Translate into an equation find three consecutive even integers whose sum is negative eighteen

Well if your sum is -18 then you know your answers are going to be negative numbers. 

make x be your first unknown negative even integer. you want your negative x and then negative x minus two and negative x minus four 

x1= x 
x2= x-2 
x3= x-4 

you know all three need to equal -18 

solve for x: 
-18= -x + (-x-2) + (-x-4) 

-18 = -x-x-2-x-4 
-18+2+4= -3x 
12=-3x 

12/-3=x 

-4=x 

then plus x into the first problem. 

x1= -4 = -4 
x2= -4-2 = -6 
x3= -4-4 = -8 

so your integers would be -4, -6, and -8 

check: 
(-4) + (-6) + (-8) = -18 

let me know if you have any questions.