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,...
Related questions
Question
Graph the solution set to the linear inequality on the number line
![### Graphing Linear Inequalities
**Question Details:**
- **Task:** Graph the solution set to the linear inequality
\[
-12x + 2 > 1
\]
on the number line below.
**Graph Details:**
- **Number Line:** The image displays a horizontal number line with arrows on both ends, indicating it extends infinitely in both directions.
**Solution Steps:**
1. **Solve the Inequality:**
- Start with the inequality: \(-12x + 2 > 1\).
- Subtract 2 from both sides: \(-12x > -1\).
- Divide by -12 and reverse the inequality sign (since dividing by a negative number reverses the inequality): \(x < \frac{1}{12}\).
2. **Graph the Solution:**
- On the number line, identify the point \(\frac{1}{12}\).
- Use an open circle at \(\frac{1}{12}\) to indicate that this point is not included in the solution (the inequality is less than, not less than or equal to).
- Shade the region to the left of \(\frac{1}{12}\) to represent all the values that are solutions to the inequality \(x < \frac{1}{12}\).
This activity helps in understanding how to graphically represent solutions to linear inequalities on a number line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb228e09-4164-47f7-a050-f68b9f7ba773%2Fec3de42c-3f12-4955-ba17-4abe8984b03f%2Fme0cr1_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Linear Inequalities
**Question Details:**
- **Task:** Graph the solution set to the linear inequality
\[
-12x + 2 > 1
\]
on the number line below.
**Graph Details:**
- **Number Line:** The image displays a horizontal number line with arrows on both ends, indicating it extends infinitely in both directions.
**Solution Steps:**
1. **Solve the Inequality:**
- Start with the inequality: \(-12x + 2 > 1\).
- Subtract 2 from both sides: \(-12x > -1\).
- Divide by -12 and reverse the inequality sign (since dividing by a negative number reverses the inequality): \(x < \frac{1}{12}\).
2. **Graph the Solution:**
- On the number line, identify the point \(\frac{1}{12}\).
- Use an open circle at \(\frac{1}{12}\) to indicate that this point is not included in the solution (the inequality is less than, not less than or equal to).
- Shade the region to the left of \(\frac{1}{12}\) to represent all the values that are solutions to the inequality \(x < \frac{1}{12}\).
This activity helps in understanding how to graphically represent solutions to linear inequalities on a number line.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
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
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education