document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155334>Question 155334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the polynomial inequality and graph the solution set on a number lines.  express the solution set in interval notation.  5x^2-3x is greater than or equal to 8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114380 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=114380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> express the solution set in interval notation. 5x^2-3x is greater than or equal to 8<BR>\n" );
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document.write( "5x^2-3x-8 >= 0<BR>\n" );
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document.write( "1st: Solve the EQUALITY:<BR>\n" );
document.write( "Factor to get:<BR>\n" );
document.write( "5x^2-8x+5x-8 = =<BR>\n" );
document.write( "x(5x-8) + (5x-8) = 0<BR>\n" );
document.write( "(5x-8)(x+1) = 0<BR>\n" );
document.write( "x = 8/5 or x = -1<BR>\n" );
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document.write( "2nd: <BR>\n" );
document.write( "Draw a number line and plot x = -1 and x=(8/5) on it.<BR>\n" );
document.write( "Check a test-value in the INEQUALITY from each of the <BR>\n" );
document.write( "three number number-line intervals.<BR>\n" );
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document.write( "If x = -2 you get 5(-2)^2-(3*-2)-8 > 0; true so solutions in (-inf,-1)<BR>\n" );
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document.write( "If x = 0 you get 5(0)^2 - 3*0 -8 >0 ; false so no solution in (-1,8/5)<BR>\n" );
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document.write( "If x = 2 you get 5(2)^2 - 3*2 -8 > 0; true, so solutions in (8/5,+inf)<BR>\n" );
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document.write( "Final answer: {x|-inf< x <-1} U {x|-1< x <+inf}<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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