A cyclist rides at an average speed of 31 miles per hour. The cyclist's 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 - x31-s also represents this situation, what is the value of x in the compound inequality?

Question

Mathematics

Gisselle Haas

6 May, 12:03

A cyclist rides at an average speed of 31 miles per hour. The cyclist's 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 - x31-s also represents this situation, what is the value of x in the compound inequality?

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Kamora Burke · Answer 1

Since the deviation from the average speed of the cyclist can only be up to 8 miles per hour, in the first equation the value of x is,

-x < 31 - s < 8

The value of x is - 8. For the second one,

x > 31 - s < 8

The value of x should be 8.