Let's solve the equation \( 3n - 5 = -8(6 + 5n) \).

### Step 1: Distribute the \(-8\) on the right-hand side.
\[
3n - 5 = -8 \times 6 - 8 \times 5n
\]
\[
3n - 5 = -48 - 40n
\]

### Step 2: Move all the terms involving \(n\) to one side and the constants to the other.
\[
3n + 40n = -48 + 5
\]
\[
43n = -43
\]

### Step 3: Solve for \(n\).
\[
n = \frac{-43}{43} = -1
\]

So, the solution is \( n = -1 \).

Would you like more details or have any questions? 

Here are some related questions:
1. How do you check if \( n = -1 \) is a valid solution?
2. What happens if you make a mistake in distributing a negative sign?
3. How does distributing affect the equation in the first step?
4. How can you solve equations involving fractions instead of integers?
5. Can this method be used for inequalities?

**Tip:** Always distribute carefully when dealing with negative signs to avoid errors in your solution.

Explore the solution to the linear equation 3n - 5 = -8(6 + 5n). This problem involves algebraic manipulation, including the distributive property and solving for variables. Suitable for students in Grades 8-10.

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