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
100%
Did i do this right? Could someone check my work?
![**Educational Website Content**
**Solve the Inequality:**
\[ -2x + 6 - 8x > 2(5x + 1) \]
Options:
- **A**: \( x < 1 \)
- **B**: \( x \geq \frac{1}{5} \)
- **C**: \( x \leq 5 \)
- **D**: \( x > 5 \)
**Solve:**
\[ \frac{2}{5}(w - 12) = -25 \]
Find the value of \( w \).
\[ w = \_\_\_\_\_\_\_ \quad (\text{Form: \#\#}) \]
**Steps to Solve (shown in handwriting):**
1. Distribute and simplify the left side:
\[ -2x + 6 - 8x > 2(5x + 1) \]
\[ -10x + 6 > 2(5x + 1) \]
2. Expand and simplify the right side:
\[ -10x + 6 > 10x + 2 \]
3. Add \( 10x \) to both sides to eliminate the variable on the right:
\[ 6 > 20x + 2 \]
4. Subtract \( 2 \) from both sides:
\[ 4 > 20x \]
5. Divide both sides by 20:
\[ \frac{4}{20} > x \]
\[ x < \frac{1}{5} \]
6. Conclusion (write "A" for the correct inequality).
**Note**: This example involves distributing, simplifying, and solving for the variable in an inequality, followed by solving a linear equation. Practice similar steps for mastery.
No graphs or diagrams present.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe927df63-f1e3-498b-a31a-923bb5077d27%2F9b1ad978-32e4-4a93-9cf2-ceb82cf942be%2Fna357df.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
**Solve the Inequality:**
\[ -2x + 6 - 8x > 2(5x + 1) \]
Options:
- **A**: \( x < 1 \)
- **B**: \( x \geq \frac{1}{5} \)
- **C**: \( x \leq 5 \)
- **D**: \( x > 5 \)
**Solve:**
\[ \frac{2}{5}(w - 12) = -25 \]
Find the value of \( w \).
\[ w = \_\_\_\_\_\_\_ \quad (\text{Form: \#\#}) \]
**Steps to Solve (shown in handwriting):**
1. Distribute and simplify the left side:
\[ -2x + 6 - 8x > 2(5x + 1) \]
\[ -10x + 6 > 2(5x + 1) \]
2. Expand and simplify the right side:
\[ -10x + 6 > 10x + 2 \]
3. Add \( 10x \) to both sides to eliminate the variable on the right:
\[ 6 > 20x + 2 \]
4. Subtract \( 2 \) from both sides:
\[ 4 > 20x \]
5. Divide both sides by 20:
\[ \frac{4}{20} > x \]
\[ x < \frac{1}{5} \]
6. Conclusion (write "A" for the correct inequality).
**Note**: This example involves distributing, simplifying, and solving for the variable in an inequality, followed by solving a linear equation. Practice similar steps for mastery.
No graphs or diagrams present.
![The image appears to depict a series of mathematical steps for solving an inequality. Here is the transcription of the content:
1. **Initial Inequality:**
\[
-2x + 6 \div 6 > 2(5x + 1)
\]
2. **Simplification Step:**
\[
10x + 6 > 2(5x + 1)
\]
3. **Expansion and Simplification:**
\[
-10x + 6 - 10x - 2
\]
4. **Further Simplification Steps:**
\[
6 > 20x + 2
\]
5. **Subtracting 2 from Both Sides:**
\[
4 > 20x
\]
6. **Dividing Both Sides by 4:**
\[
x < \frac{1}{5}
\]
This guide demonstrates solving a linear inequality by simplifying terms and isolating the variable. Each step involves operations such as distributing, combining like terms, and performing arithmetic operations to isolate the variable on one side of the inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe927df63-f1e3-498b-a31a-923bb5077d27%2F9b1ad978-32e4-4a93-9cf2-ceb82cf942be%2Ff2zynao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image appears to depict a series of mathematical steps for solving an inequality. Here is the transcription of the content:
1. **Initial Inequality:**
\[
-2x + 6 \div 6 > 2(5x + 1)
\]
2. **Simplification Step:**
\[
10x + 6 > 2(5x + 1)
\]
3. **Expansion and Simplification:**
\[
-10x + 6 - 10x - 2
\]
4. **Further Simplification Steps:**
\[
6 > 20x + 2
\]
5. **Subtracting 2 from Both Sides:**
\[
4 > 20x
\]
6. **Dividing Both Sides by 4:**
\[
x < \frac{1}{5}
\]
This guide demonstrates solving a linear inequality by simplifying terms and isolating the variable. Each step involves operations such as distributing, combining like terms, and performing arithmetic operations to isolate the variable on one side of the inequality.
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
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