The three consecutive odd integers are -3, -1, and 1. This satisfies the condition: four times the middle integer equals two less than the sum of the first and third integers.
Let's represent the three consecutive odd integers as n, n+2, and
n+4 , where n is the first odd integer. According to the given conditions:
1. Four times the middle integer: 4(n+2)
2. Sum of the first and third integers: (n) + (n+4)
3. Two less than the sum: (n) + (n+4) - 2
Now, we set up the equation:
4(n+2) = (n) + (n+4) - 2
Solving for n :
4n + 8 = 2n + 2
Combine like terms:
2n = -6
Divide by 2:
n = -3
So, the three consecutive odd integers are -3, -1, and 1 .