1. **Problem Statement:** Set a sample algebra question: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. **Formula and Rules:** To solve a linear equation, isolate the variable $x$ by performing inverse operations. 3. **Step-by-step Solution:** - Subtract 3 from both sides: $$2x + 3 - 3 = 11 - 3$$ - Simplify: $$2x = 8$$ - Divide both sides by 2: $$\frac{2x}{2} = \frac{8}{2}$$ - Simplify: $$x = 4$$ 4. **Explanation:** We used basic algebraic operations to isolate $x$. Subtracting 3 removes the constant term on the left, and dividing by 2 removes the coefficient of $x$, leaving $x$ alone. 5. **Final Answer:** $$x = 4$$