In order to find the larger integer, we simply add 2 to x.
This may sound confusing, but consider that 1 is an odd number. Add 2, and you get 3. Add 2, and you get 5, and so on. By adding 2 to an odd number, you'll get another odd number (this works for even numbers too!).
The equation should be
x + (x + 2) = 52
2x + 2 = 52
2x = 50
x = 25
25+2=27
The larger integer is 27