The given inequality is:

\[
|p| + 2 > 5
\]

### Step-by-Step Solution:

1. **Isolate the absolute value term**:
   \[
   |p| > 5 - 2
   \]
   \[
   |p| > 3
   \]

2. **Break down the absolute value inequality**:
   When \( |p| > 3 \), it means \( p \) is either greater than 3 or less than -3. So we have two cases:

   - \( p > 3 \)
   - \( p < -3 \)

### Final Answer:
The solution to the inequality is:
\[
p > 3 \quad \text{or} \quad p < -3
\]

This can be written as:
\[
p \in (-\infty, -3) \cup (3, \infty)
\]

Would you like more details or have any questions?

Here are 5 related questions to practice:
1. Solve the inequality: \( |x| + 4 > 7 \).
2. Solve the inequality: \( |2x - 1| > 5 \).
3. What is the solution to \( |p| - 3 > 2 \)?
4. Solve the inequality: \( 3|x| + 1 > 10 \).
5. What does \( |x| = 0 \) imply about \( x \)?

**Tip**: When solving absolute value inequalities, always remember to consider both the positive and negative cases of the variable inside the absolute value.

Learn how to solve the absolute value inequality |p| + 2 > 5 with a step-by-step solution. This problem explores key algebraic concepts such as absolute value and inequalities, and is suitable for students in Grades 7-9.

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