Chapter 1: Q18. (page 37)

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line.
18. $\frac{d}{2} > - 4$

Short Answer

Expert verified

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

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

Solution set on number line is

Step by step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify d2>−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

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

- 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 $(- 8, \infty)$

- Graph the solution set

Assolution 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.

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Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line.
18. $\frac{d}{2} > - 4$

Short Answer

Step by step solution

- Write properties of inequality

- Simplify d2>−4

- Write solution set

- Graph the solution set

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Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line.18. d2>-4

Short Answer

Step by step solution

- Write properties of inequality

- Simplify d2>−4

- Write solution set

- Graph the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Applied Mathematics

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Describe the solution set using set-builder or interval notation. Then graph the solution set on number line.
18. $\frac{d}{2} > - 4$