1. The problem is to express the inequality $x \leq -3$ OR $x > 4$ using interval notation. 2. Recall that the union of intervals represents "OR" conditions, while the intersection represents "AND" conditions. 3. The inequality $x \leq -3$ corresponds to the interval $(-\infty, -3]$ because it includes all numbers less than or equal to $-3$. 4. The inequality $x > 4$ corresponds to the interval $(4, \infty)$ because it includes all numbers greater than $4$, but not $4$ itself. 5. Since the condition is $x \leq -3$ OR $x > 4$, we take the union of these two intervals: $$(-\infty, -3] \cup (4, \infty)$$ 6. This matches the third option given in the problem. 7. Therefore, the correct interval notation for the inequality $x \leq -3$ OR $x > 4$ is: $$(-\infty, -3] \cup (4, \infty)$$