How do you Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven?

Let the three consecutive odd integers be represented as ( x ), ( x+2 ), and ( x+4 ). According to the problem, the sum of the smaller two integers is equal to three times the largest increased by seven. This can be expressed as the equation:

[ x + (x + 2) = 3(x + 4) + 7. ]

Simplifying this gives ( 2x + 2 = 3x + 12 + 7 ), which further simplifies to ( 2x + 2 = 3x + 19 ). Solving for ( x ), we find ( x = -17 ). Thus, the three consecutive odd integers are -17, -15, and -13.