1. The problem asks to express the solutions of the inequality $$-34 < x < 10$$ in three different ways and identify the correct interval notation. 2. This inequality means that $x$ is greater than $-34$ and less than $10$ at the same time. 3. The solution set can be expressed as: - Inequality form: $$-34 < x < 10$$ - Interval notation: Since the inequality is strict (no equal signs), the interval is open at both ends, so the solution is $$(-34, 10)$$. - Set-builder notation: $$\{x \mid -34 < x < 10\}$$ 4. Among the given options, the correct interval notation is $$(-34, 10)$$ because it excludes the endpoints $-34$ and $10$. 5. The other options either include endpoints or represent unions of intervals that do not match the original inequality. Final answer: The solution in interval notation is $$(-34, 10)$$.