The problem asks to graph the solution set of the compound inequality $x < 2$ and $x \geq -6$.

Let's break it down:

1. $x < 2$ means that all values of $x$ are less than 2, so the interval is open on 2: $(-\infty, 2)$.
2. $x \geq -6$ means that all values of $x$ are greater than or equal to -6, so the interval is $[-6, \infty)$.

The solution set is the intersection (the overlap) of these two intervals:

• The numbers that satisfy both $x \geq -6$ and $x < 2$ are in the interval $[-6, 2)$.

From the graph options visible in your image:

• The correct graph should show a solid point at $x = -6$ (indicating that -6 is included) and an open point at $x = 2$ (indicating that 2 is not included), with the line between them filled in to show the interval $[-6, 2)$.

Correct Answer: Graph C shows this solution.

For the interval notation:

• The answer in interval notation is $[-6, 2)$.

Let me know if you need any further details or clarifications!

Here are 5 relative questions you might explore:

1. How would the solution change if the inequality were $x \leq 2$ instead of $x < 2$?
2. What does the union of two inequalities represent in a graph?
3. How do you represent compound inequalities that involve "or" instead of "and"?
4. Can compound inequalities have no solution? When does that happen?
5. How do you graph a compound inequality when the solution involves both positive and negative values?

Tip: Always check if the inequality involves an open or closed interval to correctly graph and represent the solution.