Chapter 1.6, Problem 4CYU

To determine

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

Answer to Problem 4CYU

The solution is given by $m\ge 4$ or $m\le -5$ .

Explanation of Solution

Given information:

Given inequality

  $m-7\ge -3$ or $-2m+1\ge 11$

Calculation:

Consider the given inequality,

  $m-7\ge -3$ or $-2m+1\ge 11$

Now, solve the first inequality as shown,

  $\begin{array}{c}m-7\ge -3\\ m-7+7\ge -3+7\\ m\ge 4\end{array}$

Now, solve the second inequality as shown,

  $\begin{array}{c}-2m+1\ge 11\\ -2m+1-1\ge 11-1\\ -2m\ge 10\\ \frac{-2m}{-2}\le \frac{10}{-2}\\ m\le -5\end{array}$

Hence, the solution of the inequality is $m\ge 4$ or $m\le -5$ .

Now, graph the inequality as shown:

  

The closed ball suggests that the solution region is included the points $-5$ and $6$ .

The sign indicates the region is left side to the point $-5$ and right side to the point $6$ on number line.