1. **State the problem:** Solve the equation $\frac{x}{2} + 1 = 3$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operations. 3. **Step-by-step solution:** - Subtract 1 from both sides: $$\frac{x}{2} + 1 - 1 = 3 - 1$$ $$\frac{x}{2} = 2$$ - Multiply both sides by 2 to eliminate the denominator: $$2 \times \frac{x}{2} = 2 \times 2$$ $$x = 4$$ 4. **Final answer:** $$x = 4$$ This means the value of $x$ that satisfies the equation is 4.