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Let's assume the number is represented by the variable x.
The sum of 11 and 3/4 of the number is given by the expression: 11 + (3/4)x.
According to the problem, this sum is less than 112, which can be represented as: 11 + (3/4)x < 112.
Therefore, the inequality that could be used to solve this problem is: 11 + (3/4)x < 112.