Chapter 8, Problem 22CCSR

To determine

To find: The number of whole number solutions.

Answer to Problem 22CCSR

The number of whole number solutions is $9$ .

Explanation of Solution

Given information: $\left|x-5\right|\le 8$

Calculation: Since $\left|x-5\right|\le 8$

Hence, apply absolute rule

  $\begin{array}{l}-8\le x-5\le 8\\ x-5\ge -8\&x-5\le 8\\ x-5\ge -8:x\ge -3\\ x-5\le 8:x\le 13\end{array}$

Combine the intervals,

  $x\ge -3\&x\le 13$

Merging overlapping intervals,

  $-3\le x\le 13$

Hence, set $x=\left\{-3,-2,1,0,1,2,3,4,5,6,7,8,9,10,11,12,13\right\}$

But the set of whole numbers which are less or equal to 8 is $x=\left\{0,1,2,3,4,5,6,7,8,\right\}$

Therefore, the number of whole number solutions is $9$ .