1. **State the problem:** Solve the equation $$\frac{x n + n}{n} = 10$$ for $x$. 2. **Understand the expression:** The numerator is $x n + n$, and the denominator is $n$. We want to simplify this fraction. 3. **Simplify the fraction:** Use the distributive property to factor $n$ from the numerator: $$\frac{n(x + 1)}{n}$$ 4. **Cancel common factors:** Since $n \neq 0$, we can cancel $n$ in numerator and denominator: $$x + 1 = 10$$ 5. **Solve for $x$:** Subtract 1 from both sides: $$x = 10 - 1$$ $$x = 9$$ **Final answer:** $x = 9$