Chapter 1.6, Problem 1E

To determine

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

Answer to Problem 1E

The solution is given by $-12<g<-2$ .

Explanation of Solution

Given information:

Given inequality

  $-4<g+8<6$

Calculation:

Consider the given inequality,

  $-4<g+8<6$

Now, solve the inequality as shown,

  $\begin{array}{c}-4<g+8<6\\ -4-8<g+8-8<6-8\\ -12<g<-2\end{array}$

Now, graph the inequality as shown:

  

The open ball suggests that the solution region is not included the points $-12$ and $-2$ .

The sign indicates the region is left side to the point $-2$ and right side to the point $-12$ on number line.

Hence, the solution of the inequality is $-12<g<-2$ .