Question 414714
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Hi
Let x, (x+1) and (x+2) represent the three consecutive integers 
Note: As a preference is not stated in the question... 
these three consecutive integers can be either negative or positive integers.  
Question states***
 x(x+2) = (x+1) + 19
Solving for x
 x^2 +x -20 = 0
factoring
 (x+5)(x-4)= 0
 (x+5)= 0   x = -5   |the three consecutive integers are -5,-4,-3
 (x-4)= 0   x = 4    |the three consecutive integers are 4,5,6

CHECKING our Answer(s)***
 15 = -4 + 19
 24 = 5 + 19