Chapter EP, Problem 1.5.7EP

To determine

To solve: The inequality $-3\left(y-2\right)\ge -9$ and then plot the graph of the solution set on a number line.

Answer to Problem 1.5.7EP

The solution of the inequality $-3\left(y-2\right)\ge -9$ is $y\ge 5$ , and graph of the solution set of the inequality is shown in figure (1).

Explanation of Solution

Given:

The inequality is $-3\left(y-2\right)\ge -9$ .

Calculation:

Divide both sides of the inequality $-3\left(y-2\right)\ge -9$ by $-3$ .

  $\begin{array}{c}\frac{-3}{-3}\left(y-2\right)\ge \frac{-9}{-3}\\ \left(y-2\right)\ge 3\end{array}$

Add 2 to both sides of the inequality $\left(y-2\right)\ge 3$ .

  $\begin{array}{c}\left(y-2+2\right)\ge 3+2\\ y\ge 5\end{array}$

Therefore, the solution of the inequality $-3\left(y-2\right)\ge -9$ is $y\ge 5$ .

The graph of the solution set of the inequality is as follows.

Figure (1)

The graph for the inequality $y\ge 5$ contains all values that are greater than or equal to $5$ and dot shows $5$ is included in solution set.

Therefore, the solution of the inequality $-3\left(y-2\right)\ge -9$ is $y\ge 5$ , and graph of the solution set of the inequality is shown in figure (1).