To solve the equation:

\[
-6p - 3 = p - 3 - 7p
\]

### Step-by-step solution:

1. **Combine like terms on the right-hand side:**

\[
p - 7p = -6p
\]
Thus, the equation becomes:
\[
-6p - 3 = -6p - 3
\]

2. **Subtract \(-6p\) from both sides:**

\[
-6p - 3 - (-6p) = -6p - 3 - (-6p)
\]
This simplifies to:
\[
-3 = -3
\]

### Conclusion:

This is a true statement, which means the equation is **always true** for any value of \( p \). Therefore, the solution is:

\[
\text{All real numbers} \quad (p \in \mathbb{R})
\]

Would you like more details or explanations?

### Related questions:
1. How do you solve similar linear equations with variables on both sides?
2. What is the difference between "no solution" and "all real numbers" as solutions to equations?
3. Can you explain how to solve an equation with fractions on both sides?
4. What happens when variables cancel out in an equation?
5. How do you check if a solution is valid for an equation?

**Tip:** When both sides of an equation simplify to the same expression without any variables left, the solution is always all real numbers!

Discover how to solve the linear equation -6p - 3 = p - 3 - 7p with a step-by-step guide. This problem demonstrates how to combine like terms and apply properties of equality to solve for any value of p. Ideal for students in Grades 6-8.

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