the value of x? 2х+7 3х-10 A. x= -17 B. 17 X = С. x = 15 D. x = 17

Algebra and Trigonometry (6th Edition)
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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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### 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. \( x = 17 \)
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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