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Solve for \( w \).

[tex]\[
\frac{2x - 1}{y} = \frac{w + 2}{2z}
\][/tex]

A. \( w = \frac{4xz - 1}{y} - 2 \)

B. \( w = \frac{4xz - 2z}{y} \)

C. \( w = \frac{xz - z}{y} - 2 \)

D. [tex]\( w = \frac{4xz - 2z}{y} - 2 \)[/tex]



Answer :

GinnyAnswer
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]

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