Rearrange the following formula to solve for the indicated variable.
$S=2(x+xz+yz)$
Solve for $y$.

• A. $y=\frac{\frac{S}{2}-x-xz}{z}$
• B. $y=\frac{\frac{S}{2}-x+xz}{z}$
• C. $y=\frac{\frac{S}{2}-x-xz}{2z}$
• D. $y=\frac{\frac{S}{2}+x-xz}{2z}$

Answer: (A)

Verified step by step guidance

1. Start with the given formula: \(S = 2\left(x + xz + yz\right)\).
2. First, divide both sides of the equation by 2 to isolate the expression inside the parentheses: \(\frac{S}{2} = x + xz + yz\).
3. Next, group the terms involving \(y\) on one side and the rest on the other side. Subtract \(x\) and \(xz\) from both sides: \(\frac{S}{2} - x - xz = yz\).
4. To solve for \(y\), divide both sides of the equation by \(z\): \(y = \frac{\frac{S}{2} - x - xz}{z}\).
5. This expression now gives \(y\) in terms of \(S\), \(x\), and \(z\).