To solve the inequality \( 2|x + 4| + 8 \geq 18 \), follow these steps:

### Step 1: Isolate the absolute value expression
First, subtract 8 from both sides:
\[
2|x + 4| \geq 10
\]

Next, divide both sides by 2:
\[
|x + 4| \geq 5
\]

### Step 2: Break the absolute value into two inequalities
The definition of absolute value gives two possible cases:
1. \( x + 4 \geq 5 \)
2. \( x + 4 \leq -5 \)

### Case 1: \( x + 4 \geq 5 \)
Subtract 4 from both sides:
\[
x \geq 1
\]

### Case 2: \( x + 4 \leq -5 \)
Subtract 4 from both sides:
\[
x \leq -9
\]

### Final Solution:
The solution is the union of both inequalities:
\[
x \geq 1 \quad \text{or} \quad x \leq -9
\]
This can be written in interval notation as:
\[
x \in (-\infty, -9] \cup [1, \infty)
\]

Would you like further details or have any questions?  
Here are some related questions for practice:

1. Solve \( 3|x - 2| - 7 \geq 5 \).
2. Solve \( |x + 1| + 4 < 9 \).
3. What is the solution to \( 4|x + 3| \leq 20 \)?
4. Solve \( |2x - 5| + 6 = 10 \).
5. Find the solution for \( |x + 6| > 7 \).

**Tip:** Always isolate the absolute value expression before breaking it into cases.

Learn how to solve the absolute value inequality 2|x + 4| + 8 ≥ 18 with a step-by-step breakdown. This problem involves key algebraic concepts, including isolating the absolute value and solving linear inequalities. Perfect for students in Grades 8-10.

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