Chapter 1.6, Problem 16E

To determine

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

Answer to Problem 16E

The solution is given by $-2<h<2$ .

Explanation of Solution

Given information:

Given inequality

  $\left|6h\right|<12$

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$ \

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

More over

  $\begin{array}{l}\left|x+a\right|<b\\ \Rightarrow -b<x+a<b\end{array}$

Calculation:

Consider the given inequality,

  $\left|6h\right|<12$

Now, solve the inequality as shown,

  $\begin{array}{c}\left|6h\right|<12\\ -12<6h<12\\ \frac{-12}{6}<\frac{6h}{6}<\frac{12}{6}\\ -2<h<2\end{array}$

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

Now, graph the inequality as shown:

  

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

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