1. **State the problem:** Solve the equation $11w = 99$ for $w$. 2. **Formula and rules:** To solve for $w$, divide both sides of the equation by 11. Important rule: When dividing both sides of an equation by the same nonzero number, the equality remains true. 3. **Intermediate work:** $$11w = 99$$ Divide both sides by 11: $$\frac{\cancel{11}w}{\cancel{11}} = \frac{99}{11}$$ 4. **Simplify:** $$w = 9$$ 5. **Answer:** The value of $w$ is 9 inches.