document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040243>Question 1040243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (ax-3)(bx+6)=24x^2+cx-18 for all values of x and a+b=10, what are two possible values for c?<BR>\n" );
document.write( "A. 2 and 12<BR>\n" );
document.write( "B. 6 and 24<BR>\n" );
document.write( "C. 10 and 30<BR>\n" );
document.write( "D. 16 and 30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655058 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=655058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax-3%29%28bx%2B6%29=24x%5E2%2Bcx-18 ALIGN=MIDDLE  ALT=\"%28ax-3%29%28bx%2B6%29=24x%5E2%2Bcx-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abx%5E2-3bx%2B6ax-18=24x%5E2%2Bcx-18 ALIGN=MIDDLE  ALT=\"abx%5E2-3bx%2B6ax-18=24x%5E2%2Bcx-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abx%5E2%2B%286a-3b%29x-18=24x%5E2%2Bcx-18 ALIGN=MIDDLE  ALT=\"abx%5E2%2B%286a-3b%29x-18=24x%5E2%2Bcx-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28ab=24%2C6a-3b=c%29 ALIGN=MIDDLE  ALT=\"system%28ab=24%2C6a-3b=c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=10 ALIGN=MIDDLE  ALT=\"a%2Bb=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Question is, what can be c?<BR>\n" );
document.write( "Observe, three equations and three unknown variables.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28ab=24%2C6a-3b=c%2Ca%2Bb=10%29 ALIGN=MIDDLE  ALT=\"system%28ab=24%2C6a-3b=c%2Ca%2Bb=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "TWO of the equations are only in the two unknowns a and b.<BR>\n" );
document.write( "b=10-a<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2810-a%29=24 ALIGN=MIDDLE  ALT=\"a%2810-a%29=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a-a%5E2=24 ALIGN=MIDDLE  ALT=\"10a-a%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%5E2%2B10a-24=0 ALIGN=MIDDLE  ALT=\"-a%5E2%2B10a-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-10a%2B24=0 ALIGN=MIDDLE  ALT=\"a%5E2-10a%2B24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-4%29%28a-6%29=0 ALIGN=MIDDLE  ALT=\"%28a-4%29%28a-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Possible, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=4%2Cor%2Ca=6%29 ALIGN=MIDDLE  ALT=\"system%28a=4%2Cor%2Ca=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Correspondingly, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28b=6%2Cor%2Cb=4%29 ALIGN=MIDDLE  ALT=\"system%28b=6%2Cor%2Cb=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Possible c values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6a-3b ALIGN=MIDDLE  ALT=\"c=6a-3b\"   DISABLED_style= \"max-width:90%; height:auto;\" > as already found,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6%2A4-3%2A6=highlight%286%29 ALIGN=MIDDLE  ALT=\"c=6%2A4-3%2A6=highlight%286%29\"   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=c=6%2A6-3%2A4=36-12=highlight%2824%29 ALIGN=MIDDLE  ALT=\"c=6%2A6-3%2A4=36-12=highlight%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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