https://file.aiquickdraw.com/mathbot/file/17272993080075fujck5o.jpg

The inequality shown in your image is:

\[
3|v - 12| \leq 3
\]

### Let's solve this step by step:

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

   Divide both sides of the inequality by 3 to simplify:
   \[
   |v - 12| \leq 1
   \]

2. **Rewrite the inequality without the absolute value:**

   An inequality of the form \( |x| \leq a \) can be rewritten as:
   \[
   -a \leq x \leq a
   \]
   So for \( |v - 12| \leq 1 \), we can write:
   \[
   -1 \leq v - 12 \leq 1
   \]

3. **Solve for \( v \):**

   Add 12 to all parts of the inequality:
   \[
   -1 + 12 \leq v \leq 1 + 12
   \]
   Simplifying:
   \[
   11 \leq v \leq 13
   \]

### Final Solution:

The solution to the inequality is:
\[
v \in [11, 13]
\]
This means that \( v \) is between 11 and 13, inclusive.

### Graphing the Solution:

On a number line, this would be represented by a closed interval from 11 to 13, where both endpoints (11 and 13) are filled in to indicate that they are included in the solution.

---

Do you want further details on how to graph this or have any questions?  
Here are some related questions to deepen your understanding:

1. How do you solve inequalities with absolute values in general?
2. What is the difference between strict (\(<\)) and non-strict (\(\leq\)) inequalities in solutions?
3. How would the solution change if the inequality were \(3|v - 12| > 3\)?
4. Can absolute value inequalities ever have no solutions?
5. How can you check if a value is a solution to the inequality?

**Tip:** When dealing with absolute value inequalities, remember they represent distance on a number line, which makes it easier to visualize the solution.

Graph the solution to the inequality on the number line: 3|v - 12| ≤ 3

Learn how to solve the absolute value inequality 3|v - 12| ≤ 3 and graph its solution on a number line. This problem focuses on key algebraic concepts such as solving and graphing inequalities, and is suitable for students in Grades 8-10.

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