lets x is the 1st consecutive even integers
x +2 :the 2nd consecutive even integers
x +4: the 3rd consecutive even integers
So sum of all 3 equals -78 then
x + (x+2) + (x+4) = -78
x + x + 2 + x + 4 = -78
Simplify
3x + 6 = -78
Subtract (-6) to both sides
3x +6 -6 = -78 - 6
Simplify
3x = -84
Divided both sides by 3
3x/3 = -84/3
x = -28
x + 2 = -28 + 2 = -26
x +4 = - 28 + 4 = -24
Double check: -28 + -26 + -24 = -78
So the three consecutive even integers are: -24, -26, -28
The smallest integer would be -28
