https://file.aiquickdraw.com/mathbot/file/1727312068086b2levm1d.jpg

To determine which inequality corresponds to the given graph, let's analyze the information:

### Step 1: Graph Analysis
- The graph shows a shaded portion between \(-4\) and \(4\), including both endpoints.
- This suggests the solution is bounded between \(-4\) and \(4\), inclusive. 
- Mathematically, this can be expressed as: 
  \[
  -4 \leq s \leq 4
  \]
  
### Step 2: Check each option
We will solve each inequality to see if it fits the solution range \([-4, 4]\).

1. **\(3s + 7 > -5\)**:
   \[
   3s + 7 > -5 \implies 3s > -12 \implies s > -4
   \]
   This does not include \(s = -4\) and has no upper bound, so it's not the solution.

2. **\(4s + 10 \geq -26\)**:
   \[
   4s + 10 \geq -26 \implies 4s \geq -36 \implies s \geq -9
   \]
   This does not have an upper bound and starts at \(-9\), so it doesn't match.

3. **\(-3s - 4 \geq 8\)**:
   \[
   -3s - 4 \geq 8 \implies -3s \geq 12 \implies s \leq -4
   \]
   This covers values less than or equal to \(-4\) and has no upper bound on the positive side. Therefore, it doesn't match.

4. **\(-3s - 7 \leq 5\)**:
   \[
   -3s - 7 \leq 5 \implies -3s \leq 12 \implies s \geq -4
   \]
   Solving for the other side:
   \[
   -3s - 7 \leq 5 \implies s \leq 4
   \]
   Thus, this simplifies to:
   \[
   -4 \leq s \leq 4
   \]
   This matches the graph.

### Conclusion
The correct inequality is:
\[
\boxed{-3s - 7 \leq 5}
\]

Would you like more details or have any questions? Here are some related questions you might consider:

1. How do you solve multi-step inequalities?
2. What is the difference between strict and non-strict inequalities in graphing?
3. Can inequalities be combined or split into different cases?
4. How do we graph compound inequalities on a number line?
5. What happens if we multiply or divide by a negative number in an inequality?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number.

The solution to which inequality is graphed below?

Learn how to solve inequalities and graph them on a number line. This problem illustrates how to determine the solution to an inequality based on the visual representation of values between -4 and 4. Suitable for students in Grades 7-9.

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