Graph and write interval notation. \( x \leq-3 \) or \( x>3 \)

To graph the inequality \( x \leq -3 \) or \( x > 3 \), we can break it down into two parts: 1. **For \( x \leq -3 \)**: - This includes all values of \( x \) that are less than or equal to -3. On a number line, this is represented by a solid dot at -3 (indicating that -3 is included) and a line extending to the left. 2. **For \( x > 3 \)**: - This includes all values of \( x \) that are greater than 3. On a number line, this is represented by an open dot at 3 (indicating that 3 is not included) and a line extending to the right. ### Graph: ``` <---●==================== 3 ●---> -3 3 ``` - The solid dot at -3 indicates that -3 is included in the solution set. - The open dot at 3 indicates that 3 is not included in the solution set. ### Interval Notation: The solution in interval notation combines the two intervals: - For \( x \leq -3 \), the interval is \( (-\infty, -3] \). - For \( x > 3 \), the interval is \( (3, \infty) \). Thus, the complete solution in interval notation is: \[ (-\infty, -3] \cup (3, \infty) \]