To solve the given equation \(\frac{2x - 1}{y} = \frac{w + 2}{2z}\) for \(w\), follow these steps:
1. Cross-Multiply to Eliminate the Denominators:
Given:
[tex]\[
\frac{2x - 1}{y} = \frac{w + 2}{2z}
\][/tex]
Cross-multiplying both sides, we get:
[tex]\[
(2x - 1) \cdot 2z = (w + 2) \cdot y
\][/tex]
This simplifies to:
[tex]\[
2z(2x - 1) = y(w + 2)
\][/tex]
2. Distribute and Expand:
Distribute \(2z\) on the left side:
[tex]\[
4xz - 2z = y(w + 2)
\][/tex]
3. Isolate \(w\) on One Side of the Equation:
Rearrange to isolate \(w\):
[tex]\[
4xz - 2z = yw + 2y
\][/tex]
Subtract \(2y\) from both sides:
[tex]\[
4xz - 2z - 2y = yw
\][/tex]
4. Solve for \(w\):
Divide both sides by \(y\) to solve for \(w\):
[tex]\[
w = \frac{4xz - 2z - 2y}{y}
\][/tex]
This matches one of the choices given, specifically:
[tex]\[
w = \frac{4xz - 2z - 2y}{y}
\][/tex]
Thus, the correct solution is:
[tex]\[
\boxed{w = \frac{4xz - 2z - 2y}{y}}
\][/tex]
