Q20. - Algebra 2

Question

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

20. $-8p\ge 24$

Step-by-Step Solution

Answer

Solution of inequality $-8p\ge 24$ is $p\le -3$

In interval form, solution set is $\left(-\infty ,-3\right]$

Solution set on number line is 

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify − 8 p ≥ 24

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

$\begin{array}{c}-8p\ge 24\\ \frac{-8p}{\left(-8\right)}\le \frac{24}{\left(-8\right)}\\ p\le -3\end{array}$

Step 3 - Write solution set

The solution set of the inequality contains all real numbers less than or equal to $-3$  

As, $-3$ is included in the set so bracket is used with it also $-\infty$ is not included so parentheses is used with it.

In interval form solution set is $\left(-\infty ,-3\right]$

Step 4 - Graph the solution set

As solution set of the inequality is all real numbers less than or equal to $-3$

So arrow is towards $-\infty$ and dot on $-3$ shows it is included in the solution set.