Find all sets of three consecutive even integers whose sum is between 25 and 45

1st even integer is x,

2d consecutive even integer is x+2,

3d consecutive even integer is x+2+2 = x+4.

Sum is x + x+2 + x + 4 = 3x + 6.

Sum is between 25 and 45, so we can write

25< 3x+6 < 45.

25 - 6 < 3x < 45 - 6

19 < 3x < 39

19/3 < x < 13

6 1/3 < x < 13

Between 6 1/2 and 13 there are even numbers 8,10,12, so first even number can be 8, or 10, or 12.

1st set : 8, 10, 12

8+10+12 = 30 25<30<45

2d set: 10, 12, 14

10+12+14 = 36 25<36<45

3d set : 12, 14, 16

12+14+16 = 42 25<42<45