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.