Answer:
The numbers are : -20,-18,-16,-14
Step-by-step explanation:
Let 1st even integer be ![=x](https://tex.z-dn.net/?f=%3Dx)
So, next consecutive even integer would be ![=x+2](https://tex.z-dn.net/?f=%3Dx%2B2)
3rd consecutive even integer would be ![=x+4](https://tex.z-dn.net/?f=%3Dx%2B4)
4th consecutive even integer would be ![=x+6](https://tex.z-dn.net/?f=%3Dx%2B6)
Sum of first three integers would be ![=x+x+2+x+4=3x+6](https://tex.z-dn.net/?f=%3Dx%2Bx%2B2%2Bx%2B4%3D3x%2B6)
It says sum of the first three is 2 more than twice the fourth,
So we have
![3x+6=2+4(x+6)](https://tex.z-dn.net/?f=3x%2B6%3D2%2B4%28x%2B6%29)
using distribution to simplify.
![3x+6=2+(4\times x)+(4\times6)](https://tex.z-dn.net/?f=3x%2B6%3D2%2B%284%5Ctimes%20x%29%2B%284%5Ctimes6%29)
![3x+6=2+4x+24](https://tex.z-dn.net/?f=3x%2B6%3D2%2B4x%2B24)
![3x+6=4x+26](https://tex.z-dn.net/?f=3x%2B6%3D4x%2B26)
Subtracting
from both sides
![3x+6-4x=4x+26-4x](https://tex.z-dn.net/?f=3x%2B6-4x%3D4x%2B26-4x)
![-x+6=26](https://tex.z-dn.net/?f=-x%2B6%3D26)
Subtracting 6 from both sides
![-x+6-6=26-6](https://tex.z-dn.net/?f=-x%2B6-6%3D26-6)
![-x=20](https://tex.z-dn.net/?f=-x%3D20)
∴ ![x=-20](https://tex.z-dn.net/?f=x%3D-20)
So first integer =-20
2nd integer ![=-20+2=-18](https://tex.z-dn.net/?f=%3D-20%2B2%3D-18)
3rd integer ![=-18+2=-16](https://tex.z-dn.net/?f=%3D-18%2B2%3D-16)
4th integer ![=-16+2=-14](https://tex.z-dn.net/?f=%3D-16%2B2%3D-14)
So, the numbers are : -20,-18,-16,-14