document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9334>Question 9334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each inequality. State the solution set using interval notation and graph the solition set.\r<BR>\n" );
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document.write( "4x^2 - 8x > or =  0\r<BR>\n" );
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document.write( "3x - x^2 > 0\r<BR>\n" );
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document.write( "Thanks in advance for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5108 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmaven53><B>mathmaven53(29)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmaven53><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=5108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^2 - 8x >= 0\r<BR>\n" );
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document.write( " Factor left side\r<BR>\n" );
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document.write( " 4x(x - 2) >=0\r<BR>\n" );
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document.write( " Then case I) 4x <=0 and x - 2 <= 0\r<BR>\n" );
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document.write( "  so x <= 0 and x <= 2\r<BR>\n" );
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document.write( " So x <= 0\r<BR>\n" );
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document.write( " This is graphed on a number line by putting a solid dot at 0 and an arrow pointing to the left of point 0\r<BR>\n" );
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document.write( " case II) 4x >= 0 and x-2 >= 0\r<BR>\n" );
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document.write( " so x >= 0 and x >= 2\r<BR>\n" );
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document.write( " So x >= 2\r<BR>\n" );
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document.write( " The solution of 4x^2 - 8x >= 0 is x<= 0 or x>= 2<BR>\n" );
document.write( "Interval notation of solution: (-infinity,0] or [2,infinity)<BR>\n" );
document.write( " We graphed the first part of the solution<BR>\n" );
document.write( "The second is graphed by putting a solid dot at point 2 on a number line and drawing an arrow to the right of this point\r<BR>\n" );
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document.write( "To solve 3x - x^2 > 0 \r<BR>\n" );
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document.write( " factor left side\r<BR>\n" );
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document.write( " x(3 - x) > 0\r<BR>\n" );
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document.write( " Then case i) x < 0 and 3 - x < 0\r<BR>\n" );
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document.write( "  x< 0 and 3 < x\r<BR>\n" );
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document.write( " This is false\r<BR>\n" );
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document.write( " so case ii) x > 0 and 3 - x > 0\r<BR>\n" );
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document.write( " x > 0 and 3 > x\r<BR>\n" );
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document.write( " 0 < x < 3<BR>\n" );
document.write( "Interval notation is (0,3)<BR>\n" );
document.write( " To graph this solution, put open dots at points 0 and 3 on a number line<BR>\n" );
document.write( "and draw a line segment between them.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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