The graph shows a number line with the shaded region between -6 and 5, inclusive of the endpoints. To express this graph as an absolute value inequality, we need to define an inequality that describes the distance of the variable $x$ from the midpoint of the interval.

Steps:

1. The endpoints are at $-6$ and $5$, and the midpoint between them is: $\text{Midpoint} = \frac{-6 + 5}{2} = -\frac{1}{2}$

2. The distance from the midpoint $-\frac{1}{2}$ to either endpoint (which is the same for both sides) is: $\text{Distance} = 5 - \left( -\frac{1}{2} \right) = 5 + \frac{1}{2} = \frac{11}{2}$

3. The absolute value inequality for this situation describes all values of $x$ that are within $\frac{11}{2}$ units of $-\frac{1}{2}$: $|x + \frac{1}{2}| \leq \frac{11}{2}$

Final Answer:

The absolute value inequality for the graph is: $|x + \frac{1}{2}| \leq \frac{11}{2}$

This inequality represents all values of $x$ between $-6$ and $5$.

Do you want more details or have any questions?

Here are 5 related questions to think about:

1. How would the inequality change if the endpoints were not included?
2. Can you express this inequality as a compound inequality instead of using absolute value?
3. What happens to the inequality if you shift the graph by 2 units to the right?
4. How would you solve this inequality algebraically to get the interval notation?
5. Can this inequality be applied to real-world scenarios involving distances?

Tip: When working with absolute value inequalities, remember that the inequality symbol (less than or greater than) tells you whether you're dealing with a range of values within a specific distance (for $\leq$) or beyond a certain distance (for $\geq$).