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

1. **Isolate the absolute value term:**

   \[
   2|x + 4| + 8 \geq 18
   \]

   Subtract 8 from both sides:

   \[
   2|x + 4| \geq 10
   \]

2. **Divide by 2:**

   \[
   |x + 4| \geq 5
   \]

3. **Set up the two cases for the absolute value:**

   - **Case 1:** \( x + 4 \geq 5 \)

     Solve for \( x \):

     \[
     x \geq 1
     \]

   - **Case 2:** \( x + 4 \leq -5 \)

     Solve for \( x \):

     \[
     x \leq -9
     \]

4. **Combine the solutions:**

   The solution to the inequality is:

   \[
   x \leq -9 \quad \text{or} \quad x \geq 1
   \]

   In interval notation, this is:

   \[
   (-\infty, -9] \cup [1, \infty)
   \]

This is the final answer. 

Do you want more details or have any questions about this process?

Here are 5 related questions to explore further:
1. How would the solution change if the inequality was \( 2|x + 4| + 8 > 18 \)?
2. What if the inequality was \( 2|x + 4| + 8 \leq 18 \)?
3. How would you solve \( |2x + 3| \geq 7 \)?
4. What are the general steps for solving absolute value inequalities?
5. How does the graph of \( |x + 4| \) relate to the solution?

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

Discover how to solve the absolute value inequality 2|x + 4| + 8 ≥ 18 with this detailed, step-by-step guide. Learn key concepts in algebra and understand the application of absolute value properties and inequality theorems. Ideal for students in Grades 9-11.

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