Chapter 1.6, Problem 34PPS

To determine

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

Answer to Problem 34PPS

The solution is given by $m>-5$ or $m<-12$ ..

Explanation of Solution

Given information:

Given inequality

  $m-7>-12$ or $-3m+2>38$

Calculation:

Consider the given inequality,

  $m-7>-12$ or $-3m+2>38$

Now, solve the first inequality as shown,

  $\begin{array}{c}m-7>-12\\ m-7+7>-12+7\\ m>-5\end{array}$

Now, solve the second inequality as shown,

  $\begin{array}{c}-3m+2>38\\ -3m+2-2>38-2\\ -3m>36\\ m<-12\end{array}$

Hence, the solution of the inequality is $m>-5$ or $m<-12$ .

Now, graph the inequality as shown:

  

The open ball suggests that the solution region is not included the points $-5$ and $-12$ .

The sign indicates the region is left side to the point $-12$ and right side to the point $-5$ on number line.