Which number line shows the solution to the inequality -2(3x – 1) < 8? O A. + +++O ++ -5 -4 -3 -2 -1 0 1 2 3 4 5 ++ ов. O B. + ++ -5 -4 -3 -2 -1 0 1 2 3 4 5 +0I+ + O C. + ++ +OI+ ++ + -5 -4 -3 -2 -1 0 1 2 3 4 5 O D. ++ ++0+ 1 2 -5 -4 -3 -2 -1 0 1 3 4 5
Which number line shows the solution to the inequality -2(3x – 1) < 8? O A. + +++O ++ -5 -4 -3 -2 -1 0 1 2 3 4 5 ++ ов. O B. + ++ -5 -4 -3 -2 -1 0 1 2 3 4 5 +0I+ + O C. + ++ +OI+ ++ + -5 -4 -3 -2 -1 0 1 2 3 4 5 O D. ++ ++0+ 1 2 -5 -4 -3 -2 -1 0 1 3 4 5
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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![### Inequality Number Line Representation
**Question:**
Which number line shows the solution to the inequality \(-2(3x - 1) < 8\)?
**Options:**
**A.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at –1.
- The line extends to the right from the open circle.
**B.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at –1.
- The line extends to the left from the open circle.
**C.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at 2.
- The line extends to the right from the open circle.
**D.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at 2.
- The line extends to the left from the open circle.
### Explanation of the problem:
To solve the inequality \(-2(3x - 1) < 8\), follow these steps:
1. Distribute the -2:
\[
-2 \cdot 3x + 2 < 8 \\
-6x + 2 < 8
\]
2. Subtract 2 from both sides:
\[
-6x < 6
\]
3. Divide both sides by -6 (and reverse the inequality):
\[
x > -1
\]
The solution to this inequality is \(x > -1\).
### Detailed Graph Explanation:
Among the given options, option A and B have the same open circle at -1, and C and D have the same open circle at 2. Since our solution is \(x > -1\):
- There will be an open circle at -1 (not filled because -1 is not included in the solution).
- The line extends to the right from -1.
Thus, the correct graph is option **A**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F134eae91-dd6f-48be-900f-3863236bf515%2Fc75f5650-27fa-4b7d-9a00-064e18d72c46%2F7fmala_processed.png&w=3840&q=75)
Transcribed Image Text:### Inequality Number Line Representation
**Question:**
Which number line shows the solution to the inequality \(-2(3x - 1) < 8\)?
**Options:**
**A.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at –1.
- The line extends to the right from the open circle.
**B.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at –1.
- The line extends to the left from the open circle.
**C.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at 2.
- The line extends to the right from the open circle.
**D.**
Number line with the following features:
- Points are labeled from -5 to 5.
- An open circle is placed at 2.
- The line extends to the left from the open circle.
### Explanation of the problem:
To solve the inequality \(-2(3x - 1) < 8\), follow these steps:
1. Distribute the -2:
\[
-2 \cdot 3x + 2 < 8 \\
-6x + 2 < 8
\]
2. Subtract 2 from both sides:
\[
-6x < 6
\]
3. Divide both sides by -6 (and reverse the inequality):
\[
x > -1
\]
The solution to this inequality is \(x > -1\).
### Detailed Graph Explanation:
Among the given options, option A and B have the same open circle at -1, and C and D have the same open circle at 2. Since our solution is \(x > -1\):
- There will be an open circle at -1 (not filled because -1 is not included in the solution).
- The line extends to the right from -1.
Thus, the correct graph is option **A**.
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