Let's solve the equation:

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

### Step 1: Simplify both sides of the equation

On the right side, combine like terms \( p \) and \( -7p \):

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

### Step 2: Eliminate \( -6p \) from both sides

Since both sides have the same terms, \( -6p - 3 \), subtract \( -6p - 3 \) from both sides:

\[
0 = 0
\]

### Final Conclusion:

This equation is an identity, meaning that it holds true for all values of \( p \). Therefore, the solution is:

\[
\text{All real numbers.}
\]

Let me know if you have any questions or need further explanation!

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Here are 5 questions to consider:
1. What is the difference between an identity and a conditional equation?
2. How can you check if an equation is an identity?
3. What does it mean if an equation has no solution?
4. How do we solve equations involving variables on both sides?
5. How would the solution change if constants were different on both sides?

**Tip:** Always simplify and combine like terms on both sides of the equation first to make the solving process easier.

Learn how to solve the linear equation -6p - 3 = p - 3 - 7p, resulting in an identity that holds true for all real numbers. This example demonstrates simplifying and combining like terms on both sides of the equation. Suitable for students in Grades 6-8.

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