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.