Let's solve the equation step by step:

Given:
\[
-3p - 4(4p - 8) = 3(-8p - 1)
\]

### Step 1: Expand both sides of the equation
Expand \( -4(4p - 8) \) on the left side and \( 3(-8p - 1) \) on the right side.

\[
-3p - 4 \cdot 4p + 4 \cdot 8 = 3 \cdot -8p + 3 \cdot -1
\]

This simplifies to:
\[
-3p - 16p + 32 = -24p - 3
\]

### Step 2: Combine like terms
Combine the terms involving \( p \) on both sides.

\[
-19p + 32 = -24p - 3
\]

### Step 3: Move all terms involving \( p \) to one side and constants to the other side
Add \( 24p \) to both sides:

\[
-19p + 24p + 32 = -3
\]

This simplifies to:
\[
5p + 32 = -3
\]

Now, subtract 32 from both sides:

\[
5p = -3 - 32
\]

\[
5p = -35
\]

### Step 4: Solve for \( p \)
Divide both sides by 5:

\[
p = -7
\]

The solution is:
\[
p = -7
\]

Would you like further details or have any questions about the steps?

### Related Questions:
1. How do you solve multi-step equations involving variables on both sides?
2. What are the properties of equality used when solving linear equations?
3. How does distributing negative numbers affect the signs of terms in an equation?
4. What are some strategies for combining like terms in complex expressions?
5. How can you verify the solution of a linear equation?

### Tip:
Always simplify the equation as much as possible before isolating the variable to make solving easier.

Learn how to solve the linear equation -3p - 4(4p - 8) = 3(-8p - 1) step-by-step, using key algebraic concepts like the distributive property and combining like terms. This guide is ideal for students in Grades 8-10.

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