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The question asks to identify an absolute value equation that has the solutions \( x = 3.4 \) and \( x = 9.4 \).

For an absolute value equation of the form \( |x - a| = b \), the solutions are given by \( x = a + b \) and \( x = a - b \).

Given the solutions \( x = 3.4 \) and \( x = 9.4 \), we can compute the midpoint and the distance between these two solutions:

- Midpoint: \( \frac{3.4 + 9.4}{2} = 6.4 \)
- Distance from the midpoint to either solution: \( 9.4 - 6.4 = 3 \)

Thus, the equation can be written as:
\[
|x - 6.4| = 3
\]

This matches the third option in the list:
\[
|x - 6.4| = 3
\]

Would you like more details or have any questions?

Here are some related questions to consider:
1. How do you solve absolute value equations with two solutions?
2. What is the significance of the midpoint in absolute value problems?
3. How can we graph the absolute value function \( |x - 6.4| = 3 \)?
4. What are other forms of absolute value equations that could have two specific solutions?
5. How does changing the value inside the absolute value affect the solutions?

**Tip:** When solving absolute value equations, always check for two possible solutions by considering both the positive and negative cases.

Identify an absolute value equation that has the solutions x = 3.4 and x = 9.4.

Learn how to identify an absolute value equation with solutions x = 3.4 and x = 9.4 using the formula |x - a| = b. This problem covers absolute value and algebra concepts suitable for students in Grades 6-8.

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