document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116812>Question 116812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and check each of the following equations for x.\r<BR>\n" );
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document.write( "x over 6 - x over 8 = 1\r<BR>\n" );
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document.write( "x over x - 2   MINUS   x + 1 over x  EQUALS 8 over x squared - 2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85630 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve and check each of the following equations for x.<BR>\n" );
document.write( "x over 6 - x over 8 = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6 ALIGN=MIDDLE  ALT=\"x%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Find a value that is a multiple of 6 & 8. 24 is good one (you can use 48 also)<BR>\n" );
document.write( "Multiply equation by 24<BR>\n" );
document.write( "24*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6 ALIGN=MIDDLE  ALT=\"x%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 24*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F8 ALIGN=MIDDLE  ALT=\"x%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 24(1)<BR>\n" );
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document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "4x - 3x = 24<BR>\n" );
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document.write( "x = 24<BR>\n" );
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document.write( "Check solution in original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F6 ALIGN=MIDDLE  ALT=\"24%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F8 ALIGN=MIDDLE  ALT=\"24%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "4 - 3 = 1<BR>\n" );
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document.write( "x over x - 2 MINUS x + 1 over x EQUALS 8 over x squared - 2x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28x-2%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%29%2Fx ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28%28x%5E2+-+2x%29%29 ALIGN=MIDDLE  ALT=\"8%2F%28%28x%5E2+-+2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can factor the last denominator to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28x-2%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%29%2Fx ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28x%28x+-+2%29%29 ALIGN=MIDDLE  ALT=\"8%2F%28x%28x+-+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "It's now apparent that x(x-2) is the common denominator of these fractions<BR>\n" );
document.write( "Multiply equation by x(x-2)<BR>\n" );
document.write( "x(x-2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28x-2%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - x(x-2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%29%2Fx ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x(x-2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28x%28x+-+2%29%29 ALIGN=MIDDLE  ALT=\"8%2F%28x%28x+-+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "x*x - (x-2)(x+1) = 8<BR>\n" );
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document.write( "x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1)<BR>\n" );
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document.write( "Remove the brackets, change the signs<BR>\n" );
document.write( "x^2 - x^2 + x + 2 = 8<BR>\n" );
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document.write( "x^2's are eliminated, subtract 2 from both sides<BR>\n" );
document.write( "x = 8 - 2<BR>\n" );
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document.write( "x = 6<BR>\n" );
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document.write( "Check solution in original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%286-2%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%286-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286%2B1%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28%286%2B1%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F%28%286%5E2+-+2%286%29%29%29 ALIGN=MIDDLE  ALT=\"8%2F%28%286%5E2+-+2%286%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F4 ALIGN=MIDDLE  ALT=\"6%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F6 ALIGN=MIDDLE  ALT=\"7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F24 ALIGN=MIDDLE  ALT=\"8%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Convert to a common denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F24 ALIGN=MIDDLE  ALT=\"36%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2F24 ALIGN=MIDDLE  ALT=\"28%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F24 ALIGN=MIDDLE  ALT=\"8%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >; confirms our solution of x=6<BR>\n" );
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document.write( "Did this help you understand this stuff?? </SPAN>\n" );
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