The variable z is inversely proportional to x. when x is 3, z has the value 6.. what is the value of z when x = 8 round to at least the thousandths place if needed.

Inverse variation is of the form y=k/x or if you prefer yx=k.

z=6.3 bar  I assume you mean 6.33333333 forever

10z-z=63.3333...-6.3333

9z=57

z=57/9  (exact)

Now back to the problem...

xz=k, we are told x=3 and we have shown z=57/9 so we can solve for k, the constant of variation

k=3(57/9)=19

So our equation is:

xz=19, now we wish to know what z is when x=8 so

8z=19  divide both sides by 8

z=19/8  

z=2.375  (exact, no rounding necessary)