document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74812>Question 74812</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078603900/algebrahomeworkh>Algebra I</A><BR>\n" );
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document.write( "              solve the inequality <BR>\n" );
document.write( "               <BR>\n" );
document.write( "               5x<10(3x+4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53750 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=53750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x<10(3x+4)<BR>\n" );
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document.write( "You can treat problems such as this just like you would go about solving an equation ...<BR>\n" );
document.write( "with one big exception.  Any time that you multiply or divide both sides of the inequality<BR>\n" );
document.write( "by a NEGATIVE quantity, you have to reverse the direction of the inequality arrow.<BR>\n" );
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document.write( "Let's do your problem.  Probably the first thing you see is that you have a multiplication<BR>\n" );
document.write( "on the right side.  Multiply it out to get:<BR>\n" );
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document.write( "5x < 30x + 40<BR>\n" );
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document.write( "Get all the terms containing x on one side of the inequality.  Do this by subtracting<BR>\n" );
document.write( "5x from both sides.  When you do the inequality becomes:<BR>\n" );
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document.write( "0 < 25x + 40<BR>\n" );
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document.write( "Now get the number on the other side of the inequality.  Do that by subtracting 40 from<BR>\n" );
document.write( "both sides to get:<BR>\n" );
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document.write( "-40 < 25x<BR>\n" );
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document.write( "Finally, we are trying to solve for +x so divide both sides of the equation by +25, the <BR>\n" );
document.write( "multiplier of x.  When you do that you get:<BR>\n" );
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document.write( "-40/25 < x<BR>\n" );
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document.write( "And 25 goes into -40 ... -1.6 times. So the solution is:<BR>\n" );
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document.write( "-1.6 < x<BR>\n" );
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document.write( "You can read this as x must be greater than -1.6, and you can also write this as:<BR>\n" );
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document.write( "x > -1.6<BR>\n" );
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document.write( "And you could also write the -1.6 as -8/5 so you could write the solution as x > -8/5.<BR>\n" );
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document.write( "Notice that we did not need to use the property that if you multiply or divide both sides<BR>\n" );
document.write( "by a negative number, you reverse the direction of the inequality sign.<BR>\n" );
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document.write( "Hope this allows you to do a few more inequality problems.  Remember that as far as math<BR>\n" );
document.write( "operations are concerned, you can use the same methods as you would to solve an equation. </SPAN>\n" );
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