Let's solve the equation \( 3n - 2(-2 - 7n) = 4(1 - 8n) \).

### Step 1: Distribute on both sides
On the left side, distribute the \(-2\) across the terms inside the parentheses:
\[
-2(-2 - 7n) = -2(-2) + (-2)(-7n) = 4 + 14n
\]
So the equation becomes:
\[
3n + 4 + 14n = 4 - 32n
\]

### Step 2: Combine like terms
On the left side, combine the \(n\) terms:
\[
3n + 14n = 17n
\]
This gives:
\[
17n + 4 = 4 - 32n
\]

### Step 3: Move all terms involving \(n\) to one side
Add \(32n\) to both sides to move all the \(n\) terms to one side:
\[
17n + 32n + 4 = 4
\]
\[
49n + 4 = 4
\]

### Step 4: Isolate the variable \(n\)
Subtract 4 from both sides to isolate the \(n\) term:
\[
49n = 0
\]

### Step 5: Solve for \(n\)
Finally, divide by 49:
\[
n = 0
\]

The solution is \( n = 0 \).

Would you like more details or have any questions?

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Here are some related questions to explore:

1. How would the equation change if the constant on the right side was different?
2. Can you solve a similar equation with a different distribution pattern?
3. What happens if you change the coefficients of \(n\) on either side?
4. How does solving the equation change if the term involving \(n\) was inside another set of parentheses?
5. What is the significance of the distribution step in solving equations?

**Tip:** Always combine like terms after distribution to simplify the equation as much as possible before isolating the variable.

Learn how to solve the linear equation 3n - 2(-2 - 7n) = 4(1 - 8n) with a step-by-step solution. This problem involves using the distributive property to simplify expressions and isolate the variable n. Suitable for students in Grades 7-9.

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