The given inequality is a compound inequality involving "or" (symbolized by "ó"). We will solve each inequality separately and then combine the solutions.

### Step 1: Solve \( x + 2 > 5 \)
Subtract 2 from both sides:
\[
x > 5 - 2
\]
\[
x > 3
\]

### Step 2: Solve \( x + 1 < -2 \)
Subtract 1 from both sides:
\[
x < -2 - 1
\]
\[
x < -3
\]

### Step 3: Combine the solutions
The compound inequality uses "or" (denoted by "ó"), so the solution is either:
- \( x > 3 \) **or** 
- \( x < -3 \)

This means the solution is all values of \( x \) that satisfy either condition.

### Final Solution:
\[
x > 3 \quad \text{or} \quad x < -3
\]
In interval notation, the solution is:
\[
(-\infty, -3) \cup (3, \infty)
\]

Would you like more details or have any questions?

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Here are 5 related questions to explore further:
1. How would the solution change if the inequality used "and" instead of "or"?
2. What is the graphical representation of this compound inequality on a number line?
3. How would the solution be different if one inequality included a "greater than or equal to" sign?
4. How do you solve compound inequalities that involve absolute values?
5. Can this inequality be rewritten as a single absolute value inequality?

**Tip:** When solving compound inequalities with "or," the solution is the union of both inequalities—meaning it includes all values that satisfy either part.

Learn how to solve the compound inequality x + 2 > 5 or x + 1 < -2 with step-by-step guidance. Understand key algebraic concepts such as solving inequalities, compound inequality solutions, and expressing results in interval notation. This problem is suitable for students in Grades 8-10.

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