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To solve the inequality \( |2x + 8| \leq 11 \) or \( |2y + 8| \leq 11 \), we will break down the absolute values and determine the solution sets for each.

### Step 1: Solve \( |2x + 8| \leq 11 \)
This inequality splits into two inequalities:
\[
-11 \leq 2x + 8 \leq 11
\]
Subtract 8 from all sides:
\[
-19 \leq 2x \leq 3
\]
Now, divide by 2:
\[
-9.5 \leq x \leq 1.5
\]
This gives the solution for \( x \) in the range \([-9.5, 1.5]\).

### Step 2: Solve \( |2y + 8| \leq 11 \)
Similarly, this becomes:
\[
-11 \leq 2y + 8 \leq 11
\]
Subtract 8 from all sides:
\[
-19 \leq 2y \leq 3
\]
Divide by 2:
\[
-9.5 \leq y \leq 1.5
\]
Thus, \( y \) is also within the range \([-9.5, 1.5]\).

### Step 3: Interpret the "or" condition
The solution set is a union of two rectangles on the graph:
- One rectangle corresponds to \( -9.5 \leq x \leq 1.5 \) for all values of \( y \).
- The other rectangle corresponds to \( -9.5 \leq y \leq 1.5 \) for all values of \( x \).

Thus, the solution is the combined region formed by both inequalities.

### Step 4: Analyze the graphs
The correct graph will show a horizontal and vertical shaded region from \( x = -9.5 \) to \( x = 1.5 \), and from \( y = -9.5 \) to \( y = 1.5 \). Based on the solution structure, you should look for the graph where both these regions are shaded.

Looking at the provided images, the graph in the **top right corner** (second from the left) seems to match this description, as it shows the overlapping shaded regions corresponding to these bounds.

Would you like more details on any part of the solution?

### Related Questions:
1. How do you solve absolute value inequalities in general?
2. What is the difference between "and" and "or" in compound inequalities?
3. How can you graph inequalities involving absolute values on a coordinate plane?
4. How does the "union" of two solution sets look geometrically?
5. Can absolute value inequalities have disjoint solution regions?

#### Tip:
When graphing absolute value inequalities, always remember that the solution can result in two different regions based on the nature of the inequality (either "and" or "or").

Graph the solution set of the following linear inequality: |2x + 8| ≤ 11 or |2y + 8| ≤ 11

Solve and graph the absolute value inequalities |2x + 8| ≤ 11 or |2y + 8| ≤ 11. This problem involves breaking down the inequality into simpler linear inequalities, graphing the solution set, and understanding the union of solution regions. Suitable for high school algebra students in Grades 9-12.

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