Let's solve the equation \( 7(n + 51) = 77 \).

### Step-by-step solution:

1. Distribute the \( 7 \) on the left-hand side:
   \[
   7 \cdot n + 7 \cdot 51 = 77
   \]
   \[
   7n + 357 = 77
   \]

2. Subtract \( 357 \) from both sides:
   \[
   7n = 77 - 357
   \]
   \[
   7n = -280
   \]

3. Divide both sides by \( 7 \) to isolate \( n \):
   \[
   n = \frac{-280}{7}
   \]
   \[
   n = -40
   \]

Thus, the solution is \( n = -40 \).

Would you like more details or further explanations?

Here are 5 related questions for further practice:
1. Solve \( 6(n + 30) = 90 \).
2. What is the solution to \( 9(n - 4) = 72 \)?
3. If \( 8(n + 15) = 64 \), find \( n \).
4. Solve \( 5(n + 10) = 60 \).
5. What is \( n \) if \( 3(n + 25) = 150 \)?

**Tip**: Always distribute first when solving equations like this one before simplifying.

This page explains how to solve the linear equation 7(n + 51) = 77 using algebraic techniques such as distribution and solving for the variable n. A step-by-step solution is provided, perfect for students in Grades 6-8.

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