We can use the equation 5b + 6 = 56. We can also make this an inequality, but this will work fine. B stands for burgers.
We need to isolate b, so we need to subtract 6. This gives us 5b = 50. Then, we divide by 5 to isolate b. 5/5 is 1, and 50/5 is 10. This means that the most he can buy is 10 cheeseburgers.