If we solve each inequality separately, we will find two solution sets. Since the compound inequality includes the word "or," the union of those sets is the solution to the compound inequality.
Now we must compare our solution sets. From the first inequality, x≤12, we know that the solution set consists of all numbers to the left of 12 on the number line, including 12 itself. We will graph the endpoint with a closed circle at 12.
From the second inequality, x>3, we know the solution set includes all values to the right of 3, without including 3. Thus, we'll graph the endpoint with an open circle at 3.
The union of these solution sets is all real numbers.
This means that any real number will solve the first, second, or both inequalities.