document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72905>Question 72905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -4<-3x-13<26 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52140 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=52140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -4<-3x-13<26<BR>\n" );
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document.write( "Add 13 to all three sections of this inequality to get:<BR>\n" );
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document.write( "-4 + 13 < -3x - 13 + 13 < 26 + 13<BR>\n" );
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document.write( "This simplifies to <BR>\n" );
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document.write( "+9 < -3x < 39<BR>\n" );
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document.write( "Divide all three sections by -3 and you get:<BR>\n" );
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document.write( "-3 < x < -13<BR>\n" );
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document.write( "BUT a rule of inequalities is that if you multiply or divide by a negative number, the inequality<BR>\n" );
document.write( "arrows flip around in the other direction.  Don't forget this rule! And since we divided by<BR>\n" );
document.write( "negative 3 we have to flip the arrows to get:<BR>\n" );
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document.write( "-3 > x > -13<BR>\n" );
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document.write( "This says that on the number line x lies between -3 and -13.<BR>\n" );
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document.write( "Let's pick a number in this domain and substitute it into the original problem to make<BR>\n" );
document.write( "sure that it works.  -10 is an easy number to choose and it is between -3 and -13.<BR>\n" );
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document.write( "The original problem was:<BR>\n" );
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document.write( "-4<-3x-13<26<BR>\n" );
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document.write( "Substituting -10 for x we get<BR>\n" );
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document.write( "-4 < 30-13 < 26<BR>\n" );
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document.write( "And solving the middle section results in:<BR>\n" );
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document.write( "-4 < +17 < +26<BR>\n" );
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document.write( "That's correct ... + 17 lies between -4 and + 26.  That adds a little \"comfort factor\" that<BR>\n" );
document.write( "our answer is correct.<BR>\n" );
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document.write( "Hope this helps you to understand inequalities a little better. </SPAN>\n" );
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