Chapter 1.6, Problem 14PPS

To determine

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

Answer to Problem 14PPS

The solution is given by $r<-2.25$ or $r>3$ .

Explanation of Solution

Given information:

Given inequality

  $4r+3<-6$ or $3r-7>2$

Calculation:

Consider the given inequality,

  $4r+3<-6$ or $3r-7>2$

Now, solve the first inequality as shown,

  $\begin{array}{c}4r+3<-6\\ 4r+3-3<-6-3\\ 4r<-9\\ \frac{4r}{4}<\frac{-9}{4}\\ r<-2.25\end{array}$

Now, solve the second inequality as shown,

  $\begin{array}{c}3r-7>2\\ 3r-7+7>2+7\\ 3r>9\\ \frac{3r}{3}>\frac{9}{3}\\ r>3\end{array}$

Hence, the solution of the inequality is $r<-2.25$ or $r>3$ .

Now, graph the inequality as shown:

  

The open ball suggests that the solution region is not included the points $-2.25$ and $3$ .

The sign indicates the region is left side to the point $-2.25$ and right side to the point $3$ on number line.