We will solve the equation step-by-step:

Given:
\[
10 ( 2x - 7 ) - 3n = 7
\]

### Step 1: Expand the parentheses
\[
10 \times (2x - 7) = 20x - 70
\]
So the equation becomes:
\[
20x - 70 - 3n = 7
\]

### Step 2: Move constants to the right side of the equation
\[
20x - 70 = 7 + 3n
\]
\[
20x = 77 + 3n
\]

### Step 3: Solve for \( x \)
Divide both sides by 20:
\[
x = \frac{77 + 3n}{20}
\]

This is the solution in terms of \( n \).

Would you like me to explain any of these steps in more detail?

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Here are 5 related questions to expand your understanding:
1. How would the solution change if the equation had a different constant on the right side?
2. What happens if we divide both sides of the equation by a constant instead of expanding first?
3. Can you solve this for \( n \) in terms of \( x \) instead?
4. How would this approach work for a quadratic equation?
5. What happens if the parentheses contain a more complex expression?

**Tip:** Always check if you can simplify the equation before solving, such as by factoring or expanding parentheses.

Learn how to solve the linear equation 10(2x - 7) - 3n = 7 step-by-step. This problem covers key algebraic concepts such as distributing constants and solving for variables. Suitable for students in Grades 7-9.

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