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

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step-by-step explanation:

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