document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40422>Question 40422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -2x^2+7x-10<=(-3)x+2\r<BR>\n" );
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document.write( "Possible answers\r<BR>\n" );
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document.write( "a. (-inf,-3) U (-2,+inf)<BR>\n" );
document.write( "b. (-inf,2) U (3, inf)<BR>\n" );
document.write( "c. (-3,-2)<BR>\n" );
document.write( "d. (2,3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #25778 by </B><A HREF=/tutors/aboutme.mpl?userid=fazlerabbi><B>fazlerabbi(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fazlerabbi><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=25778\">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=-2%2Ax%5E2%2B7%2Ax-10+%3C=+%28-3%29%2Ax%2B2 ALIGN=MIDDLE  ALT=\"-2%2Ax%5E2%2B7%2Ax-10+%3C=+%28-3%29%2Ax%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Ax%5E2%2B10%2Ax-10+%3C=+2 ALIGN=MIDDLE  ALT=\"-2%2Ax%5E2%2B10%2Ax-10+%3C=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >       subtracted (-3)*x from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B5%2Ax-5+%3C=+1 ALIGN=MIDDLE  ALT=\"-x%5E2%2B5%2Ax-5+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >           multiplied both sides by 1/2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B5%2Ax-6+%3C=+0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B5%2Ax-6+%3C=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >           subtracted 1 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5%2Ax%2B6+%3E=+0 ALIGN=MIDDLE  ALT=\"x%5E2-5%2Ax%2B6+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >            multiplied both sided by -1\r<BR>\n" );
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document.write( "Factoring left side yields<BR>\n" );
document.write( "(x-3)(x-2) >= 0\r<BR>\n" );
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document.write( "The values of x for which x-2=0 or x-3=0 are x=2 and x=5. These points divide the coordinate line into three intervals,<BR>\n" );
document.write( "    (-inf,2], (2,3) and [3, +inf)\r<BR>\n" );
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document.write( "We need to check points of which of these three intervals give positive sign for the product (x-3(x-2). We shall choose arbitrary points on each of these intervals to determine the sign; these points are called test points. Lets say 1, 2.5 and 4 will be the test points for intervals (-inf,2], (2,3) and [3, +inf) respectively.\r<BR>\n" );
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document.write( "For interval (-inf,2] with test point 1 sign of (x-2)(x-3) is (-)(-) = +<BR>\n" );
document.write( "For interval (2,3) with test point 2.5  sign of (x-2(x-3)  is (+)(-) = -<BR>\n" );
document.write( "For interval [3,+inf)with test point 4 sign of (x-2(x-3) is  (+)(+) = +\r<BR>\n" );
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document.write( "The pattern of signs suggest that the solution set is <BR>\n" );
document.write( "(-inf,2] U [3,+inf)<BR>\n" );
document.write( "  </SPAN>\n" );
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