Question

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line.

$-0.6p<-9$

Short answer

Solution of inequality $-0.6p<-9$ is $p>15$

In set-builder form, solution set is $\left\{p|p>15\right\}$

Solution set on number line is

Step-by-step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify −0.6p<−9

To simplify given inequality, use division property of inequalities. Divide by same negative number reverse the sign of inequality as shown below

$\begin{array}{c}-0.6p<-9\\ \frac{-0.6p}{-0.6}>\frac{-9}{-0.6}\\ p>15\end{array}$

- Write solution set

The solution set of the inequality $p>15$ contains all real numbers greater than 15

In set-builder form

Solution set is $\left\{p|p>15\right\}$

- Graph the solution set

Assolution set of the inequality $p>15$ contains all real numbers greater than 15

So arrow is towards $\infty$ and open circle on 15 denotes it is not included in the solution set.