W is between X and Y on XY. WX = x + 10, WY = x-6, and XY = 10. Which of the following equations could be used to find the value of x? O x-6=10 O x + 10 = 10 O(x+10) + (x - 6) = 10
W is between X and Y on XY. WX = x + 10, WY = x-6, and XY = 10. Which of the following equations could be used to find the value of x? O x-6=10 O x + 10 = 10 O(x+10) + (x - 6) = 10
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Understanding Equations in Geometry
**Question:**
W is between X and Y on line segment \( XY \). The lengths of the segments are given as follows:
- \( WX = x + 10 \)
- \( WY = x - 6 \)
- \( XY = 10 \)
Which of the following equations could be used to find the value of \( x \)?
**Options:**
1. \( x - 6 = 10 \)
2. \( x + 10 = 10 \)
3. \( (x + 10) + (x - 6) = 10 \)
**Explanation:**
To solve this problem, we need to understand that the sum of segments \( WX \) and \( WY \) should be equal to the length of \( XY \):
\[ WX + WY = XY \]
Given the values:
\[ WX = x + 10 \]
\[ WY = x - 6 \]
\[ XY = 10 \]
By substituting these values into the equation, we get:
\[ (x + 10) + (x - 6) = 10 \]
From this, we can see that the correct option is:
\[ (x + 10) + (x - 6) = 10 \]
So, option 3 is correct.
**Diagram Explanation:**
The problem does not include a diagram, but you can visualize it as follows:
1. Imagine a straight line segment \( XY \), where \( W \) is some point between \( X \) and \( Y \).
2. The length from \( X \) to \( W \) is represented as \( WX = x + 10 \).
3. The length from \( W \) to \( Y \) is represented as \( WY = x - 6 \).
4. The total length of the line segment from \( X \) to \( Y \) is \( XY = 10 \).
Thus, you need to sum up the individual lengths of segments \( WX \) and \( WY \) to equal the total length \( XY \).
Therefore, the equation that can be used to find the value of \( x \) is:
\[ (x + 10) + (x - 6) = 10 \]
This type of problem helps to understand how equations can be formed and solved based on geometric concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdba27eaf-9f49-41ba-9572-cf4a0c1baf7b%2F7fcffc25-333d-4b16-a444-d4f1a19063c0%2Ftrle71s_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Equations in Geometry
**Question:**
W is between X and Y on line segment \( XY \). The lengths of the segments are given as follows:
- \( WX = x + 10 \)
- \( WY = x - 6 \)
- \( XY = 10 \)
Which of the following equations could be used to find the value of \( x \)?
**Options:**
1. \( x - 6 = 10 \)
2. \( x + 10 = 10 \)
3. \( (x + 10) + (x - 6) = 10 \)
**Explanation:**
To solve this problem, we need to understand that the sum of segments \( WX \) and \( WY \) should be equal to the length of \( XY \):
\[ WX + WY = XY \]
Given the values:
\[ WX = x + 10 \]
\[ WY = x - 6 \]
\[ XY = 10 \]
By substituting these values into the equation, we get:
\[ (x + 10) + (x - 6) = 10 \]
From this, we can see that the correct option is:
\[ (x + 10) + (x - 6) = 10 \]
So, option 3 is correct.
**Diagram Explanation:**
The problem does not include a diagram, but you can visualize it as follows:
1. Imagine a straight line segment \( XY \), where \( W \) is some point between \( X \) and \( Y \).
2. The length from \( X \) to \( W \) is represented as \( WX = x + 10 \).
3. The length from \( W \) to \( Y \) is represented as \( WY = x - 6 \).
4. The total length of the line segment from \( X \) to \( Y \) is \( XY = 10 \).
Thus, you need to sum up the individual lengths of segments \( WX \) and \( WY \) to equal the total length \( XY \).
Therefore, the equation that can be used to find the value of \( x \) is:
\[ (x + 10) + (x - 6) = 10 \]
This type of problem helps to understand how equations can be formed and solved based on geometric concepts.
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