Answer: 26, 28, 30
Explanation:
Let's define a variable x to represent the least of the three consecutive even integers. This means that the three integers are x, x + 2, and x + 4.
We can write the given information as an equation:
3 * (x + 4) = 2 * x + 38
We can solve for x by moving all the terms with x to one side of the equation and all the other terms to the other side:
3 * (x + 4) - 2 * x = 38
Then we can distribute the 3 and the -2 to get:
3 * x + 12 - 2 * x = 38
And then we can combine like terms on each side of the equation:
x + 12 = 38
Finally, we can subtract 12 from both sides to solve for x:
x = 26
Therefore, the three consecutive even integers are 26, 28, and 30.
We can check our solution by substituting these values back into the original equation and verifying that it holds true:
3 * (26 + 4) = 2 * 26 + 38
3 * 30 = 52 + 38
90 = 90
The equation holds true, so our solution is correct.