Graph the compound inequality on the number line. \[ x \leq-7 \text { or } x \geq-3 \]

To graph the compound inequality \( x \leq -7 \) or \( x \geq -3 \) on a number line, we can follow these steps: 1. **Identify the critical points**: The critical points from the inequalities are \( -7 \) and \( -3 \). 2. **Graph the first inequality \( x \leq -7 \)**: - This means that all values of \( x \) that are less than or equal to \( -7 \) are included. - On the number line, we will place a closed circle at \( -7 \) (indicating that \( -7 \) is included) and shade to the left. 3. **Graph the second inequality \( x \geq -3 \)**: - This means that all values of \( x \) that are greater than or equal to \( -3 \) are included. - On the number line, we will place a closed circle at \( -3 \) (indicating that \( -3 \) is included) and shade to the right. 4. **Combine the graphs**: - Since the compound inequality uses "or," we will combine both shaded regions. This means the graph will show all values to the left of \( -7 \) and all values to the right of \( -3 \). ### Final Representation: - The number line will have a closed circle at \( -7 \) with shading to the left, and a closed circle at \( -3 \) with shading to the right. This visually represents the solution to the compound inequality \( x \leq -7 \) or \( x \geq -3 \).