/*! 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 83 Solve each absolute value inequa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 83

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

Short Answer

Expert verified
\(x \in (-\infty,-3) \cup (5,\infty)\)

Step by step solution

01

Isolate the Absolute Value

One could start with isolating the absolute value by dividing both sides of the inequality by -4, remembering to reverse the direction of the inequality because negative number division was involved and that changes inequality direction. Hence, the inequality becomes \(|1-x| > 4\).
02

Split the Absolute Value

After isolating the absolute value, split it up into two separate inequalities, one for the positive case and one for the negative. The resulting system of inequalities will be \(1-x > 4\) and \(1-x < -4\).
03

Solve the Two Inequalities

Next, solve each inequality separately. For \(1-x > 4\), subtract 1 from both sides to get \(-x > 3\), then multiply by -1 (and flip the inequality) to get \(x < -3\). For \(1-x < -4\), subtract 1 from both sides to get \(-x < -5\), then multiply by -1 (and flip the inequality) to get \(x > 5\).
04

Express the Solution

The solution is the set of all x that satisfy either inequality. In interval notation, that would be \(x \in (-\infty,-3) \cup (5,\infty)\) as this is the union of two disjoint intervals.

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

In a round-robin chess tournament, each player is paired with every other player once. The formula $$N=\frac{x^{2}-x}{2}$$ models the number of chess games, \(N,\) that must be played in a round-robin tournament with \(x\) chess players. Use this formula to solve Exercises \(131-132\). In a round-robin chess tournament, 36 games were played. How many players were entered in the tournament?

In a round-robin chess tournament, each player is paired with every other player once. The formula $$N=\frac{x^{2}-x}{2}$$ models the number of chess games, \(N,\) that must be played in a round-robin tournament with \(x\) chess players. Use this formula to solve Exercises \(131-132\). In a round-robin chess tournament, 21 games were played. How many players were entered in the tournament?

The price of a dress is reduced by \(40 \% .\) When the dress still does not sell, it is reduced by \(40 \%\) of the reduced price. If the price of the dress after both reductions is \(\$ 72,\) what was the original price?

In your own words, describe a step-by-step approach for solving algebraic word problems.

The length of a rectangular sign is 3 feet longer than the width. If the sign's area is 54 square feet, find its length and width.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.