Chapter 1.4, Problem 26E

a.

To determine

To represent: the shortest miniature poodle height 10 in. and the tallest miniature poodle height 15 in. on a number line.

Answer to Problem 26E

  

Explanation of Solution

The heights 10 in. and 15 in. on a number line are given below:

  

b.

To determine

To write: an absolute equation that represents the shortest miniature poodle height 10 in. and the tallest miniature poodle height 15 in.

Answer to Problem 26E

  $\left|h-12.5\right|=2.5$

Explanation of Solution

Let h (in inches) be the height of the miniature poodle.

Now the shortest height is 10 in. and the tallest is 15 in, then the mid-point between 10 and 15 is given by:

  $\begin{array}{c}10+\frac{15-10}{2}=10+\frac{5}{2}\\ =10+2.5\\ =12.5\end{array}$

  

Then, the required absolute

  $\left|h-12.5\right|=2.5$

Check:

  $\begin{array}{c}\left|10-12.5\right|=2.5\\ \left|-2.5\right|=2.5\\ 2.5=2.5\end{array}$

And

  $\begin{array}{c}\left|15-12.5\right|=2.5\\ \left|2.5\right|=2.5\\ 2.5=2.5\end{array}$

Both the statements are true.