1. The problem asks to convert interval notation solutions of an absolute value inequality into set-builder notation. 2. Recall that interval notation like $(-\infty, -34) \cup [10, \infty)$ means all $x$ such that $x < -34$ or $x \geq 10$. 3. Similarly, $(-\infty, -34] \cup (-10, \infty)$ means all $x$ such that $x \leq -34$ or $x > -10$. 4. Set-builder notation uses conditions on $x$ to describe these sets. For example, $\{x \mid x < -34 \text{ or } x \geq 10\}$ matches the first interval. 5. Now, analyze the given options: - $\{x \mid x > -34 \text{ or } x > 10\}$ means $x$ is greater than $-34$ or greater than $10$, which simplifies to $x > -34$ (since $x > 10$ is included in $x > -34$). This does not match the intervals given. - $\{x \mid x < -34 \text{ or } x < 10\}$ means $x$ is less than $-34$ or less than $10$, which simplifies to $x < 10$ (since $x < -34$ is included in $x < 10$). This does not match the intervals given. - $\{x \mid -34 < x < 10\}$ means $x$ is strictly between $-34$ and $10$, which corresponds to the interval $(-34, 10)$, not the unions given. - $\{x \mid 34 > x > -10\}$ means $x$ is between $-10$ and $34$, which is unrelated to the intervals given. 6. Therefore, none of the provided set-builder notations exactly match the given interval unions. 7. The correct set-builder notation for $(-\infty, -34) \cup [10, \infty)$ is $\{x \mid x < -34 \text{ or } x \geq 10\}$. 8. The correct set-builder notation for $(-\infty, -34] \cup (-10, \infty)$ is $\{x \mid x \leq -34 \text{ or } x > -10\}$. Final answer: None of the given options correctly represent the intervals in set-builder notation.