by \"juggling words\", or invoking \"voodoo rules\", but by using ideas.<BR>\n" );
document.write( "With inequalities you can add the same number to both sides and you get an equivalent inequality<BR>\n" );
document.write( "You can subtract the same number from both sides with the same result (subtracting is just adding the opposite number).<BR>\n" );
document.write( "You can multiply/divide by a positive number both sides and get an equivalent inequality.<BR>\n" );
document.write( "However, multiplying/dividing by a negative number requires flipping the inequality sign. </SPAN>\n" );
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