The sum of three consecutive integers is - 78. determine the smallest integer.

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