Here is the graph displaying the interval notations for the three inequalities. Let me know if you'd like any further clarifications or details!

1. The correct interval for x > -3 is (-3, ∞).
2. The correct interval for -3 < x ≤ 3 or 7 ≤ x is (-3, 3] ⋃ [7, ∞).
3. The correct interval for x ≤ -3 or 7 ≤ x is (-∞, -3] ⋃ [7, ∞).

Would you like to go into more detail or ask any questions?

Follow-up Questions:

1. What is the difference between open and closed intervals?
2. How do you graph inequalities involving two or more intervals?
3. Can you explain union (⋃) of intervals and how it works?
4. What happens when two intervals overlap?
5. How do you solve a compound inequality like x > -3 and x ≤ 5?

Tip: Open intervals exclude the boundary values, while closed intervals include them.