/*! 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 82 Solve each absolute value inequa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 82

Solve each absolute value inequality. $$-4|1-x|<-16$$

Short Answer

Expert verified
The solution to the inequality \( -4|1-x|<-16 \) is \( x<-3 \) and \( x>-5 \)

Step by step solution

01

Removal of Multiplier

First, we get rid of the multiplier next to the absolute value. As the multiplier is -4, the inequality becomes \(|1-x|>4\), we divided both sides by -4, also we need to remember to flip the inequality symbol when we do this because we divided by a negative value.
02

Breaking down the Absolute Value

Next, we have \( |1-x|>4 \) we can decide on breaking down the absolute value. This leads us to two separate inequalities: \(1-x>4\) and \(-1+x<-4\) (the negative inequality reverses the order of 1 and x and changes the inequality sign).
03

Solve the Inequalities

Now, we solve both inequalities individually to find the range for \(x\) in each case. Solving the first inequality, \( 1-x>4 \), we get \( x<-3 \). Solving the second inequality, \( -1+x<-4 \), we get \( x>-5 \).
04

Combine the Solutions

Finally, we combine the solution sets from the two previously solved inequalities which yields the final answer.

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

Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I subtracted \(\frac{3 x-5}{x-1}\) from \(\frac{x-3}{x-1}\) and obtained a constant.

$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$.

In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

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.