Chapter 3.7, Problem 6STP

A student reads an average of 34 pages per day. The number of pages she reads per day varies from the average by up to 8 pages.

a. Write an absolute value inequality that represents the range of the number of pages she reads per day.

b. Solve your inequality.

To determine

To calculate: We are asked to write absolute value inequality that represents the situation.

Answer to Problem 6STP

  $\left|x-34\right|$

  $\le 8$

Explanation of Solution

Given information: A student reads an average of 34 pages per day. The number of pages she reads per day varies from the average by up to 8 pages.

Formula: $Ix-hI\le k$ . Where ‘h’ is the average pages per day. K represents the variation of pages read.

Calculation:

Here it is given that an average of 34 pages per day. So, h=34

The pages she reads varies 8 per day. So, k=8

Plug in these values into the equation

  $\left|x-34\right|$

  $\le 8$

To determine

To calculate: We are asked to Solve the inequality.

Answer to Problem 6STP

  $26\le x\le 42$

Explanation of Solution

Given information: $\left|x-34\right|\le 8$

Calculation:

If we solve the absolute value inequality, we can rewrite the inequality as

  $-8\le x-34\le 8$

Solve the compound inequality for x.

Add each side 34.

We get $26\le x\le 42$