To translate the given statement into an inequality, we start with the phrase "11 and three fourths of a number." This can be expressed as:
\[ 11 \frac{3}{4} = \frac{47}{4} \]
So, the statement "11 and three fourths of a number is less than 112" can be interpreted as:
\[ \frac{47}{4} + x < 112 \]
Where \( x \) represents the number.
To write the inequality with \( x \) first, we can rearrange it:
\[ x < 112 - \frac{47}{4} \]
This gives us the inequality:
\[ x < 112 - \frac{47}{4} \]
And that is the inequality representing the problem.