1. **State the problem:** Solve the inequality $\frac{x+3}{2} \geq 5$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator (if positive) to eliminate the fraction. Since 2 is positive, the inequality direction remains the same. 3. **Multiply both sides by 2:** $$\frac{x+3}{2} \times 2 \geq 5 \times 2$$ $$x + 3 \geq 10$$ 4. **Isolate $x$ by subtracting 3 from both sides:** $$x + 3 - 3 \geq 10 - 3$$ $$x \geq 7$$ 5. **Interpretation:** The solution means all values of $x$ greater than or equal to 7 satisfy the inequality. **Final answer:** $$x \geq 7$$