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,...
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![**Question 20:**
Which number line represents the solution to the inequality below?
\[ 3x + 12 > 45 \]
Below this question are four options labeled A, B, C, and D. Each option shows a number line with different markers and shaded regions indicating various solutions.
- **Option A:** The number line is marked from 8 to 20. There is a solid circle at 11 and a red arrow extending to the right from this point.
- **Option B:** The number line is marked from 8 to 20. There is an open circle at 11 and a red arrow extending to the right from this point.
- **Option C:** The number line is marked from 8 to 20. There is a solid circle at 11 and a red arrow extending to the left from this point.
- **Option D:** The number line is marked from 8 to 20. There is an open circle at 11 and a red arrow extending to the left from this point.
### Explanation of Solution:
To solve the inequality \( 3x + 12 > 45 \):
1. Subtract 12 from both sides:
\[ 3x > 33 \]
2. Divide both sides by 3:
\[ x > 11 \]
The solution to this inequality is \( x > 11 \).
### Correct Graphical Representation:
The number line that represents \( x > 11 \) should have an open circle at 11 (since 11 is not included in the solution) and an arrow extending to the right indicating all numbers greater than 11.
Thus, **Option B** is the correct graphical representation of the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b4ac02d-8fa9-4cd1-ad8a-49ffeef4197d%2F1dd42b79-3a25-4cd8-a9e0-7bc6d37c9f59%2F19gzeul_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 20:**
Which number line represents the solution to the inequality below?
\[ 3x + 12 > 45 \]
Below this question are four options labeled A, B, C, and D. Each option shows a number line with different markers and shaded regions indicating various solutions.
- **Option A:** The number line is marked from 8 to 20. There is a solid circle at 11 and a red arrow extending to the right from this point.
- **Option B:** The number line is marked from 8 to 20. There is an open circle at 11 and a red arrow extending to the right from this point.
- **Option C:** The number line is marked from 8 to 20. There is a solid circle at 11 and a red arrow extending to the left from this point.
- **Option D:** The number line is marked from 8 to 20. There is an open circle at 11 and a red arrow extending to the left from this point.
### Explanation of Solution:
To solve the inequality \( 3x + 12 > 45 \):
1. Subtract 12 from both sides:
\[ 3x > 33 \]
2. Divide both sides by 3:
\[ x > 11 \]
The solution to this inequality is \( x > 11 \).
### Correct Graphical Representation:
The number line that represents \( x > 11 \) should have an open circle at 11 (since 11 is not included in the solution) and an arrow extending to the right indicating all numbers greater than 11.
Thus, **Option B** is the correct graphical representation of the solution.
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