https://file.aiquickdraw.com/mathbot/file/1726689280521odfa9nma.jpg

The equation in the image is:

\[
|8 - 5n| = 13
\]

To solve for \( n \), we need to consider both cases since the absolute value gives two possible equations:

### Case 1: Positive value
\[
8 - 5n = 13
\]

1. Subtract 8 from both sides:
   \[
   -5n = 13 - 8
   \]
   \[
   -5n = 5
   \]

2. Divide by -5:
   \[
   n = \frac{5}{-5} = -1
   \]

### Case 2: Negative value
\[
8 - 5n = -13
\]

1. Subtract 8 from both sides:
   \[
   -5n = -13 - 8
   \]
   \[
   -5n = -21
   \]

2. Divide by -5:
   \[
   n = \frac{-21}{-5} = \frac{21}{5}
   \]

### Final Solutions:
The solutions are:
\[
n = -1 \quad \text{or} \quad n = \frac{21}{5}
\]

Do you have any questions or would you like further details on these steps?

Here are 5 related questions:
1. How do you solve absolute value equations with more complex expressions?
2. What happens if the right-hand side of an absolute value equation is negative?
3. How can you check if your solutions for \( n \) are correct?
4. How would you solve absolute value inequalities?
5. What is the general form of an absolute value equation, and how does it affect the solution?

**Tip:** Always remember to check both the positive and negative scenarios when solving absolute value equations.

Solve the absolute value equation |8 - 5n| = 13.

Learn how to solve the absolute value equation |8 - 5n| = 13 step-by-step. This problem covers key algebraic concepts and the absolute value property, making it suitable for students in Grades 8-10.

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