Chapter EP, Problem 1.6.23EP

To determine

To Find: The solution for the inequality and graph for it on the number line.

Answer to Problem 1.6.23EP

Therequired solution is $h<-5,h>5$ and the graph is shown in Figure 1

Explanation of Solution

Given:

Thegiven inequalityis,

  $\left|3h\right|+15<0$

Calculation:

Consider the absolute value of $x$ is,

  $\left|x\right|=\{\begin{array}{l}x,\text{if}x\ge 0\\ -x,\text{if}x<0\end{array}$

Consider the given inequality is,

  $\begin{array}{l}\left|3h\right|<-15\\ 3h<-15\\ h<-5\end{array}$ or $\begin{array}{l}\left|3h\right|>15\\ 3h>15\\ h>5\end{array}$

The graph of the inequality on the number line is shown in Figure 1

Figure 1