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.