document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31166>Question 31166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help!\r<BR>\n" );
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document.write( "Solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282x-1%29+%3C+x-2+ ALIGN=MIDDLE  ALT=\"+sqrt%282x-1%29+%3C+x-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thank you thank you thank you thank you thank you thank you thank (in advance!!) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17871 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17871\">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=+sqrt%282x-1%29+%3C+x-2+ ALIGN=MIDDLE  ALT=\"+sqrt%282x-1%29+%3C+x-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > then square both sides to give<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x-1+%3C+%28x-2%29%5E2+ ALIGN=MIDDLE  ALT=\"+2x-1+%3C+%28x-2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x-1+%3C+x%5E2-4x%2B4+ ALIGN=MIDDLE  ALT=\"+2x-1+%3C+x%5E2-4x%2B4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+%3C+x%5E2-6x%2B5+ ALIGN=MIDDLE  ALT=\"+0+%3C+x%5E2-6x%2B5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or more usually re-ordered as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2-6x%2B5+%3E+0+ ALIGN=MIDDLE  ALT=\"+x%5E2-6x%2B5+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This is asking \"which values of x in this quadratic give POSITIVE y-values\" --> this is the meaning of the \">0\"\r<BR>\n" );
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document.write( "First, lets find where the quadratic EQUALS zero\r<BR>\n" );
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document.write( "so (x-5)(x-1) = 0<BR>\n" );
document.write( "so x-5=0 or x-1=0<BR>\n" );
document.write( "so x=5 or x=1\r<BR>\n" );
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document.write( "So, we now know the position of the quadratic: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C8%2C-6%2C6%2Cx%5E2-6x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C8%2C-6%2C6%2Cx%5E2-6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at this, we can see that POSITIVE y-values (the thing asked for) happens when x is less than 1 or when x is greater than 5.\r<BR>\n" );
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document.write( "So answers are x<1 or x>5.\r<BR>\n" );
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document.write( "The only caveat i have is that the first line squares both sides: there may well be the possibility of multiplying by negative numbers here, in which case the inequality would swap round... i am hoping this is not required to be thought about for your answer.\r<BR>\n" );
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document.write( "jon.\r<BR>\n" );
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