Final answer:
To find three consecutive positive odd integers, assume the first odd integer as x, and the subsequent odd integers will be x + 2 and x + 4. Using the given equation, solve for x by simplifying it. The resulting values will be the consecutive odd integers.
Step-by-step explanation:
To find three consecutive positive odd integers, let's assume the first odd integer as x.
The second odd integer would be x + 2, since it is consecutive.
The third odd integer would be x + 4, again because it is consecutive.
According to the given information, the equation would be: 4x - (x + 2) = (x + 4) + 12.
Simplifying the equation, we get 3x - 2 = x + 16.
Bringing the x terms to one side and the constants to the other side, we get 3x - x = 16 + 2.
Simplifying further, we get 2x = 18.
Divide both sides by 2 to solve for x, giving us x = 9.
Therefore, the three consecutive odd integers are 9, 11, and 13.