Chapter 1.6, Problem 44PPS

(a)

To determine

To write an absolute value inequality for templates with each line color.

Explanation of Solution

Given:

Suppose a certain template is 24.42 inches long and the following table is-

Calculation:

The absolute value for the given colors and its tolerance can be written as follows using the information given in the table.

Red color: $\left|x-24.42\right|\le 0.07$

Blue color: $\left|x-24.42\right|\le 0.25$

Green: $\left|x-24.42\right|\le 0.5$

(b)

To determine

To find the acceptable lengths for that part of a car if the template has each line color.

Explanation of Solution

For red color: $\left|x-24.42\right|\le 0.07$

Simplify the above inequality;

  $\begin{array}{l}-0.07\le x-24.42\le 0.07\\ 24.35\le x\le 24.49\end{array}$

For blue color: $\left|x-24.42\right|\le 0.25$

Simplify the above inequality;

  $\begin{array}{l}-0.25\le x-24.42\le 0.25\\ 24.17\le x\le 24.67\end{array}$

For green color: $\left|x-24.42\right|\le 0.5$

Simplify the above inequality;

  $\begin{array}{l}-0.5\le x-24.42\le 0.5\\ 23.92\le x\le 24.92\end{array}$

(c)

To determine

To graph the solution set for each line color on a number line.

Explanation of Solution

This tolerance can be drawn on the number line for each color so it can be easily determine the color of that tolerance which tolerates the other two colors.

For red color:

For blue color:

For green color:

(d)

To determine

To find which line color includes the tolerances of the other line colors.

Explanation of Solution

From the above number lines it is clearly observed that the red line color has the minimum tolerance. As per the tolerance given in the table, they are arranged into ascending order as $0.07<0.25<0.5$ , therefore the further line colors would be fitting fit inside their tolerances.