Chapter 4, Problem 30CCSR

Solution

To find: absolute value inequality models the different sizes of hat.

The absolute value inequality models the different sizes of hat is $\left|x-57.5\right|\le 6.5$

Given: A hat company is designing a one-size-fits-all hat with a strap in the back that makes the hat smaller or larger. Head sizes normally ranges from 51 to 64 centimetres.

Concept Used:

Solving inequality and graphing absolute value function.

Calculation:

Head sizes normally ranges from 51 to 64 centimetres.

Let’s find the middle value of ranges:

  $\begin{array}{c}\text{Middle value}=\frac{51+64}{2}\\ =\frac{115}{2}\\ =57.5\end{array}$

Now, the absolute value inequality models the different sizes of hat is $\left|x-57.5\right|\le 6.5$ .

It is $6.5\text{ cm}$ aways from each end.

Now, Graphing the solution:

  

Conclusion:

The absolute value inequality models the different sizes of hat is $\left|x-57.5\right|\le 6.5$