Let's analyze the problem shown in your image.

Inequality:

You are asked to graph the solution set for the inequality: $7 \geq x \geq -3$ This represents a double inequality, meaning that $x$ must be between $-3$ and $7$, inclusive.

Interval Notation:

In interval notation, this can be written as: $[-3, 7]$ This indicates that the endpoints, $-3$ and $7$, are included (hence the square brackets).

Graphing the solution:

You are asked to choose the correct graph. The solution should show a line segment from $-3$ to $7$ with closed circles on both $-3$ and $7$ because both values are included (due to the $\geq$).

Correct Graph:

Looking at the options:

• Option D is the correct graph because it shows the interval from $-3$ to $7$ with closed circles at both endpoints.

Would you like a further breakdown of this problem or any related topics?

Here are 5 relative questions for expanding understanding:

1. What is the difference between interval notation and set notation?
2. How do you graph inequalities that use strict inequalities ($<$ or $>$)?
3. What happens if an inequality has more than two variables, and how does that affect the graph?
4. How would the graph change if one of the endpoints were not included (e.g., $x > -3$)?
5. Can inequalities be solved similarly to equations? What are the main differences?

Tip: Always double-check whether the inequality includes or excludes the endpoints, as this will affect whether to use open or closed circles on the graph.