The graph shows a number line with a filled circle at 4 and an arrow extending to the right. This indicates that the solution set includes the number 4 and all numbers greater than 4.

To match this graph with an inequality:

• The filled circle at 4 means 4 is included in the solution (so it must be "greater than or equal to").
• The arrow to the right indicates that the numbers are greater than 4.

Therefore, the correct inequality that matches this graph is A. $4 \leq x$.

Would you like further details or have any questions? Here are some related questions to explore:

1. How would the graph change if the inequality was $4 > x$?
2. What does an open circle on a graph represent in an inequality?
3. How can you graph $x \geq 5$ on a number line?
4. How do you solve an inequality like $4 \leq x < 7$?
5. How can you verify the solution to an inequality graphically?

Tip: Always remember, a filled circle means the value is included (≥ or ≤), while an open circle means it is not included (> or <).