/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 Solve each absolute value inequa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 69

Solve each absolute value inequality. $$|x|>3$$

Short Answer

Expert verified
The solutions to the inequality \(|x| > 3\) are \(x > 3\) and \(x < -3\).

Step by step solution

01

Understand the Problem

The equations says that the absolute value of 'x' is greater than 3. This means that 'x' is either greater than 3 or less than -3. This concept can be clearly explained through a number line.
02

Break into Two Inequalities

The inequality \(|x| > 3\) can be broken down into two inequalities: \(x > 3\) and \(x < -3\). This is because absolute value of 'x' gives positive values, so we're looking for values of 'x' that are more than 3 units away from 0 on either side.
03

Solve Both Inequalities

Solving both \(x > 3\) and \(x < -3\) will give the solution to this problem. For \(x > 3\), any value larger than '3' would satisfy the equation. Similarly, for \(x < -3\), any value lesser than '-3' would satisfy the equation.
04

Represent on a Number Line

Both of the solutions can be represented on a number line. Any point on the right side of '3' or on the left side of '-3' would satisfy the original inequality \(|x| > 3\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$T=D+p m \text { for } p$$

Will help you prepare for the material covered in the next section. $$\text { Multiply: }(7-3 x)(-2-5 x)$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$B=\frac{F}{S-V} \text { for } S$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$E=m c^{2} \text { for } m$$

Will help you prepare for the material covered in the next section. $$\text{Rationalize the denominator: }\frac{7+4 \sqrt{2}}{2-5 \sqrt{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.