Twice the larger of 2 consecutive integers equal 15 less than 3 times the smaller

the two integers are 17 and 18

Step-by-step explanation:

Let x represent the smaller integer. Then x+1 is the larger. The problem statement tells us

... 2 × larger = -15 + 3 × smaller

... 2(x+1) = -15 + 3x . . . substitute variable expressions for 'larger' and 'smaller'

... 2x +2 = 3x -15 . . . . . eliminate parentheses

... 17 = x . . . . . . . . . . . . .add 15-2x

The smaller integer is 17, so the larger is 18.

Check

2×18 = 36 = 3×17 -15 = 51-15