Question

The sum 11 and three fourths of a number is less than 112. What are all the possible values of the number> Write an inequality that could be used to solve this problem. Use the letter x as the variable and write the inequality so that the x comes first. Where necessary, write numbers as fractions ( rather than decimals). Do not solve the inequality

Answer 1

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.