Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterA: Appendix
SectionA.4: Factoring And Quadratic Equations
Problem 38E: Determine the length x by solving either the equation x4=6x+5 or the equivalent equation xx+5=24.
Related questions
Question
![### Solve the Equation
Given the equation:
\[ \frac{3x}{4} = -13 \]
Determine the value of \( x \).
### Multiple Choice Options
A. \( \frac{13}{3} \)
B. \( 25 \)
C. \( -5, 5 \)
D. No solution
### Explanation
To solve for \( x \), we can multiply both sides of the equation by 4 to eliminate the fraction:
\[ 3x = -13 \times 4 \]
\[ 3x = -52 \]
Then, divide both sides by 3 to solve for \( x \):
\[ x = \frac{-52}{3} \]
\[ x = -\frac{52}{3} \]
Since \( -\frac{52}{3} \) is not one of the given choices, we should double-check our options:
- Option A: \( \frac{13}{3} \) is incorrect.
- Option B: \( 25 \) is incorrect.
- Option C: \( -5, 5 \) is incorrect.
- Option D: **No solution** is the correct choice.
Therefore, the correct answer is **D. No solution**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F227fd297-25c6-41a3-8d4d-df25e1639e4d%2F3aa16061-fbaa-42ca-b4f7-2ccac96425bf%2F1dy0ox7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solve the Equation
Given the equation:
\[ \frac{3x}{4} = -13 \]
Determine the value of \( x \).
### Multiple Choice Options
A. \( \frac{13}{3} \)
B. \( 25 \)
C. \( -5, 5 \)
D. No solution
### Explanation
To solve for \( x \), we can multiply both sides of the equation by 4 to eliminate the fraction:
\[ 3x = -13 \times 4 \]
\[ 3x = -52 \]
Then, divide both sides by 3 to solve for \( x \):
\[ x = \frac{-52}{3} \]
\[ x = -\frac{52}{3} \]
Since \( -\frac{52}{3} \) is not one of the given choices, we should double-check our options:
- Option A: \( \frac{13}{3} \) is incorrect.
- Option B: \( 25 \) is incorrect.
- Option C: \( -5, 5 \) is incorrect.
- Option D: **No solution** is the correct choice.
Therefore, the correct answer is **D. No solution**.
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