document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80895>Question 80895</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078651131/algebrahomeworkh>Glenco Mathematics Algebra 1 </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am really stumped as to how to solve this inequality.   <BR>\n" );
document.write( "I would appreciate ANY answers. I just, for some reason, cannot work this one.\r<BR>\n" );
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document.write( "3a + 8/2 < 10 \r<BR>\n" );
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document.write( "Thanks so much. :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58041 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=58041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can work problems of this type just as you would solve an equation with the exception that<BR>\n" );
document.write( "if you divide or multiply by a negative quantity, then you must reverse the direction<BR>\n" );
document.write( "of the inequality sign.<BR>\n" );
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document.write( "So let's start with the given expression:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%2B+8%2F2+%3C+10 ALIGN=MIDDLE  ALT=\"3a+%2B+8%2F2+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F2+=+4 ALIGN=MIDDLE  ALT=\"8%2F2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we can replace it by 4 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%2B+4+%3C+10 ALIGN=MIDDLE  ALT=\"3a+%2B+4+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 4 on the left side by subtracting 4 from both sides of the inequality<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%3C+6 ALIGN=MIDDLE  ALT=\"3a+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now reduce the left side to just \"+a\" by dividing both sides of the inequality by +3<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+6%2F3 ALIGN=MIDDLE  ALT=\"a+%3C+6%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+2 ALIGN=MIDDLE  ALT=\"a+%3C+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The original inequality should be satisfied as long as the value of \"a\" is less than 2.<BR>\n" );
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document.write( "Let's build our self confidence by trying some values for \"a\".  Suppose we let \"a\" equal<BR>\n" );
document.write( "zero. That value is obviously less than +2. If we substitute zero for a in the original<BR>\n" );
document.write( "inequality we get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a+%2B+8%2F2+%3C+10 ALIGN=MIDDLE  ALT=\"3a+%2B+8%2F2+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+4+%3C+10 ALIGN=MIDDLE  ALT=\"0+%2B+4+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That works. Similarly, if we let a = +1<BR>\n" );
document.write( "the original inequality becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A1+%2B+8%2F2+%3C+10 ALIGN=MIDDLE  ALT=\"3%2A1+%2B+8%2F2+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this further simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+4+%3C+10 ALIGN=MIDDLE  ALT=\"3+%2B+4+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That works also.<BR>\n" );
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document.write( "Now let's set a = +3.  That is outside the limit we found since +3 is not less than +2.<BR>\n" );
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document.write( "With a = +3 the original inequality becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3+%2B+8%2F2+%3C+10 ALIGN=MIDDLE  ALT=\"3%2A3+%2B+8%2F2+%3C+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+4+%3C10 ALIGN=MIDDLE  ALT=\"9+%2B+4+%3C10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and this obviously is not true.<BR>\n" );
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document.write( "From these spot checks, it seems as though our answer is correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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document.write( "Cheers. </SPAN>\n" );
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