To solve the given equation [tex]\( w = \frac{z - y}{2} - z \)[/tex] for [tex]\( y \)[/tex], follow these steps:
1. Start with the original equation:
[tex]\[ w = \frac{z - y}{2} - z \][/tex]
2. Add [tex]\( z \)[/tex] to both sides of the equation to begin isolating the fraction that contains [tex]\( y \)[/tex]:
[tex]\[ w + z = \frac{z - y}{2} \][/tex]
3. Multiply both sides of the equation by 2 to eliminate the denominator:
[tex]\[ 2(w + z) = z - y \][/tex]
4. Subtract [tex]\( z \)[/tex] from both sides to isolate the term that includes [tex]\( y \)[/tex]:
[tex]\[ 2(w + z) - z = -y \][/tex]
5. Multiply both sides of the equation by -1 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = -(2(w + z) - z) \][/tex]
This can be simplified further:
[tex]\[ y = (-2(w + z) + z) \][/tex]
[tex]\[ y = z - 2(w + z) \][/tex]
Thus, the solution for [tex]\( y \)[/tex] in terms of the given variables is:
[tex]\[ y = z - 2(w + z) \][/tex]
Therefore, the correct choice is:
C. [tex]\( y = z - 2(w + z) \)[/tex]
