a cyclist rides at an average speed of 31 miles per hour. the cyclists speed, s, can differ from the average…

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?\n-8\n-8 or 8\n8\n8 and -8

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?\n-8\n-8 or 8\n8\n8 and -8

Answer

Answer:

C. 8

Explanation:

Step1: Recall absolute - value inequality rule

The absolute - value inequality (|a|\leq b) is equivalent to (-b\leq a\leq b). For (|31 - s|\leq8), it is equivalent to (-8\leq31 - s\leq8).

Step2: Analyze the compound inequality

The compound inequality (-x\leq31 - s) and (x\geq31 - s) is equivalent to (-x\leq31 - s\leq x). Comparing with (-8\leq31 - s\leq8), we can see that (x = 8).