Three consecutive integers exist where the smallest is fifteen less than twice the larger. find the integers

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

your integers are 13, 14, and 15.