Final answer:
To find three consecutive even integers, assign the first integer as 'x'. The second integer is 'x + 2' and the third integer is 'x + 4'. By solving the equation 'x + (x + 2) = (x + 4) + (-10)', we find that the integers are -10, -8, and -6.
Step-by-step explanation:
To find three consecutive even integers, we can assign the first integer as 'x'. The second integer would then be 'x + 2' since it is consecutive and even. The third integer would be 'x + 4' for the same reasons. Now, we are given that the sum of the first and second integers is equal to the sum of the third integer and -10. Representing this algebraically, we have: x + (x + 2) = (x + 4) + (-10). Solving this equation gives us 'x = -10'. Therefore, the three consecutive even integers are -10, -8, and -6.