Chapter 6.1, Problem 51HP

To determine

Find the compound inequality has a graph that includes the entire number line.

Answer to Problem 51HP

Option B is the correct option, which has a graph that includes the entire number line.

Explanation of Solution

Given:

4 equations are given.

  $\begin{array}{l}\text{A:}-4p>8\text{or}2p<16\\ \text{B:}-2q<6\text{or}2q<8\\ \text{C:}-2r<4\text{or}4r<-8\\ \text{D:}-s>2\text{or}2s>-16\end{array}$

Concept Used:

Solve each equation separately.

Calculation:

Option A	Option B	Option C	Option D
$\begin{array}{l}-4p>8\text{or}2p<16\\ \frac{-4p}{-4}<\frac{8}{-4}\text{or}\frac{2p}{2}<\frac{16}{2}\\ p<-2orp<8\end{array}$	$\begin{array}{l}-2q<6\text{or}2q<8\\ \frac{-2q}{-2}>\frac{6}{-2}\text{or}\frac{2}{2}q<\frac{8}{2}\\ q>-3\text{or}q<4\end{array}$	$\begin{array}{l}-2r<4\text{or}4r<-8\\ \frac{-2r}{-2}>\frac{4}{-2}\text{or}\frac{4r}{4}<\frac{-8}{4}\\ r>-2\text{or}r<-2\end{array}$	$\begin{array}{l}-s>2\text{or}2s>-16\\ \frac{-s}{-1}<\frac{2}{-1}\text{or}\frac{2s}{2}>\frac{-16}{2}\\ s<-2\text{or}s>-8\end{array}$

Option B is the correct option, which has a graph that includes the entire number line.

Thus, option B is the correct option, which has a graph that includes the entire number line.