https://file.aiquickdraw.com/mathbot/file/1728994319988l09rl0h8.jpg

The problem in the image asks to solve the absolute value inequality:

\[
\frac{|x + 6|}{8} \leq 1
\]

### Step 1: Isolate the absolute value expression
First, multiply both sides of the inequality by 8 to eliminate the denominator:

\[
|x + 6| \leq 8
\]

### Step 2: Solve the absolute value inequality
An absolute value inequality of the form \(|A| \leq B\) can be rewritten as a compound inequality:

\[
-8 \leq x + 6 \leq 8
\]

### Step 3: Solve for \(x\)
Subtract 6 from all parts of the inequality:

\[
-8 - 6 \leq x \leq 8 - 6
\]
\[
-14 \leq x \leq 2
\]

### Final Answer:
The solution to the inequality is:

\[
x \in [-14, 2]
\]

Thus:
- \(x \leq 2\)
- \(x \geq -14\)

Would you like further details or have any questions? Here are 5 related questions:

1. How do you solve absolute value inequalities with "greater than" signs?
2. What are the differences between solving strict inequalities and non-strict inequalities?
3. How do you check the solution to an absolute value inequality?
4. How does solving inequalities differ from solving equations?
5. How can you graph the solution of \(-14 \leq x \leq 2\) on a number line?

**Tip**: Always remember that absolute value inequalities represent ranges or intervals, depending on the inequality type.

Solve the absolute value inequality: (|x + 6|) / 8 ≤ 1

This detailed solution explains how to solve the absolute value inequality (|x + 6|) / 8 ≤ 1. It covers isolating the absolute value, rewriting it as a compound inequality, and solving the final inequality for x. Suitable for students in Grades 8-10.

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