https://file.aiquickdraw.com/mathbot/file/1729545305932vgpk8apm.jpg

The equation provided in the image is:

\[
-7p - 6 + 6p = 2p + 9
\]

Let's solve this step-by-step:

1. **Combine like terms on both sides:**

   On the left side, combine the \(p\)-terms:
   \[
   -7p + 6p = -p
   \]
   So, the equation simplifies to:
   \[
   -p - 6 = 2p + 9
   \]

2. **Move all the \(p\)-terms to one side and constants to the other side:**

   Add \(p\) to both sides to eliminate the negative \(p\) on the left side:
   \[
   -6 = 3p + 9
   \]

3. **Isolate the variable:**

   Subtract 9 from both sides:
   \[
   -6 - 9 = 3p
   \]
   \[
   -15 = 3p
   \]

4. **Solve for \(p\):**

   Divide both sides by 3:
   \[
   p = \frac{-15}{3} = -5
   \]

Thus, the solution is:
\[
p = -5
\]

Would you like a more detailed explanation or have any further questions?

Here are some related questions you could explore:
1. How do you solve equations with variables on both sides?
2. What are some common mistakes when solving multi-step equations?
3. Can equations have no solution or infinite solutions?
4. How does distributing work when solving equations?
5. How do you check if your solution is correct?

**Tip:** Always check your solution by substituting it back into the original equation to verify it satisfies both sides.

Learn how to solve the linear equation -7p - 6 + 6p = 2p + 9. This step-by-step solution covers key algebraic concepts such as combining like terms and isolating variables, suitable for Grade 8 students.

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