Chapter 1.4, Problem 26E

(a)

To determine

To represent: the height on the number line

Answer to Problem 26E

Here, the given heights are represented on the number line.

Explanation of Solution

Given:

Height of two miniature poodles 10 Inch and 15 Inch.

Calculation:

Given the data:

  $\begin{array}{l}{h}_{min}=10\\ h_{\max }=15\end{array}$

Represent $h_{min}$ and $h_{\max }$ on a number line:

  

Conclusion:

Hence, the given heights are represented on the number line.

(b)

To determine

To find: the absolute value equation that represents the heights

Answer to Problem 26E

Here, the absolute value equation that represents the heights is $|x-12.5|=2.5$

Explanation of Solution

Calculation:

Consider $h_{min}$ and $h_{\max }$ as solution to an absolute value equation. Find the halfway point between the solutions:

  $h=\frac{h_{min}+h_{\max }}{2}=\frac{10+15}{2}=\frac{25}{2}=12.5$

find the distance to each solution.

  $h_{sol}=\frac{h_{min}+h_{\max }}{2}=\frac{15-10}{2}=\frac{5}{2}=2.5$

Use the half way point and the distance to each solution to write an absolute value equation

  $\begin{array}{l}|x-h|=h_{sol}\\ |x-12.5|=2.5\end{array}$

  

check the result:

  $|x-12.5|=2.5$

Conclusion:

Hence, the absolute value equation that represents the heights is $|x-12.5|=2.5$