Q9. - Algebra 2

Question

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

 $-0.6p<-9$

Step-by-Step Solution

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 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify &#8722; 0.6 p &#60; &#8722; 9

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

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

Step 3 - 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 $\left\{p|p>15\right\}$

Step 4 - Graph the solution set

As solution 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.