Chapter EP, Problem 1.5.4EP

To determine

To solve: The inequality $-3x>6$ and then plot the graph of the solution set on a number line.

Answer to Problem 1.5.4EP

The solution of the inequality $-3x>6$ is $x>-2$ , and graph of the solution set of the inequality is shown in figure (1).

Explanation of Solution

Given:

The inequality is $-3x>6$ .

Calculation:

Divide both sides of the inequality $-3x>6$ by $-3$ .

  $\begin{array}{c}\frac{-3}{-3}x>\frac{6}{-3}\\ x>-2\end{array}$

Therefore, the solution of the inequality $-3x>6$ is $x>-2$ .

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

Figure (1)

The graph for the inequality $x>-2$ contains all values that are greater than $-2$ and dot shows $-2$ is not included in solution set.

Therefore, the solution of the inequality $-3x>6$ is $x>-2$ , and graph of the solution set of the inequality is shown in figure (1).