document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182381>Question 182381</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078279992/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> how would you solve for x. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x-3%29+=+sqrt%28+x-1%29+ ALIGN=MIDDLE  ALT=\"sqrt%284x-3%29+=+sqrt%28+x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136884 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math sqrt{4x-3} = sqrt{x-1}\">\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4x-3 = x-1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 3x = 2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x = \frac{2}{3}\">\r<BR>\n" );
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document.write( "However, when you check the answer you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  i \frac{sqrt{3}}{3} = i \frac{sqrt{3}}{3}\">\r<BR>\n" );
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document.write( "which is certainly true enough and indicates that the answer is valid, but only to the extent that there are no restrictions on the value of the variable in your original equation such that the equation must always be defined in the real numbers.  Your original equation is undefined in the reals for any value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x < 1\"> because the radicand on the right would then be < 0.\r<BR>\n" );
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document.write( "Consequently, your solution set either contains the single value <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{2}{3}\"> if there are no restrictions on the value of <i>x</i> or is the empty set if <i>x</i> is restricted.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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