The larger of two consecutive integers is 7 greater than twice the smaller. find the integers.

Let the smallest integer be x 
Since the numbers are 2 consecutive integers, let the largest integer be x+1 

The larger of two integers is 7 greater than twice the smaller.
The equation is 

x + 1 = 2x + 7

x - 2x = 7 - 1
-x = 6
x = -6 

Since x is the smallest integer, - 6 is the smallest integer
Since x+1 is the largest integer, - 6+1 = -5 is the largest integer 

The larger of two integers is 7 greater than twice the smaller. 
-5 = 2(-6)+7