### Instruction: In a set of five consecutive integers, the largest integer is less than twice the average of the five integers. What is the smallest integer that could be in the set?### Response: Let the five consecutive integers be x, x+1, x+2, x+3, and x+4.
The largest integer is x+4.
The average of the five integers is (x + x+1 + x+2 + x+3 + x+4) / 5 = (5x + 10) / 5 = x + 2.
The problem says that x+4 is less than twice the average, so x+4 < 2(x+2).
I want to find the smallest possible value of x that satisfies this inequality.
I can simplify the inequality by expanding the brackets and subtracting x from both sides: x+4 < 2x + 4 -> 0 < x.
So x has to be a positive integer.
The smallest positive integer is 1.
Therefore, the smallest integer that could be in the set is x = 1.