Chapter 2.4, Problem 10E

To determine

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

Answer to Problem 10E

The solution is $t>-4$ and the graph is,

  

Explanation of Solution

Given:

  $2>-3t-10$

Concept used:

When multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed to produce an equivalent inequality.

Calculation:

  $2>-3t-10$

Adding 10 on both sides, we get

  $\begin{array}{l}2+10>-3t-10+10\\ \Rightarrow 12>-3t\end{array}$

Dividing by $-3$ on both sides, we get

  $\begin{array}{l}\frac{12}{-3}<\frac{-3t}{-3}\\ \Rightarrow -4<t\\ \Rightarrow t>-4\end{array}$

Now the graph is,