Chapter 1: Q12. (page 44)

Solve each inequality. Graph the solution set on a number line.
$|4 k - 8| < 20$ .

Short Answer

Expert verified

The solution of the given absolute inequality is $- 3 < k < 7$ .

Step by step solution

-Write the inequalities

A For all real numbers a, b and $b > 0$ ; it is true that if $|a| < b$ then $- b < a < b$ . The given absolute inequality is $|4 k - 8| < 20$ .

– Apply the definition of an absolute compound inequality

Use the definition of absolute value inequality and write the compound inequality as follows:

$\begin{matrix} | 4 k - 8 | < 20 \\ - 20 < 4 k - 8 < 20 \\ - 20 + 8 < 4 k - 8 + 8 < 20 + 8 \\ - 12 < 4 k < 28 \end{matrix}$

Therefore, the solution of the given absolute inequality is $- 3 < k < 7$

– Graph of the solution set

The graph for the inequality $- 3 < k < 7$ is as shown below

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each inequality. Graph the solution set on a number line.
$|4 k - 8| < 20$ .

Short Answer

Step by step solution

-Write the inequalities

– Apply the definition of an absolute compound inequality

– Graph of the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Statistics

Applied Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.4k-8<20.

Short Answer

Step by step solution

-Write the inequalities

– Apply the definition of an absolute compound inequality

– Graph of the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Statistics

Applied Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set on a number line.
$|4 k - 8| < 20$ .