document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31742>Question 31742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve:<BR>\n" );
document.write( "(x-2)/(x^2 -2x-3)>=0<BR>\n" );
document.write( "the answer to this is (-1,3)U(3 infinity) right?\r<BR>\n" );
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document.write( "Solve 5/(x+4)<=1<BR>\n" );
document.write( "The answer to this is (negative infinity, -4)U[1, infinity)<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Alexus Bandona<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18348 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=18348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x-2)/(x^2 -2x-3)>=0<BR>\n" );
document.write( "=> (x-2)(x^2-3x+x-3) >= 0<BR>\n" );
document.write( "=> (x-2)(x-3)(x+1) >= 0<BR>\n" );
document.write( "The boundary points are x=-1, x=2, and x=3;<BR>\n" );
document.write( "Let us consider some test values based on the boundary points.<BR>\n" );
document.write( "for x=-2(x<-1), (x-2)(x-3)(x+1) = (-2-2)(-2-3)(-2+1) = (-4)(-5)(-1) = -20 (<0)<BR>\n" );
document.write( "=> x < -1 does not satisfy the inequality<BR>\n" );
document.write( "for x=0 (-1<x<2), (x-2)(x-3)(x+1)=(0-2)(0-3)(0+1)=(-2)(-3)(1)=6 (>0) <BR>\n" );
document.write( "=> -1<x<2 satisfies the inequality<BR>\n" );
document.write( "for x=2.5 (2<x<3),<BR>\n" );
document.write( "(x-2)(x-3)(x+1)=(2.5-2)(2.5-3)(2.5+1)=(.5)(-.5)(3.5)=a negative number (<0)<BR>\n" );
document.write( "=> does not satisfy the inequality<BR>\n" );
document.write( "for x = 5 (x>3),<BR>\n" );
document.write( "(x-2)(x-3)(x+1)=(5-2)(5-3)(5+1)=(3)(2)(6)=36 (>0) ... satisfies the inequality<BR>\n" );
document.write( "So, all x-values for which -1<x<2 and x>3 satisfy the given inequality; the given inequality has equal sign, meaning the boundary points are inclusive<BR>\n" );
document.write( "Final result: the inequality is satisfies for all real x's meeting:<BR>\n" );
document.write( "x >= -1 and x <= 2;<BR>\n" );
document.write( "x >= 3;<BR>\n" );
document.write( "In interval notation: x belongs to [-1,2]U[3,infinity)  </SPAN>\n" );
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