The sum of 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 ∞ as the variable, and write the inequality so that the a term comes first. Where necessary, write numbers as fractions (rather than decimals). Do not solve the inequality.
Let the number be represented by the variable $x$. The given information can be translated into the inequality \[x/4 + 11 < 112.\]Multiplying both sides by 4 gives $x + 44 < 448$, or $x < 404$. Combining with x > -∞ we have \[-\infty < x < 404.\]So the possible values of $x$ are all real numbers that are less than 404 and greater than $-\infty$.
