1. **Stating the problem:** We want to solve a simple algebraic equation as an example. 2. **Example problem:** Solve for $x$ in the equation $$2x + 3 = 7$$. 3. **Formula and rules:** To solve for $x$, we isolate $x$ by performing inverse operations. We subtract 3 from both sides and then divide both sides by 2. 4. **Step-by-step solution:** - Subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ $$2x = 4$$ - Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{4}{2}$$ $$x = 2$$ 5. **Explanation:** We first removed the constant term 3 by subtracting it from both sides to keep the equation balanced. Then, we divided both sides by the coefficient of $x$, which is 2, to solve for $x$. The cancellation notation shows the division of the coefficient. 6. **Final answer:** $$x = 2$$