Question

a cyclist rides at an average speed of 31 miles per hour. the cyclists speed, s, can differ from the average by as much as 8 miles per hour. the absolute - value inequality |31 - s| ≤ 8 represents this situation. if the compound inequality -x ≤ 31 - s and x ≥ 31 - s also represents this situation, what is the value of x in the compound inequality?
-8
-8 or 8
8
8 and -8

Explanation:

Step1: Recall absolute - value inequality rule

The absolute - value inequality \(|a|\leq b\) is equivalent to \(-b\leq a\leq b\). In the given absolute - value inequality \(|31 - s|\leq8\), it can be rewritten as \(-8\leq31 - s\leq8\).
This compound inequality can be split into two inequalities: \(-8\leq31 - s\) and \(31 - s\leq8\), which is the same as \(-x\leq31 - s\) and \(x\geq31 - s\) when \(x = 8\).

Answer:

C. 8