/*! 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 75 Solve each absolute value inequa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 75

Solve each absolute value inequality. $$\left|\frac{2 x+2}{4}\right| \geq 2$$

Short Answer

Expert verified
The solution of the absolute value inequality is \( x \geq 3 \) or \( x \leq -5 \).

Step by step solution

01

Express the absolute value inequality into two separate inequalities

The given absolute value inequality is \( \left|\frac{2 x+2}{4}\right| \geq 2 \). An absolute value inequality \( |a| \geq c \) can be expressed as \( a \geq c \) or \( a \leq -c \). Thus, we can write the original inequality as \( \frac{2 x+2}{4} \geq 2 \) or \( \frac{2 x+2}{4} \leq -2 \).
02

Solve the first inequality \(\frac{2 x+2}{4} \geq 2 \)

To solve this inequality, multiply both sides by 4 to get rid of the denominator: \( 2x + 2 \geq 8 \). Next, subtract 2 from both sides: \( 2x \geq 6 \), and then divide by 2. We get \( x \geq 3 \).
03

Solve the second inequality \(\frac{2 x+2}{4} \leq -2 \)

Apply the same steps as in Step 2: multiply by 4 to get \( 2x + 2 \leq -8 \), subtract 2 to get \( 2x \leq -10 \), and finally divide by 2 to get \( x \leq -5 \).
04

Combine the solutions of the two inequalities

The final solution set of the original absolute value inequality is all values of x that satisfy one of these inequalities. Therefore, the solution is \( x \geq 3 \) or \( x \leq -5 \).

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 Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y=2 x^{2}-3 x \text { and } y=2 $$

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

The rectangular swimming pool in the figure shown measures 40 feet by 60 feet and is surrounded by a path of uniform width around the four edges. The perimeter of the rectangle formed by the pool and the surrounding path is 248 feet. Determine the width of the path.

An automobile repair shop charged a customer \(\$ 448\), listing \(\$ 63\) for parts and the remainder for labor. If the cost of labor is \(\$ 35\) per hour, how many hours of labor did it take to repair the car?

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.