Chapter MPS, Problem 1.13MPS

(a)

To determine

To Find: Absolute value Inequality of the given situation.

Answer to Problem 1.13MPS

  $\left|350-c\right|\le 125$

Explanation of Solution

Given:

  $\begin{array}{l}\text{sale price}=\$350\\ \text{price variation}=\$125\end{array}$

Formula Used:

  $\begin{array}{l}\left|x-c\right|\le r\left(\text{Absolute value inequality}\right)\\ c=\text{central value}\\ r=\text{Range}\end{array}$

Calculation:

  $\begin{array}{l}\text{Let }c\text{ be the price of computer}\\ \Rightarrow \left|350-c\right|\le 125\end{array}$

(b)

To determine

To Find: solution of the inequality and range of the price of computer

Answer to Problem 1.13MPS

  $\left\{c|225\le c\le 475\right\}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{sale price}=\$350\\ \text{price variation}=\$125\end{array}$

Formula Used:

  $\begin{array}{l}\left|x-c\right|\le r\left(\text{Absolute value inequality}\right)\\ -r\le x-c\le r\left(\text{Compound inequality}\right)\\ c=\text{central value}\\ r=\text{Range}\end{array}$

Calculation:

  $\begin{array}{l}\left|350-c\right|\le 125\\ \Rightarrow -125\le 350-c\le \text{125 }\left(\text{Rewriting the absolute value inequality as a compound inequality, to soilve for }c\right)\\ \Rightarrow -125-350\le 350-c-350\le \text{125}-350\left(\text{subtract each side by }350\right)\\ \Rightarrow -475\le -c\le -225\\ \Rightarrow 475\ge c\ge 225\end{array}$

Conclusion:

The solution set is $\left\{c|225\le c\le 475\right\}$ .Thus the range of the price of computer fall between $\$225\text{ and }\$475$ .