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 start absolute value 31 minus s end absolute value is less than or equal to 8 represents this situation. If the compound inequality negative x is less than or equal to 31 minus s and x is greater than or equal to 31 minus s also represents this situation, what is the value of x in the compound inequality?
An absolute value inequality |31 − s| ≤ 8 means that 31 − s is between −8 and 8: −8 ≤ 31 − s ≤ 8. The compound inequality has the form −x ≤ 31 − s ≤ x, so x is 8. The correct choice is 8.
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