Question

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?

Answer 1

8

Explanation:

Answer 2

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