Solve for $x$ in the equation $t = \omega - \frac{q}{x}$.

1. Problem Description

Solve for $x$ in the equation $t = \omega - \frac{q}{x}$.

2. Solution Steps

We are given the equation $t = \omega - \frac{q}{x}$. We want to isolate $x$.

First, subtract $\omega$ from both sides of the equation:

$t - \omega = -\frac{q}{x}$

Multiply both sides by $x$:

$x(t - \omega) = -q$

Divide both sides by $(t - \omega)$:

$x = \frac{-q}{t - \omega}$

We can multiply the numerator and denominator by -1 to get:

$x = \frac{q}{\omega - t}$

3. Final Answer

$x = \frac{q}{\omega - t}$