1. The total number of students in the school must be divisible by 7 and 4, which means it must be divisible by 28. Since the number is no more than 40, there were 28 students in total. The number of prize winners is $(1 / 7 + 1 / 4 + 1 / 4) \cdot 28 = 18$ people. Therefore, 10 students did not receive any medals.
Answer: $x=10$.

Answer to the variant: $4-2: x=18$.