Question

A movie theater is holding a contest for people who are in line before 8 p.m. The people who are within eight places of the 99th person in line will win a free movie ticket. Based on this information, which inequality can be used to find all of the winners of the movie tickets?

A.
|x + 99| < 8
B.
|99 + 8| < x
C.
|x - 99| < 8
D.
|x - 99| < x

Answer 1

Answer: The correct inequality that can be used to find all of the winners of the movie tickets is:

C. |x - 99| < 8

Here, x represents the position of a person in the line. The 99th person in line is the reference point, so we need to find the people who are within eight places of this person, either ahead or behind. This means that their position should be between 99 - 8 = 91 and 99 + 8 = 107.

Using absolute value, we can write this as:

|x - 99| < 8

This inequality means that the distance between x and 99 should be less than 8, which is exactly what we need to find the people who are within eight places of the 99th person in line.

Explanation: