Q18. - Algebra 2

Question

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

18. $\frac{d}{2}>-4$

Step-by-Step Solution

Answer

Solution of inequality $\frac{d}{2}>-4$ is $d>-8$

In interval form, solution set is $\left(-8,\infty \right)$

Solution set on number line is 

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify d 2 > − 4

To simplify given inequality, use multiplication property of inequalities. Multiply by same positive number does not change the sign of inequality as shown below

$\begin{array}{c}\frac{d}{2}>-4\\ \frac{d}{2}\times 2>-4\times 2\\ d>-8\end{array}$

Step 3 - Write solution set

The solution set of the inequality contains all real numbers greater than $-8$ 

As, $-8$ is not included in the set so parentheses is used with it also $\infty$ is not included so parentheses is used with it.

In interval form solution set is $\left(-8,\infty \right)$

Step 4 - Graph the solution set

As solution set of the inequality is all real numbers greater than $-8$

So arrow is towards $\infty$ and open circle on $-8$ shows it is not included in the solution set.