To solve the inequality \(-36 < 3p - 6 < -15\), we'll break it down into two separate inequalities and solve for \(p\) in each.

### Step 1: Solve the first part \(-36 < 3p - 6\)
Add \(6\) to both sides:
\[
-36 + 6 < 3p 
\]
\[
-30 < 3p 
\]
Divide by \(3\):
\[
-10 < p 
\]
This can be written as:
\[
p > -10
\]

### Step 2: Solve the second part \(3p - 6 < -15\)
Add \(6\) to both sides:
\[
3p - 6 + 6 < -15 + 6
\]
\[
3p < -9 
\]
Divide by \(3\):
\[
p < -3
\]

### Step 3: Combine the results
The solution is the intersection of the two solutions:
\[
-10 < p < -3
\]

This means that \(p\) must be greater than \(-10\) and less than \(-3\).

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. Solve the inequality \(4p - 7 < 5\).
2. Find the solution to \(-2 < 2p + 4 \leq 10\).
3. Determine the solution set for \(3 < 5 - 2p < 9\).
4. Solve the compound inequality \( -15 < 5p + 10 < 20\).
5. If \(p\) is a solution of \(-12 < 3p - 9 < -3\), what is the range of \(p\)?

**Tip:** When solving compound inequalities, remember to treat each part of the inequality separately before combining the results.

Learn how to solve the compound inequality -36 < 3p - 6 < -15 step-by-step with detailed explanations and practice questions. This problem covers key algebraic concepts including inequalities and linear equations. Suitable for students in Grades 7-9.

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