Question 397439
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 {{{4z/a}}} is the simplified form of {{{4(z/8)+z/2}}}.  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>

1. {{{4(z/8)+z/2=4z/a}}}<br>
2. {{{4z/8+z/2=4z/a}}}<br>
3.{{{z/2+z/2=4z/a}}}  *4/8 reduces to 1/2, times z is z/2<br>
4. {{{2z/2=4z/a}}} *Add the fractions<br>
5. {{{z=4z/a}}} *Reduce<br>
6. {{{a*z=4z}}} *Multiply both sides by a, to get rid of the fraction<br>
7. {{{a=4z/z}}} *Divide both sides by z, to isolate<br>
8. {{{a=4}}} *Since {{{z/z=1}}}, {{{4z/z=4*1}}}, or 4.<br>

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.