Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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]


Sagot :

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]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.