/*! 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 140 Explain why \(|x|<-4\) has no... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 140

Explain why \(|x|<-4\) has no solution.

Short Answer

Expert verified
The expression \(|x|<-4\) has no solution because the absolute value of a number is non-negative, meaning it can never be less than a negative number.

Step by step solution

01

Understanding the Absolute Value

Firstly, to analyse the equation \(|x|<-4\), it's important to understand what an absolute value signifies. Absolute value, denoted by \(|x|\), of a number refers to the distance of that number from zero on the number line, regardless of the direction. Therefore, it is always non-negative.
02

Analyzing the Combining of Absolute Value and Negation

Next, consider the requirement that the absolute value of \(x\) is less than -4. Because the absolute value of a number is always non-negative, it cannot be less than any negative number, including -4.
03

Summarizing the Conclusion

From the above exploration, it is clarified that an absolute value can't be less than a negative number. Therefore, the mathematical expression \(|x|<-4\) has no solution in the realm of real numbers.

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I find the hardest part in solving a word problem is writing the equation that models the verbal conditions.

Solve each absolute value equation or indicate that the equation has no solution. $$ |x+1|+6=2 $$

A basketball player's hang time is the time spent in the air when shooting a basket. The formula $$t=\frac{\sqrt{d}}{2}$$ models hang time, \(t,\) in seconds, in terms of the vertical distance of a player's jump, \(d,\) in feet. (image cannot copy) If hang time for a shot by a professional basketball player is 0.85 second, what is the vertical distance of the jump, rounded to the nearest tenth of a foot?

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$7-(-9+2 i)-(-17-i)$$

In Exercises \(1-12\), plot the given point in a rectangular coordinate system. $$ (-3,-5) $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.