To solve the equation \( |x + 2| = 7 \), we need to consider the two possible cases for absolute value equations:

### Case 1: 
\[ x + 2 = 7 \]
Solving for \( x \):
\[
x = 7 - 2
\]
\[
x = 5
\]

### Case 2:
\[ x + 2 = -7 \]
Solving for \( x \):
\[
x = -7 - 2
\]
\[
x = -9
\]

### Final Solution:
The solutions to the equation \( |x + 2| = 7 \) are:
\[
x = 5 \quad \text{or} \quad x = -9
\]

Would you like any further explanation or details?

Here are 5 related questions to explore:
1. What is the general method for solving absolute value equations?
2. How would you solve the equation \( |x - 3| = 10 \)?
3. What happens when \( |x + 2| = -5 \)? 
4. How do you graph \( |x + 2| = 7 \) on the number line?
5. What is the geometric interpretation of absolute value in equations?

**Tip:** Always check both cases when solving absolute value equations, since the expression inside the absolute value can take either positive or negative values.

Explore how to solve the absolute value equation ∣x+2∣=7 with step-by-step solutions. Learn the key concepts of absolute value equations, including handling two possible cases and understanding the property of absolute values. Perfect for students in Grades 6-8.

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