document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248625>Question 248625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a and b are positive integers, a < b and ab &#8804; a + 3b, how many possible values are there for a? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181166 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=181166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+b ALIGN=MIDDLE  ALT=\"a+%3C+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add 3b to each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+3b+%3C+b+%2B+3b ALIGN=MIDDLE  ALT=\"a+%2B+3b+%3C+b+%2B+3b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+3b+%3C+4b ALIGN=MIDDLE  ALT=\"a+%2B+3b+%3C+4b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The reason we did this is that the left side above now matches the right side of the other inequality:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab+%3C=+a+%2B+3b ALIGN=MIDDLE  ALT=\"ab+%3C=+a+%2B+3b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab+%3C=+a+%2B+3b ALIGN=MIDDLE  ALT=\"ab+%3C=+a+%2B+3b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+3b+%3C+4b ALIGN=MIDDLE  ALT=\"a+%2B+3b+%3C+4b\"   DISABLED_style= \"max-width:90%; height:auto;\" > then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab+%3C+4b ALIGN=MIDDLE  ALT=\"ab+%3C+4b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by the transitive property.<br><BR>\n" );
document.write( "This inequality we can solve. We can divide both sides by b (without having to be concerned about reversing the inequality because we know that b is positive):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+4 ALIGN=MIDDLE  ALT=\"a+%3C+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Between this and the fact that a is also positive, the possible values for a are:<BR>\n" );
document.write( "1, 2 and 3. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );