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

To find an absolute value equation that has the solutions \( x = 8 \) and \( x = 18 \), you can use the following approach:

1. Identify the two solutions, which are 8 and 18.
2. The solutions indicate that the distance from \( x \) to the midpoint of these two solutions is the same.

**Step-by-step process to create the equation:**

1. **Find the midpoint of the solutions 8 and 18:**
   \[
   \text{Midpoint} = \frac{8 + 18}{2} = \frac{26}{2} = 13
   \]

2. **Determine the distance from each solution to the midpoint:**
   \[
   \text{Distance} = 18 - 13 = 5 \quad \text{(or equivalently, } 13 - 8 = 5\text{)}
   \]

3. **Formulate the absolute value equation:**

   An absolute value equation with solutions \( x = 8 \) and \( x = 18 \) can be written as:
   \[
   |x - 13| = 5
   \]

   This equation means that \( x \) is 5 units away from 13, either to the left (which gives \( x = 8 \)) or to the right (which gives \( x = 18 \)).

**Final Absolute Value Equation:**
\[
|x - 13| = 5
\]

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

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you solve an absolute value equation like \( |x - 4| = 7 \)?
2. What does the graph of the equation \( |x - 13| = 5 \) look like?
3. How can absolute value equations be used to solve real-world problems involving distance?
4. What is the general form of an absolute value equation with two solutions?
5. Can an absolute value equation have more than two solutions? If so, under what conditions?

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios, as they can lead to different solutions.

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

Discover how to write an absolute value equation with the solutions x = 8 and x = 18. This guide provides a step-by-step solution and explains the key algebraic concepts and formulas involved. Perfect for students in Grades 8-10.

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