https://file.aiquickdraw.com/mathbot/file/1726143978026nhr0oppz.jpg

The problem asks to write equations involving absolute values for the graphs shown.

Let's break down the graphs based on the image:

### Graph 24:
- The line segment starts at \( x = -3 \) and ends at \( x = 3 \), which means the center of this line segment is at 0.
- This suggests that the absolute value expression is centered at 0 and spans 3 units in both directions. Therefore, the equation can be written as:
  \[
  |x| \leq 3
  \]

### Graph 25:
- The line segment starts at \( x = -8 \) and ends at \( x = -4 \). The center of this segment is the midpoint of \(-8\) and \(-4\), which is \(-6\).
- The distance from the center to either endpoint is 2. Therefore, the equation is:
  \[
  |x + 6| \leq 2
  \]

### Graph 26:
- Similar to Graph 24, the line segment starts at \( x = -3 \) and ends at \( x = 3 \), centered at 0.
- The equation is the same as in Graph 24:
  \[
  |x| \leq 3
  \]

### Graph 27:
- The line segment starts at \( x = -6 \) and ends at \( x = -4 \), with the center at \(-5\).
- The distance from the center to the endpoints is 1. Therefore, the equation is:
  \[
  |x + 5| \leq 1
  \]

Would you like more details on any of these graphs or their corresponding equations?

Here are 5 related questions to expand on the topic:
1. How do you find the midpoint of a line segment on a number line?
2. What is the general form of an absolute value inequality involving a midpoint and a distance?
3. How can we solve absolute value inequalities algebraically?
4. What are the key differences between solving absolute value equations and inequalities?
5. How can we graph an absolute value inequality?

**Tip:** Always double-check the distance from the center to the endpoints to ensure the correct expression in the absolute value inequality.

Write an equation involving absolute value for each graph.

Learn how to write equations involving absolute value for segments on a number line. This covers the core concepts of finding midpoints, distances, and formulating absolute value inequalities. Ideal for students in Grades 7-9.

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