Chapter 3.6, Problem 15P

Write each interval as an inequality. Then graph the solutions.

$(-\infty ,0]$ or $(5,\infty )$

To determine

To write: the inequality representation of given interval and then to graph the solutions.

Explanation of Solution

Given information:

The given interval is shown below $(-\infty ,0]\text{ or (5,}\infty \text{)}$

Concept used:

The open circle indicates excluding the point.

Closed circle indicates including the point.

Calculation:

Let x is any real value.

Then,

  $\begin{array}{l}(-\infty ,0]\Rightarrow x\le 0\\ \text{ (5,}\infty \text{)}\Rightarrow x>5\end{array}$

and so,

  $\begin{array}{l}(-\infty ,0]\text{ or (5,}\infty \text{)}\\ x\le 0\text{ or }x>5\end{array}$

Graph:

The graph of given interval is shown below.

  

Hence, the inequality representation of given interval is $x\le 0\text{ or }x>5$