Final answer:
To find the three consecutive even integers, we can set up an equation by representing them as x, x+2, and x+4. Solving the equation will give us the values of x and the three integers.
Step-by-step explanation:
Let's represent the three consecutive even integers as x, x+2, and x+4. We are given that twice the first integer added to the second integer is equal to the third integer.
So, we can write the equation as: 2x + (x+2) = x+4.
Simplifying the equation, we get 3x + 2 = x+4. Subtracting x from both sides, we have 2x + 2 = 4. Finally, subtracting 2 from both sides, we find that 2x = 2. Dividing both sides by 2, we get x = 1.
Therefore, the three consecutive even integers are 1, 3, and 5.