Consecutive integers are integers that appear one after the other. so let's call them x, x+1, and x+2.
the smallest (which is x) is 15 less than twice the larger. "the larger" is a bit unclear, but i'm assuming it is referring to the x+1 integer, because it doesn't say the "largest". so x = 2(x+1) - 15. let's try to solve for x.
x = 2(x+1) - 15 x = 2x + 2 - 15 x = 2x - 13 subtract 2x from both sides. -x = -13 x = 13 x+1 = 14 x+2 = 15
