Answer:
,
and ![10](https://tex.z-dn.net/?f=10)
Step-by-step explanation:
Let
smallest consecutive even integer.
Since the second and third consecutive even integers can be expressed by our smallest even consecutive integer, we can express them as:
Second consecutive even integer = ![x+2](https://tex.z-dn.net/?f=x%2B2)
Third consecutive even integer = ![x+4](https://tex.z-dn.net/?f=x%2B4)
From "<em>the sum of the second and third is 3 times the first integer</em>", we can write:
![x+2+x+4 = 3x](https://tex.z-dn.net/?f=x%2B2%2Bx%2B4%20%3D%203x)
(collect like-terms)
![x=6](https://tex.z-dn.net/?f=x%3D6)
∴ The first consecutive even integer is 6
Now, we can use substitution to find the values of the second and third consecutive even integers:
Second consecutive integer = ![x+2](https://tex.z-dn.net/?f=x%2B2)
![=6+2](https://tex.z-dn.net/?f=%3D6%2B2)
![=8](https://tex.z-dn.net/?f=%3D8)
Third consecutive integer = ![x+4](https://tex.z-dn.net/?f=x%2B4)
![=6+4](https://tex.z-dn.net/?f=%3D6%2B4)
![=10](https://tex.z-dn.net/?f=%3D10)
∴ The three consecutive even integers are
,
and
.
Hope this helps :)