We are given the following expression:
![-y+z((8)/(2)+4)=5z+4](https://img.qammunity.org/2023/formulas/mathematics/college/77iojcqfswqvo7eftaykute1uw8gpquzib.png)
We need to find the value of z when y = 6. Thus:
![-6+z((8)/(2)+4)=5z+4](https://img.qammunity.org/2023/formulas/mathematics/college/brhfzpe0wywfaj6unwf0ddwvsmxnp2u9yp.png)
First, we can solve the parentheses:
![\begin{gathered} -6+z(4+4)=5z+4 \\ . \\ -6+8z=5z+4 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/fi42jaf5hd27yglmcgybfqsx06y2e0a35c.png)
Now, we can add 6 on both sides, and subtract 5z on both sides:
![8z-5z=4+6](https://img.qammunity.org/2023/formulas/mathematics/college/tsv4vrcyegvwjy7f9mgrg489fdu5h3fq4q.png)
Simplify:
![3z=10](https://img.qammunity.org/2023/formulas/mathematics/college/6mpg4pqf27jlm9divzxz2fhaao2heit24j.png)
Divide by 3 on both sides:
![z=(10)/(3)\approx3.333333...](https://img.qammunity.org/2023/formulas/mathematics/college/7u4mx42m1zmylml94nmq4wb7svdh2890et.png)
Rounded to 2 decimals, the answer is:
z = 3.33,
Thus, OPTION A is the correct answer.