Homework Help is Here – Start Your Trial Now!
Math
Algebra
Graph the solution of the inequality | – 2x + 6| – 8 < 4.

Graph the solution of the inequality | – 2x + 6| – 8 < 4.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
### Transcription for Educational Website **Topic: Solving Inequalities Involving Absolute Values** #### Problem Statement: Graph the solution of the inequality \( |\ -2x + 6| - 8 < 4 \). #### Steps to Solve the Inequality: 1. **Isolate the Absolute Value Expression:** \[ |\ -2x + 6| - 8 < 4 \] \[ |\ -2x + 6| < 12 \] 2. **Set Up a Compound Inequality:** \[ -12 < -2x + 6 < 12 \] 3. **Solve the Compound Inequality:** - For the left part of the inequality: \[ -12 < -2x + 6 \] \[ -18 < -2x \] \[ 9 > x \] or \[ x < 9 \] - For the right part of the inequality: \[ -2x + 6 < 12 \] \[ -2x < 6 \] \[ x > -3 \] 4. **Combine the Results:** \[ -3 < x < 9 \] #### Graphing the Solution: To graph the solution of the inequality \(-3 < x < 9\), follow these steps: - Draw a number line. - Add open circles at \(x = -3\) and \(x = 9\) because the inequality does not include the endpoints (i.e., it is a strict inequality). - Shade the region between \(-3\) and \(9\) to represent all the numbers \(x\) that satisfy the inequality. The final graph represents all possible values of \(x\) that make the inequality true.
Transcribed Image Text:### Transcription for Educational Website **Topic: Solving Inequalities Involving Absolute Values** #### Problem Statement: Graph the solution of the inequality \( |\ -2x + 6| - 8 < 4 \). #### Steps to Solve the Inequality: 1. **Isolate the Absolute Value Expression:** \[ |\ -2x + 6| - 8 < 4 \] \[ |\ -2x + 6| < 12 \] 2. **Set Up a Compound Inequality:** \[ -12 < -2x + 6 < 12 \] 3. **Solve the Compound Inequality:** - For the left part of the inequality: \[ -12 < -2x + 6 \] \[ -18 < -2x \] \[ 9 > x \] or \[ x < 9 \] - For the right part of the inequality: \[ -2x + 6 < 12 \] \[ -2x < 6 \] \[ x > -3 \] 4. **Combine the Results:** \[ -3 < x < 9 \] #### Graphing the Solution: To graph the solution of the inequality \(-3 < x < 9\), follow these steps: - Draw a number line. - Add open circles at \(x = -3\) and \(x = 9\) because the inequality does not include the endpoints (i.e., it is a strict inequality). - Shade the region between \(-3\) and \(9\) to represent all the numbers \(x\) that satisfy the inequality. The final graph represents all possible values of \(x\) that make the inequality true.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Inequality
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS