https://file.aiquickdraw.com/mathbot/file/1727404696452tcj4enmw.jpg

To solve part (a) of the question, we need to describe the union of the intervals shown in the two number line graphs using a compound inequality.

### Analysis of the Graphs:
1. **Top graph (green):**
   - The green line starts at \(-4\) (closed circle) and extends to 1 (open circle). 
   - This indicates that the inequality for the green line is: 
     \[
     -4 \leq x < 1
     \]

2. **Bottom graph (red):**
   - The red line starts at \(-2\) (closed circle) and extends to 3 (closed circle).
   - This means the inequality for the red line is: 
     \[
     -2 \leq x \leq 3
     \]

### Union of the Two Graphs:
The union combines both intervals. Visually, the union covers the range from \(-4\) to 3.

- Starting from \(-4\), the green line includes all values up to (but not including) 1, while the red line overlaps from \(-2\) and continues up to 3. 
- The union will therefore cover all values from \(-4\) to 3, with:
   - A closed boundary at \(-4\),
   - An open boundary at 1,
   - And a closed boundary at 3.

### Compound Inequality:
The union of these intervals can be written as:
\[
-4 \leq x < 1 \quad \text{or} \quad -2 \leq x \leq 3
\]

This is the compound inequality describing the union of the points in the graph.

Would you like any further details on this? 

Here are 5 related questions to expand on this concept:
1. What is the difference between union and intersection in terms of inequalities?
2. How would you graph the intersection of these two sets?
3. Can you explain how to solve compound inequalities involving "or" conditions?
4. What are other methods to represent this union, such as interval notation?
5. How do you solve inequalities when there are more complex combinations of "and" and "or" statements?

**Tip:** When dealing with compound inequalities, it helps to carefully consider both the boundaries (open and closed) and overlap between the intervals!

For the graphs shown above, find the following: a) Write a compound inequality to describe the union of the points shown in the graphs.

Learn how to write a compound inequality to describe the union of two intervals from graph representations. This problem involves understanding inequalities, open and closed boundaries, and set theory. Suitable for students in Grades 8-10.

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