Chapter 2, Problem 30CR

To determine

To write and solve an absolute value inequality that represents the acceptable heights of a guardrail.

Answer to Problem 30CR

The height must be at least 99 centimeters and at most 113 centimeters.

Explanation of Solution

Given information:

A safety regulation states that the height of a guardrail should be 106 centimeters with an absolute deviation of no more than 7 centimeters.

Calculation:

Assume that $h$ is the height of a guardrail.

This deviation should be no more than 7 centimeters. Hence, the absolute value inequality is,

  $\left|h-106\right|\le 7$

Write the inequality $\left|h-106\right|\le 7$ in the form of compound inequalities as follows,

$h-106\ge -7$ and $h-106\le 7$

Add 106 to each side,

$h\ge 99$ and $h\le 113$

Thus, the solution is $99\le h\le 113$ .

It can be seen from the above solution that the height must be at least 99 centimeters and at most 113 centimeters.