Chapter 5, Problem 32SGR

To determine

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

Answer to Problem 32SGR

The solution is $t\in \left(1,7\right)$ and the graph is,

  

Explanation of Solution

Given:

  $-4<2t-6<8$

Calculation:

  $-4<2t-6<8$

Adding 6 to the above inequality, we get

  $\begin{array}{l}\Rightarrow -4+6<2t-6+6<8+6\\ \Rightarrow 2<2t<14\end{array}$

Now dividing by 2, we get

  $\begin{array}{l}\Rightarrow \frac{2}{2}<\frac{2t}{2}<\frac{14}{2}\\ \Rightarrow 1<t<7\\ \Rightarrow t\in \left(1,7\right)\end{array}$

Now the graph is,