Question

solve \\(\frac{2x - 1}{y} = \frac{w + 2}{2z}\\) for \\(w\\).
\\(w = \frac{4xz - 1}{y} - 2\\)
\\(w = \frac{4xz - 2z}{y}\\)
\\(w = \frac{xz - z}{y} - 2\\)
\\(w = \frac{4xz - 2z}{y} - 2\\)

Explanation:

Step1: Cross-multiply to eliminate denominators

$$2z(2x - 1) = y(w + 2)$$

Step2: Expand left-hand side

$$4xz - 2z = y(w + 2)$$

Step3: Isolate term with $w$

$$\frac{4xz - 2z}{y} = w + 2$$

Step4: Solve for $w$

$$w = \frac{4xz - 2z}{y} - 2$$

Answer:

$w = \frac{4xz - 2z}{y} - 2$