To graph the solution set for x > 3 or x ≤ 0, we can start by drawing a number line and marking the points x = 3 and x = 0:
|------------------|------------------|------------------|
-inf 0 3 inf
The solution set for x > 3 includes all values of x that are to the right of 3, but not including 3 itself. So we can shade in the part of the number line to the right of 3:
|------------------|==================|------------------|
-inf 0 3 inf
The solution set for x ≤ 0 includes all values of x that are less than or equal to 0. So we can shade in the part of the number line to the left of 0, including 0 itself:
|==================|------------------|------------------|
-inf 0 3 inf
The final solution set is the union of the two shaded regions, which is everything except the interval (0, 3]:
|==================| |==================|
-inf 0 3 inf
This is the graph of the solution set for x > 3 or x ≤ 0.