document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835237>Question 835237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the inequality algebraically.\r<BR>\n" );
document.write( "\n" );
document.write( "7x-6&#8805;3x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503544 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x^2 - 7x + 6 \le 0\">\r<BR>\n" );
document.write( "\n" );
document.write( "The zeros of the LHS occur at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = \frac{7 \pm \sqrt{49 - 4(3)(6)}}{2}\">, which are non-real, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x) = 3x^2 - 7x + 6\"> doesn't cross the x-axis. Since it is continuous, it is either positive everywhere or negative everywhere. Clearly it must be positive everywhere (check by substituting a large value of x), so it can never be negative. There are no solutions. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );