document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194066>Question 1194066</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for x.<BR>\n" );
document.write( "|3x  x|<BR>\n" );
document.write( "|16x x|=35<BR>\n" );
document.write( "The solution set is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826158 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We have a 2 by 2 matrix on the left hand side. We are applying the determinant to it because of the vertical bars.\r<BR>\n" );
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document.write( "The determinant of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ad-bc ALIGN=MIDDLE  ALT=\"ad-bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This only works for 2 by 2 matrices.<BR>\n" );
document.write( "We compute the product of the diagonals, then subtract those products.\r<BR>\n" );
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document.write( "In the case of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3x%2Cx%2C16x%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C3x%2Cx%2C16x%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "the determinant is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ad+-+bc+=+3x%2Ax+-+x%2A16x+=+3x%5E2+-+16x%5E2+=+-13x%5E2 ALIGN=MIDDLE  ALT=\"ad+-+bc+=+3x%2Ax+-+x%2A16x+=+3x%5E2+-+16x%5E2+=+-13x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set this equal to the 35 and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13x%5E2+=+35 ALIGN=MIDDLE  ALT=\"-13x%5E2+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+35%2F%28-13%29 ALIGN=MIDDLE  ALT=\"x%5E2+=+35%2F%28-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28-35%2F13%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-35%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-35%2F13%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-35%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+i%2Asqrt%2835%2F13%29 ALIGN=MIDDLE  ALT=\"x+=+i%2Asqrt%2835%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i%2Asqrt%2835%2F13%29 ALIGN=MIDDLE  ALT=\"x+=+-i%2Asqrt%2835%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We see that the solution set consists of nonreal complex numbers of the form a+bi, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i+=+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If your teacher has not covered imaginary numbers or complex numbers just yet, then the answer would be \"no real solutions\".<BR>\n" );
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