Chapter 8, Problem 45CR

To determine

Solve the inequality $-0.3z\le -2.4$ and graph the solution on number line

Answer to Problem 45CR

  $z\ge 8$

The graph of the solution on number line is below:

  

Explanation of Solution

Given:

The inequality, $-0.3z\le -2.4$

Concept used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• Inequality sign get reverse on multiplying or dividing by a negative number

Calculation:

In order to solve the mixed inequality $-0.3z\le -2.4$ first isolate the variable term z by performing some basic operations. Here to isolate z terms on the left side, first divide both sides by $-0.3$ and then the Inequality sign get reverse on multiplying or dividing by a negative number and then simplify further as shown below:

  $\begin{array}{l}-0.3z\le -2.4\\ \frac{-0.3z}{-0.3}\le \frac{-2.4}{-0.3}\\ z\ge 8\end{array}$

Thus, the solution of the given inequality is $z\ge 8$ .

The graph of the inequality solution $z\ge 8$ is below: