document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23332>Question 23332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this inequality<BR>\n" );
document.write( "x-x^2 < or equal to 0\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "pabblo </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12103 by </B><A HREF=/tutors/aboutme.mpl?userid=philberg99><B>philberg99(10)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=philberg99><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=12103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this problem, think about graphing the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-x%5E2 ALIGN=MIDDLE  ALT=\"x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-2%2C+2%2C+-2%2C+2%2C+x-x%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+200%2C+-2%2C+2%2C+-2%2C+2%2C+x-x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we look at which x values gives a positive output, or which x values have a y value that is above the x axis.  This yields the interval [0,1] as the answer.\r<BR>\n" );
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document.write( "Where does 0 and 1 come from?  They're the solutions to the equation 0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-x%5E2 ALIGN=MIDDLE  ALT=\"x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x(1-x).  So x = 0 or 1-x = 0.  Thus x = 0 or 1. </SPAN>\n" );
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