document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397439>Question 397439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If we simplify the expression 4(z/8)+ z/2 as 4z/a then what is the value of a? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #283978 by </B><A HREF=/tutors/aboutme.mpl?userid=JoeCollins><B>JoeCollins(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JoeCollins><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=283978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This question takes a bit of reasoning.  When you simplify expressions, you don't actually change the value of them, you just rewrite them in a simplified form.  The question claims that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4z%2Fa ALIGN=MIDDLE  ALT=\"4z%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the simplified form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28z%2F8%29%2Bz%2F2 ALIGN=MIDDLE  ALT=\"4%28z%2F8%29%2Bz%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the value of the simplified form is equal to the expanded form we can set the two expressions equal to each other and solve for a:<br>\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28z%2F8%29%2Bz%2F2=4z%2Fa ALIGN=MIDDLE  ALT=\"4%28z%2F8%29%2Bz%2F2=4z%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4z%2F8%2Bz%2F2=4z%2Fa ALIGN=MIDDLE  ALT=\"4z%2F8%2Bz%2F2=4z%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2%2Bz%2F2=4z%2Fa ALIGN=MIDDLE  ALT=\"z%2F2%2Bz%2F2=4z%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >  *4/8 reduces to 1/2, times z is z/2<br><BR>\n" );
document.write( "4. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z%2F2=4z%2Fa ALIGN=MIDDLE  ALT=\"2z%2F2=4z%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > *Add the fractions<br><BR>\n" );
document.write( "5. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=4z%2Fa ALIGN=MIDDLE  ALT=\"z=4z%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > *Reduce<br><BR>\n" );
document.write( "6. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Az=4z ALIGN=MIDDLE  ALT=\"a%2Az=4z\"   DISABLED_style= \"max-width:90%; height:auto;\" > *Multiply both sides by a, to get rid of the fraction<br><BR>\n" );
document.write( "7. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4z%2Fz ALIGN=MIDDLE  ALT=\"a=4z%2Fz\"   DISABLED_style= \"max-width:90%; height:auto;\" > *Divide both sides by z, to isolate<br><BR>\n" );
document.write( "8. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > *Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Fz=1 ALIGN=MIDDLE  ALT=\"z%2Fz=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4z%2Fz=4%2A1 ALIGN=MIDDLE  ALT=\"4z%2Fz=4%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 4.<br>\r<BR>\n" );
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document.write( "So a equals 4.  If you substitute 4 for a in step 5 and simplify, you will get z=z, which is a true statement.  Hope that helps. </SPAN>\n" );
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