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The image asks for an absolute value equation that has the solutions \( x = 8 \) and \( x = 18 \).

To write an absolute value equation for this, we follow these steps:

1. The absolute value equation typically takes the form \( |x - c| = d \), where \( c \) is the midpoint of the two solutions, and \( d \) is the distance from the midpoint to either solution.
   
2. Find the midpoint between 8 and 18:
   \[
   c = \frac{8 + 18}{2} = 13
   \]
   
3. Find the distance from the midpoint to either solution:
   \[
   d = 18 - 13 = 5
   \]

4. The absolute value equation is then:
   \[
   |x - 13| = 5
   \]

This equation has the solutions \( x = 8 \) and \( x = 18 \).

Would you like more details or have any further questions?

Here are five related questions you might find interesting:

1. What is the general form of an absolute value equation with two solutions?
2. How do you solve an absolute value equation?
3. How can you graph absolute value equations like the one derived?
4. What are some real-world applications of absolute value equations?
5. How can the concept of absolute value be extended to complex numbers?

**Tip:** When solving an absolute value equation, always check for two possible solutions because the equation can equal both positive and negative values.

Write an absolute value equation that has the solutions x = 8 and x = 18.

Learn how to write an absolute value equation with the solutions x = 8 and x = 18. This problem covers key algebraic concepts, including finding the midpoint and the distance in an absolute value equation. Suitable for students in Grades 7-9.

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