Answer:
The numbers are : -20,-18,-16,-14
Step-by-step explanation:
Let 1st even integer be [tex]=x[/tex]
So, next consecutive even integer would be [tex]=x+2[/tex]
3rd consecutive even integer would be [tex]=x+4[/tex]
4th consecutive even integer would be [tex]=x+6[/tex]
Sum of first three integers would be [tex]=x+x+2+x+4=3x+6[/tex]
It says sum of the first three is 2 more than twice the fourth,
So we have
[tex]3x+6=2+4(x+6)[/tex]
using distribution to simplify.
[tex]3x+6=2+(4\times x)+(4\times6)[/tex]
[tex]3x+6=2+4x+24[/tex]
[tex]3x+6=4x+26[/tex]
Subtracting [tex]4x[/tex] from both sides
[tex]3x+6-4x=4x+26-4x[/tex]
[tex]-x+6=26[/tex]
Subtracting 6 from both sides
[tex]-x+6-6=26-6[/tex]
[tex]-x=20[/tex]
∴ [tex]x=-20[/tex]
So first integer =-20
2nd integer [tex]=-20+2=-18[/tex]
3rd integer [tex]=-18+2=-16[/tex]
4th integer [tex]=-16+2=-14[/tex]
So, the numbers are : -20,-18,-16,-14
