https://file.aiquickdraw.com/mathbot/file/1728457050398wv4slm9h.jpg

To solve this problem, we need to find an absolute value equation that matches the given points on the number line.

The two points shown are at \(x = -3\) and \(x = 1\). In an absolute value equation of the form \( |x - a| = b \), \(a\) is the midpoint of these two numbers, and \(b\) is the distance from the midpoint to either of the points.

1. **Step 1: Find the midpoint**
   - The midpoint between \(-3\) and \(1\) is:
     \[
     \frac{-3 + 1}{2} = \frac{-2}{2} = -1
     \]
     So, the midpoint is \(-1\).

2. **Step 2: Find the distance from the midpoint**
   - The distance from \(-1\) to either \(-3\) or \(1\) is:
     \[
     |-3 - (-1)| = |1 - (-1)| = 2
     \]
     Therefore, the distance is 2.

3. **Step 3: Write the equation**
   - The absolute value equation that satisfies this is:
     \[
     |x + 1| = 2
     \]
     (since \(x + 1 = x - (-1)\)).

Thus, the correct answer is:
\[
\boxed{|x + 1| = 2}
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions:
1. What is the general form of an absolute value equation?
2. How do you determine the midpoint between two points?
3. Can an absolute value equation have more than two solutions?
4. How does shifting affect the graph of an absolute value equation?
5. How do you solve an absolute value equation like \( |x - a| = b \)?

**Tip:** When working with absolute value equations, always remember the midpoint is the center of symmetry between the two solutions.

Write an absolute value equation for the given graph.

Learn how to find the absolute value equation for points at x = -3 and x = 1 on a number line. This problem demonstrates the use of midpoints, distance calculations, and writing absolute value equations, suitable for students in Grades 8-10.

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