Final answer:
To find the smallest of the six consecutive odd integers that sum up to 96, set up an equation using the smallest integer as x. Solve the equation to find the value of x, which represents the smallest integer. The smallest integer is 11.
Step-by-step explanation:
To find the smallest of the six consecutive odd integers, we need to set up an equation. Let's assume that the smallest integer is x. Since the integers are consecutive odd numbers, the next five odd numbers will be x + 2, x + 4, x + 6, x + 8, and x + 10. To find their sum, we add all of them together and set it equal to 96: x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 96. Simplifying the equation, we get: 6x + 30 = 96. Subtracting 30 from both sides gives us: 6x = 66. Finally, dividing both sides by 6 gives us: x = 11. Therefore, the smallest of the six consecutive odd integers is 11.