The larger of two numbers is 6 more than the smaller integer. Their sum is 52, What are the numbers?

Make x the variable to represent the smaller integer. Since the larger integer is 6 more, you are going to add 6 to the 2x. Solve.
x + x + 6 = 52
2x + 6 = 52
2x = 46
x = 23
The smaller integer = 23
The larger integer = 29
Check:
23 + 29 = 52