Question: Express the following inequality using interval notation.
$\frac{1}{2}x - 16 > 17$
1. **State the problem:** We need to solve the inequality $$\frac{1}{2}x - 16 > 17$$ and express the solution in interval notation.
2. **Add 16 to both sides:**
$$\frac{1}{2}x - 16 + 16 > 17 + 16$$
$$\frac{1}{2}x > 33$$
3. **Multiply both sides by 2 to isolate $x$:**
$$2 \times \frac{1}{2}x > 2 \times 33$$
$$\cancel{2} \times \frac{1}{\cancel{2}} x > 66$$
$$x > 66$$
4. **Interpret the inequality:** The solution is all $x$ values greater than 66.
5. **Write the solution in interval notation:**
$$(66, \infty)$$
**Final answer:** The solution to the inequality $$\frac{1}{2}x - 16 > 17$$ is $$x \in (66, \infty)$$.