Chapter 3.3, Problem 10MCQ

To determine

To write: and solve an absolute value of inequality to describe the range of possible percenntage of Americans who were relatively unconcerned at about “Y2K bug”

Answer to Problem 10MCQ

  $\text{Absolute equation: }\left|x-64\right|<3$

  $\text{Possible range: }61<x<67$

Explanation of Solution

Given information:

  $\left|x-64\right|<3$

According to the survey, 64% American were “not very” or “not at all” concerned about the computer bug with the margin of error 3%.

Calculation:

According to the data, the inequality will be as follows:

  $\left|x-64\right|<3$

Here x is the number of Americans.

The inequality will have two cases, $x-64<3\text{ and }x-64>-3$ . It can be rewritten as follows:

  $\begin{array}{c}-3<x-64<3\\ -3+64<x-64+64<3+64\left[\text{Adding 64 to both the sides}\right]\\ 61<x<67\left[\text{Solved}\right]\end{array}$

Thus, the absolute equation is $\left|x-64\right|<3$ and the range of x is $61<x<67$ .