Let's solve the equation step by step:

Given:
\[
-16(x + 1) = -4(2 + 4x)
\]

### Step 1: Distribute the constants on both sides of the equation.
\[
-16 \cdot x - 16 \cdot 1 = -4 \cdot 2 - 4 \cdot 4x
\]
\[
-16x - 16 = -8 - 16x
\]

### Step 2: Simplify both sides of the equation.
\[
-16x - 16 = -8 - 16x
\]

### Step 3: Move the terms involving \(x\) to one side and constants to the other side.
To do this, we can add \(16x\) to both sides of the equation:
\[
-16x + 16x - 16 = -8 - 16x + 16x
\]
This simplifies to:
\[
-16 = -8
\]

### Step 4: Analyze the result.
The equation \(-16 = -8\) is not true, meaning there is no value of \(x\) that satisfies the original equation.

### Conclusion:
This equation has **no solution**.

Would you like further details or have any other questions?

### Related Questions:
1. How do you solve equations involving distribution?
2. What does it mean when an equation has no solution?
3. How can you check if an equation has infinite solutions?
4. What are the steps to solving linear equations with variables on both sides?
5. How do you solve equations with fractions?
6. What is the importance of simplifying both sides of an equation?
7. Can you provide examples of equations with infinite solutions?
8. What are common mistakes to avoid when solving linear equations?

#### Tip:
Always double-check your work by substituting the solution back into the original equation. This ensures that the solution satisfies the equation.

Learn how to solve the linear equation -16(x + 1) = -4(2 + 4x) step-by-step. Understand the application of the distributive property and solving linear equations. Suitable for high school students.

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