Final answer:
To find three consecutive odd integers that satisfy the given condition, let's represent the first integer as 'n', the second integer as 'n+2', and the third integer as 'n+4'. The equation 3n + 2(n+4) = 6(n+2) - 17 is used to solve for 'n', resulting in the values 13, 15, and 17.
Step-by-step explanation:
To find three consecutive odd integers that satisfy the given condition, let's represent the first integer as 'n', the second integer as 'n+2', and the third integer as 'n+4'.
The condition states that when three times the first integer is added to twice the third integer, the result is 17 less than six times the second integer. This can be written as 3n + 2(n+4) = 6(n+2) - 17.
Simplifying the equation, we get 3n + 2n + 8 = 6n + 12 - 17. Combining like terms, we have 5n + 8 = 6n - 5. Solving for 'n', we subtract 5n from both sides and add 5 to both sides, resulting in 13 = n.
Therefore, the three consecutive odd integers are 13, 15, and 17.