Final answer:
The largest possible integer is 111, which can be found by solving the inequality 2x ≤ 222.
Step-by-step explanation:
To find the largest possible integer, we need to consider the sum of two consecutive integers and ensure it is at most 223. Let's assume the first integer is x. The next consecutive integer would be x+1. Their sum is x + (x+1) = 2x + 1. We know that 2x + 1 is at most 223, so we can solve for x by subtracting 1 from both sides: 2x ≤ 222. Dividing both sides by 2 gives us x ≤ 111.
Therefore, the largest possible integer is 111. To verify this, we can calculate the sum of 111 + 112, which is 223, showing that it is at most 223. Any larger integer would result in a sum greater than 223.
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