Given that $a$, $b$, and $c$ are non-zero, solve the equation $\frac{a}{b} = 2c$ for $b$.

1. Problem Description

Given that $a$, $b$, and $c$ are non-zero, solve the equation $\frac{a}{b} = 2c$ for $b$.

2. Solution Steps

We are given the equation:

$\frac{a}{b} = 2c$

We want to solve for $b$. First, multiply both sides of the equation by $b$:

$b \cdot \frac{a}{b} = b \cdot 2c$

$a = 2bc$

Next, divide both sides of the equation by $2c$ to isolate $b$:

$\frac{a}{2c} = \frac{2bc}{2c}$

$\frac{a}{2c} = b$

So, $b = \frac{a}{2c}$.

3. Final Answer

$b = \frac{a}{2c}$