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
![**Question 6: Choose the Correct Graph for the Inequality**
Given Inequality: \(x - 7 > 2\)
**Solution Steps:**
1. Solve the inequality:
\[
x - 7 > 2
\]
Add 7 to both sides:
\[
x > 9
\]
2. Now, let's analyze the four number line graphs provided:
- **Graph A**: A number line from 5 to 14. There is a filled circle at 9, and the shading goes to the right.
- **Graph B**: A number line from 5 to 14. There is an open circle at 9, and the shading goes to the right.
- **Graph C**: A number line from 5 to 14. There is a filled circle at 9, and the shading goes to the left.
- **Graph D**: A number line from 5 to 14. There is an open circle at 9, and the shading goes to the left.
3. **Correct Graph Selection:**
The correct graph for the inequality \(x > 9\) should have an open circle at 9, with shading to the right to indicate that all numbers greater than 9 satisfy the inequality.
Therefore, **Graph B** is the correct representation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F872e2fbe-13ff-4399-ac15-da98b2e24822%2F1c0396f1-8d50-4478-887e-6cdce4066fdd%2Fseo9a3f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6: Choose the Correct Graph for the Inequality**
Given Inequality: \(x - 7 > 2\)
**Solution Steps:**
1. Solve the inequality:
\[
x - 7 > 2
\]
Add 7 to both sides:
\[
x > 9
\]
2. Now, let's analyze the four number line graphs provided:
- **Graph A**: A number line from 5 to 14. There is a filled circle at 9, and the shading goes to the right.
- **Graph B**: A number line from 5 to 14. There is an open circle at 9, and the shading goes to the right.
- **Graph C**: A number line from 5 to 14. There is a filled circle at 9, and the shading goes to the left.
- **Graph D**: A number line from 5 to 14. There is an open circle at 9, and the shading goes to the left.
3. **Correct Graph Selection:**
The correct graph for the inequality \(x > 9\) should have an open circle at 9, with shading to the right to indicate that all numbers greater than 9 satisfy the inequality.
Therefore, **Graph B** is the correct representation.
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