Chapter 1, Problem 44SGR

To determine

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

Answer to Problem 44SGR

The solution is given by $m>3$ or $m<\frac{3}{2}$ .

Explanation of Solution

Given information:

Given inequality

  $3m+5>14$ or $2m+4<7$

Calculation:

Consider the given inequality,

  $3m+5>14$ or $2m+4<7$

Now, solve the inequality $3m+5>14$ as shown,

  $\begin{array}{c}3m+5>14\\ 3m+5-5>14-5\\ 3m>9\\ m>3\end{array}$

Now, solve the inequality $2m+4<7$ as shown,

  $\begin{array}{c}2m+4<7\\ 2m+4-4<7-4\\ 2m<3\\ \frac{2m}{2}<\frac{3}{2}\\ m<\frac{3}{2}\end{array}$

Hence, the solution of the inequality is $m>3$ or $m<\frac{3}{2}$ .

Now, graph the inequality as shown:

The open ball suggests that the solution region is not included the points $\frac{3}{2}$ and $3$ .

The sign indicates the region is left side to the point $\frac{3}{2}$ or right side to the point $3$ on number line.