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To solve the inequality \(|x + 2| \geq 7\), we will break it down into two cases based on the properties of absolute values.

### Case 1: \(x + 2 \geq 7\)

1. Solve the inequality:
\[
x + 2 \geq 7
\]
\[
x \geq 7 - 2
\]
\[
x \geq 5
\]

### Case 2: \(x + 2 \leq -7\)

1. Solve the inequality:
\[
x + 2 \leq -7
\]
\[
x \leq -7 - 2
\]
\[
x \leq -9
\]

### Combine the Solutions

From the two cases, we have:
1. \(x \geq 5\)
2. \(x \leq -9\)

### Solution in Interval Notation
The complete solution set can be written in interval notation as:
\[
(-\infty, -9] \cup [5, \infty)
\]

### Graphing the Solution

To graph the solution:
- Draw a number line.
- Shade the region to the left of -9 (including -9, which is a closed circle).
- Shade the region to the right of 5 (including 5, which is also a closed circle).

### Select the Correct Choice

The final answer is:
\[
x \leq -9 \quad \text{or} \quad x \geq 5
\]
Express your answer in interval notation:
\[
(-\infty, -9] \cup [5, \infty)
\]