Question

What is another way to write the absolute value inequality \(|s - 12| < 0.122\)?

A) \(s < 12.122\)
B) \(s > 11.878\)
C) \(11.878 < s < 12.122\)
D) \(s < 11.878\)

Answer 1

The absolute value inequality |s - 12| < 0.122 is written as a double inequality 11.878 < s < 12.122, which describes a range of values s can have close to 12.

Step-by-step explanation:

The absolute value inequality |s - 12| < 0.122 describes all the values of s that are within a distance of 0.122 from the number 12. This means that s can be less than 12 by up to 0.122 and greater than 12 by up to 0.122, but not equal to or more than these differences. So, the inequality actually describes a range of values s can have. To write this in another way without the absolute value, you split this into two inequalities: s must be greater than 12 - 0.122 and less than 12 + 0.122. Therefore, we can express this as two separate inequalities: s > 11.878 and s < 12.122, which can be combined to form the double inequality 11.878 < s < 12.122.