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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![### Parallel Lines and Angles
**Problem Statement:**
24. In the figure, if line \( r \) is parallel to line \( s \), what is the value of \( x \)?
**Figure Information:**
- Two parallel lines \( r \) and \( s \) are shown.
- Two angles are marked, each represented by algebraic expressions:
- The angle on line \( r \) is labeled as \( 2x + 7 \).
- The angle on line \( s \) is labeled as \( 3x - 10 \).
**Options:**
A. \( x = -17 \)
B. \( x = \frac{17}{5} \)
C. \( x = 15 \)
D. \( x = 17 \)
**Solution Explanation:**
Since lines \( r \) and \( s \) are parallel and the angles are corresponding angles (or alternate interior angles, depending on the diagram context), their measures are equal. Therefore, we can set up the equation:
\[ 2x + 7 = 3x - 10 \]
Now, solve for \( x \):
1. Subtract \( 2x \) from both sides:
\[ 7 = x - 10 \]
2. Add 10 to both sides:
\[ 17 = x \]
Thus, the value of \( x \) is 17.
The correct answer is:
D. \( x = 17 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b4de2cd-a567-4373-911c-936e397ded87%2Fd26a4c65-fa52-4633-8d9d-868cc9df8a4c%2Fe941x09_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Parallel Lines and Angles
**Problem Statement:**
24. In the figure, if line \( r \) is parallel to line \( s \), what is the value of \( x \)?
**Figure Information:**
- Two parallel lines \( r \) and \( s \) are shown.
- Two angles are marked, each represented by algebraic expressions:
- The angle on line \( r \) is labeled as \( 2x + 7 \).
- The angle on line \( s \) is labeled as \( 3x - 10 \).
**Options:**
A. \( x = -17 \)
B. \( x = \frac{17}{5} \)
C. \( x = 15 \)
D. \( x = 17 \)
**Solution Explanation:**
Since lines \( r \) and \( s \) are parallel and the angles are corresponding angles (or alternate interior angles, depending on the diagram context), their measures are equal. Therefore, we can set up the equation:
\[ 2x + 7 = 3x - 10 \]
Now, solve for \( x \):
1. Subtract \( 2x \) from both sides:
\[ 7 = x - 10 \]
2. Add 10 to both sides:
\[ 17 = x \]
Thus, the value of \( x \) is 17.
The correct answer is:
D. \( x = 17 \)
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