To solve the absolute value inequality $|x + 8| \leq 2$, we need to rewrite it as a compound inequality:

Step 1: Rewrite the inequality

The inequality $|x + 8| \leq 2$ means that the expression inside the absolute value lies between -2 and 2: $-2 \leq x + 8 \leq 2$

Step 2: Solve the compound inequality

Now, we solve each part separately.

1. $-2 \leq x + 8$ $x \geq -2 - 8$ $x \geq -10$

2. $x + 8 \leq 2$ $x \leq 2 - 8$ $x \leq -6$

Step 3: Combine the solutions

The solution to the original inequality is: $-10 \leq x \leq -6$

So, the values that satisfy the inequality are: $x \leq -6 \quad \text{and} \quad x \geq -10$

Would you like to explore more about absolute inequalities, or do you have any questions about this topic?

Here are some related questions you can try:

1. Solve $|x - 3| \leq 5$.
2. What is the solution to $|2x + 1| > 4$?
3. Solve $|x - 4| \geq 7$.
4. How does the solution change if the inequality is $|x + 8| < 2$?
5. Explain how to solve $|3x + 2| \leq 5$.

Tip: When solving absolute value inequalities, always consider the two possible cases for the expression inside the absolute value being both positive and negative.