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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.

Solve the absolute value inequality |x + 8| ≤ 2.

Learn how to solve the absolute value inequality |x + 8| ≤ 2, with detailed steps. This algebra problem involves rewriting the inequality as a compound inequality and solving it for x. Suitable for Grades 7-9 students.

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