Find three consecutive even integers so that twice the largest is 20 less than the sum of all three

If x is the smallest of the three, then the next two integers are x + 2 and x + 4.

"Twice the largest is 20 less than the sum of all three" translates to

2 (x + 4) = (x + (x + 4) + (x + 6)) - 20

Solve for x :

2x + 8 = 3x - 10

x = 18

Then the three numbers are {18, 20, 22}.

look below

Step-by-step explanation:Let x, x+2 & x+4 be the 3 integers.

x+2(x+2)=(x+4)+20

x+2x+4=x+4+20

3x+4=x+24

3x-x=24-4

2x=20