Chapter 5, Problem 41SGR

To determine

To solve the given compound inequality and to graph the solution set.

Answer to Problem 41SGR

The solution is $y\in \left(-4,2.5\right)$ and the graph is,

  

Explanation of Solution

Given:

  $\left|-4y-3\right|<13$

Calculation:

  $\begin{array}{l}\left|-4y-3\right|<13\\ \Rightarrow -13<-4y-3<13\end{array}$

Adding 3 to the above inequality, we get

  $\begin{array}{l}\Rightarrow -13+3<-4y-3+3<13+3\\ \Rightarrow -10<-4y<16\end{array}$

Now dividing by $-4$ , we get

  $\begin{array}{l}\Rightarrow \frac{-10}{-4}>\frac{-4y}{-4}>\frac{16}{-4}\\ \Rightarrow 2.5>y>-4\\ \Rightarrow -4<y<2.5\\ \Rightarrow y\in \left(-4,2.5\right)\end{array}$

Now the graph is,