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 x as a variable, and write the inequality so that x term comes first.
Let's use the letter x as the variable for the number.
The sum of 11 and three-fourths of the number is given by the expression 11 + (3/4)x.
According to the problem, this expression is less than 112. Therefore, we can write the inequality as:
11 + (3/4)x < 112
To solve this inequality, we can follow these steps:
1. Subtract 11 from both sides of the inequality to isolate the term with the variable:
(3/4)x < 112 - 11
Simplifying, we have:
(3/4)x < 101
2. To get rid of the fraction, we multiply both sides of the inequality by 4/3:
(4/3)(3/4)x < (4/3)101
Simplifying, we have:
x < (4/3) * 101
3. Multiply to compute the right side of the inequality:
x < 4 * 101/3
Simplifying, we have:
x < 404/3
Therefore, the possible values of the number x are all real numbers less than 404/3.