1. **State the problem:** Solve the two-step equation $$\frac{1}{8}x + 11 = 12$$ for $x$ where the solution is a positive integer. 2. **Formula and rules:** The general form is $$\frac{1}{a}x + b = c$$. To solve for $x$, first isolate the term with $x$ by subtracting $b$ from both sides, then multiply both sides by $a$ to solve for $x$. 3. **Step 1: Subtract 11 from both sides** $$\frac{1}{8}x + 11 - 11 = 12 - 11$$ $$\frac{1}{8}x = 1$$ 4. **Step 2: Multiply both sides by 8 to isolate $x$** $$8 \times \frac{1}{8}x = 8 \times 1$$ $$\cancel{8} \times \frac{1}{\cancel{8}} x = 8$$ $$x = 8$$ 5. **Final answer:** The solution is $$x = 8$$, which is a positive integer as required.