1. **Problem:** Solve the equation $3x + 11 = 5x + 8$ for $x$. 2. **Formula and rules:** To solve for $x$, we use the properties of equality: we can add, subtract, multiply, or divide both sides of the equation by the same number without changing the equality. 3. **Step 1:** Subtract $3x$ from both sides to get all $x$ terms on one side: $$3x + 11 - \cancel{3x} = 5x + 8 - \cancel{3x} \implies 11 = 2x + 8$$ 4. **Step 2:** Subtract 8 from both sides to isolate the term with $x$: $$11 - 8 = 2x + 8 - 8 \implies 3 = 2x$$ 5. **Step 3:** Divide both sides by 2 to solve for $x$: $$\frac{3}{\cancel{2}} = \frac{2x}{\cancel{2}} \implies x = \frac{3}{2}$$ 6. **Answer:** The solution is $x = \frac{3}{2}$ or $1.5$.