Chapter 1.6, Problem 9CYU

To determine

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

Answer to Problem 9CYU

The solution is given by $v>3\text{or}v<-\frac{19}{3}$ .

Explanation of Solution

Given information:

Given inequality

  $\left|3v+5\right|>14$

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

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

Calculation:

Consider the given inequality,

  $\left|3v+5\right|>14$

Now, solve the inequality as shown,

  $\begin{array}{c}\left|3v+5\right|>14\\ 3v+5>14\text{or}3v+5<-14\\ 3v+5-5>14-5\text{or}3v+5-5<-14-5\\ 3v>9\text{or}3v<-19\\ v>3\text{or}v<-\frac{19}{3}\end{array}$

Hence, the solution of the inequality is $v>3\text{or}v<-\frac{19}{3}$ .

Now, graph the inequality as shown:

The open ball suggests that the solution region is not included the points $3$ and $-\frac{19}{3}$ .

The sign indicates the region is left side to the point $-\frac{19}{3}$ and right side to the point $3$ on number line.