document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93529>Question 93529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you work these problems? I have no Idea where to start! Help!\r<BR>\n" );
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document.write( "Solve and graph the solution:\r<BR>\n" );
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document.write( "-12 is greater than or equal to 24x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68110 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=68110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In equation form you are given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%3E=24x ALIGN=MIDDLE  ALT=\"-12%3E=24x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can pretty much work these using the same procedures that you would to solve an equation.<BR>\n" );
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document.write( "However, there is an exception. This exception is that in solving for x if you ever have to<BR>\n" );
document.write( "MULTIPLY or DIVIDE both sides by a NEGATIVE quantity, then you also have to reverse the <BR>\n" );
document.write( "direction of the inequality sign.<BR>\n" );
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document.write( "Let's work this problem. <BR>\n" );
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document.write( "If this were an equation, you would solve for x by dividing both sides by 24 because 24<BR>\n" );
document.write( "is the multiplier of x. So let's divide both sides by +24 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2F24%3E=%2824x%29%2F24 ALIGN=MIDDLE  ALT=\"-12%2F24%3E=%2824x%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that on the left side if you divide both the numerator and denominator by 12 you are<BR>\n" );
document.write( "left with <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;\" > and on the right side the 24 in the numerator cancels with the 24<BR>\n" );
document.write( "in the denominator. Therefore, all you are left with is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2%3E=x ALIGN=MIDDLE  ALT=\"-1%2F2%3E=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer. Now, what does it mean? It says that <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;\" > is greater than or equal<BR>\n" );
document.write( "to x. (Remember that the inequality sign always points to the smaller quantity.)<BR>\n" );
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document.write( "This also means the same as x is less than or equal to <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;\" >. For the purposes of<BR>\n" );
document.write( "graphing this answer, you can draw a number line. Then put a dot at the point <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( "x can have that value. x can also be less than that number. That means that x can be any <BR>\n" );
document.write( "value to the left of the point at <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;\" >. So you make the number line to the left of the<BR>\n" );
document.write( "point <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;\" > a very heavy line to indicate that x can be on that part of the line.  <BR>\n" );
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document.write( "Hopefully this makes some sense to you.  In solving this problem we didn't have to multiply<BR>\n" );
document.write( "or divide both sides by a negative number, so we didn't need to use the rule about <BR>\n" );
document.write( "changing the direction of the inequality sign.  It just stayed the same direction <BR>\n" );
document.write( "throughout all our work.  <BR>\n" );
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document.write( "Remember the goal is to solve inequalities for +x. If you have a problem that you can solve<BR>\n" );
document.write( "for -x, then do so. But at the very end of the problem you will need to multiply the -x by<BR>\n" );
document.write( "-1 to change it to +x. And when you multiply one side by -1 you must also multiply the<BR>\n" );
document.write( "other side by -1 ... and that means that you also need to reverse the direction of the <BR>\n" );
document.write( "inequality sign because you multiplied both sides by a minus number. </SPAN>\n" );
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