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
Related questions
Question
![**Exercise: Solve for x**
**Diagram Explanation:**
The diagram represents an angle bisector. The line segment \(\overline{AB}\) acts as an angle bisector, meaning it divides the angle into two equal parts.
- The angle ∠A on the left is split into two parts:
- The top part of the angle is labeled \((5x + 9)^\circ\).
- The bottom part of the angle is labeled \((7x - 5)^\circ\).
Given information:
- \(\overline{AB}\) is an angle bisector.
Since \(\overline{AB}\) is an angle bisector, the two angles are equal. Therefore, we can set up the following equation to solve for \(x\):
\[5x + 9 = 7x - 5\]
To solve this equation:
1. Subtract \(5x\) from both sides:
\[9 = 2x - 5\]
2. Add 5 to both sides:
\[14 = 2x\]
3. Divide by 2:
\[x = 7\]
So, the value of \( x \) is \( 7 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20047395-754f-4b4f-b55f-051358973abe%2Fd15cfa81-4531-4754-91c4-fe693c8f3c98%2Fvlidyo3.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise: Solve for x**
**Diagram Explanation:**
The diagram represents an angle bisector. The line segment \(\overline{AB}\) acts as an angle bisector, meaning it divides the angle into two equal parts.
- The angle ∠A on the left is split into two parts:
- The top part of the angle is labeled \((5x + 9)^\circ\).
- The bottom part of the angle is labeled \((7x - 5)^\circ\).
Given information:
- \(\overline{AB}\) is an angle bisector.
Since \(\overline{AB}\) is an angle bisector, the two angles are equal. Therefore, we can set up the following equation to solve for \(x\):
\[5x + 9 = 7x - 5\]
To solve this equation:
1. Subtract \(5x\) from both sides:
\[9 = 2x - 5\]
2. Add 5 to both sides:
\[14 = 2x\]
3. Divide by 2:
\[x = 7\]
So, the value of \( x \) is \( 7 \).
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