Chapter 1.6, Problem 3E

To determine

To solve: the given inequality and graph the solution on number line.

Answer to Problem 3E

The solution is given by $z>-3$ or $z<-6$ .

Explanation of Solution

Given information:

Given inequality

  $z+6>3$ or $2z<-12$

Calculation:

Consider the given inequality,

  $z+6>3$ or $2z<-12$

Now, solve the first inequality as shown,

  $\begin{array}{c}z+6>3\\ z+6-6>3-6\\ z>-3\end{array}$

Now, solve the second inequality as shown,

  $\begin{array}{c}2z<-12\\ \frac{2z}{2}<\frac{-12}{2}\\ z<-6\end{array}$

Hence, the solution of the inequality is $z>-3$ or $z<-6$ .

Now, graph the inequality as shown:

  

The open ball suggests that the solution region is not included the points $-3$ and $-6$ .

The sign indicates the region is left side to the point $-6$ and right side to the point $-3$ on number line.