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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![**Educational Website Content:**
### Algebraic Problem Solving
**Problem Statement:**
If \(\frac{2}{a - 1} = \frac{4}{y}\), and \(y \neq 0\) where \(a \neq 1\), what is \(y\) in terms of \(a\)?
A) \( y = 2a - 2 \)
B) \( y = 2a - 4 \)
C) \( y = 2a - \frac{1}{2} \)
D) \( y = \frac{1}{2}a + 1 \)
**Solution Steps:**
1. **Start with the given equation:**
\[
\frac{2}{a - 1} = \frac{4}{y}
\]
2. **Cross-multiply to solve for \(y\):**
\[
2y = 4(a - 1)
\]
3. **Simplify the equation:**
\[
2y = 4a - 4
\]
4. **Divide both sides by 2:**
\[
y = 2a - 2
\]
Thus, the correct answer is:
**A) \( y = 2a - 2 \)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a5b84fb-7138-4ebc-98eb-ad578bc5cf6d%2F073186e1-28f2-43f0-9a5a-926b2ea49d5f%2Fz0sztwt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content:**
### Algebraic Problem Solving
**Problem Statement:**
If \(\frac{2}{a - 1} = \frac{4}{y}\), and \(y \neq 0\) where \(a \neq 1\), what is \(y\) in terms of \(a\)?
A) \( y = 2a - 2 \)
B) \( y = 2a - 4 \)
C) \( y = 2a - \frac{1}{2} \)
D) \( y = \frac{1}{2}a + 1 \)
**Solution Steps:**
1. **Start with the given equation:**
\[
\frac{2}{a - 1} = \frac{4}{y}
\]
2. **Cross-multiply to solve for \(y\):**
\[
2y = 4(a - 1)
\]
3. **Simplify the equation:**
\[
2y = 4a - 4
\]
4. **Divide both sides by 2:**
\[
y = 2a - 2
\]
Thus, the correct answer is:
**A) \( y = 2a - 2 \)**
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