Let's solve the equation:

\[
-4(-1x - 1) = -4(8 + 2x)
\]

### Steps:

1. **Distribute** the \( -4 \) on both sides of the equation:

\[
4x + 4 = -32 - 8x
\]

2. **Move the \( x \)-terms** to one side by adding \( 8x \) to both sides:

\[
4x + 8x + 4 = -32
\]
\[
12x + 4 = -32
\]

3. **Move the constant term** \( 4 \) to the other side by subtracting 4 from both sides:

\[
12x = -32 - 4
\]
\[
12x = -36
\]

4. **Solve for \( x \)** by dividing both sides by 12:

\[
x = \frac{-36}{12}
\]
\[
x = -3
\]

Thus, the solution is \( x = -3 \).

Would you like further details or any additional clarifications?

### Follow-up Questions:
1. How can you check if \( x = -3 \) is correct?
2. What happens if fractions were involved instead of integers?
3. How would the solution change if the equation involved decimals?
4. Can this equation be solved graphically?
5. What if the equation contained absolute values—how would that affect the solution?
6. How do you solve equations with variables inside parentheses on both sides?
7. How would you solve this equation if exponents were involved?
8. Could you approach solving this equation using another method, like substitution?

#### Tip: Distributing first and combining like terms early helps simplify equations and makes solving much easier.

Learn how to solve the equation -4(-1x - 1) = -4(8 + 2x) with a step-by-step solution. This problem involves applying the distributive property and solving linear equations. Suitable for students in Grades 7-9.

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