Chapter 6.2, Problem 46SR

To determine

To write: The open sentence involving absolute value for given graph.

Answer to Problem 46SR

The open sentence involving absolute value for given graph is $|x-5.5|\ge 4.5$

Explanation of Solution

Given information:

The graph

  

Calculation:

From the given graph, the solution set is

  $\begin{array}{l}x\le 1\text{ or }x\ge 10\\ 1\ge x\ge 10\\ 1-5.5\ge x-5.5\ge 10-5.5\\ -4.5\ge x-5.5\ge 4.5\\ |x-5.5|\ge 4.5\end{array}$

Hence, the inequality is $|x-5.5|\ge 4.5$