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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 -x<31-s and x>31-s also represents this situation, what is the value of x in the compound inequality?

User Karric
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2 Answers

17 votes
17 votes

Answer:

8

Explanation:

User Sami Hult
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27 votes
27 votes

An absolute value inequality can have the following expression:


|P|It means that the absolute value of P is less than n.<p>For example, this expression is valid:</p>[tex]|2|<4

But this expression is not


|7|<6

We can write it mathematically as follows:


\begin{gathered} |P|-n \end{gathered}

We are given the expression


|31-s|<8

Which is equivalent to


\begin{gathered} 31-s<8\text{ and} \\ 31-s>-8 \end{gathered}

Flipping the second inequality we have


-8<31-s

Note when we compare with the given expression


-x<31-s

We get the value of x = 8

The same happens when we flip the first one. We get the very same answer

x = 8

User QAZ
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