document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18722>Question 18722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could some one help me understand this problem?\r<BR>\n" );
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document.write( "The instructions are to solve the inequality. State the solution set using interval notation and graph it:<BR>\n" );
document.write( "x - 2/x + 3 is less than 1\r<BR>\n" );
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document.write( "Thanks for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8977 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x - 2/x + 3 is less than 1 <BR>\n" );
document.write( "let y=(x - 2/x + 3)<1 <BR>\n" );
document.write( "x - 2/x + 3-1<0 ....or....x - 2/x + 2<0 <BR>\n" );
document.write( "(x^2-2+2x)/x<0...or ...(x^2+2x-2)/x<0..<BR>\n" );
document.write( "now a fraction will be -ve (<0)if n.r and d.r are of different signs..let us take the 2 cases <BR>\n" );
document.write( "dr=x is +ve...then nr should be -ve<BR>\n" );
document.write( "dr=x is -ve...then nr should be +ve.<BR>\n" );
document.write( "now solve the nr  using quadratic formula <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-2%29%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-2%29%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "hence x=(-1+sqrt3)/2...and....(-1-sqrt3)/2..for conveinience if we call these 2 values as  p(approximately=-1.37)and q(approximately=0.37),we find that if x lies between p  and q (-1.37 and 0.37 )nr is -ve and when x is less than <BR>\n" );
document.write( "p(-1.37) or greater than q(0.37) ,nr is +ve.<BR>\n" );
document.write( "now we have to combine this with the above assumption on dr<BR>\n" );
document.write( "  dr=x is +ve...then nr should be -ve..so x should be between 0 and (-1+sqrt3)/2(not -1.37 to zero as x is already taken as positive)<BR>\n" );
document.write( "dr=x is -ve...then nr should be +ve.so x should be less than ....(-1-sqrt3)/2..<BR>\n" );
document.write( "(not 0.37 to zero as x is already taken as negative)<BR>\n" );
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