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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![### Solve the Equation
Given equation: \((8 + y)(2y - 5) = 0\)
**Instruction:**
If there is more than one solution, separate them with commas.
#### Steps to Solve:
1. Since the equation is in factored form and equals zero, use the Zero Product Property, which states that if \(a \cdot b = 0\), then \(a = 0\) or \(b = 0\).
2. Set each factor equal to zero and solve for \(y\):
\[
8 + y = 0 \quad \text{or} \quad 2y - 5 = 0
\]
3. Solve each equation separately:
\[
8 + y = 0 \implies y = -8
\]
\[
2y - 5 = 0 \implies 2y = 5 \implies y = \frac{5}{2}
\]
4. Combine the solutions:
\[
y = -8, \frac{5}{2}
\]
### Final Answer
\(y = -8, \frac{5}{2}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cc5796-f97a-4aed-8678-3b416fd803c7%2F44911914-7d0c-4b42-91ea-176bb87b2961%2Fu25ht_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solve the Equation
Given equation: \((8 + y)(2y - 5) = 0\)
**Instruction:**
If there is more than one solution, separate them with commas.
#### Steps to Solve:
1. Since the equation is in factored form and equals zero, use the Zero Product Property, which states that if \(a \cdot b = 0\), then \(a = 0\) or \(b = 0\).
2. Set each factor equal to zero and solve for \(y\):
\[
8 + y = 0 \quad \text{or} \quad 2y - 5 = 0
\]
3. Solve each equation separately:
\[
8 + y = 0 \implies y = -8
\]
\[
2y - 5 = 0 \implies 2y = 5 \implies y = \frac{5}{2}
\]
4. Combine the solutions:
\[
y = -8, \frac{5}{2}
\]
### Final Answer
\(y = -8, \frac{5}{2}\)
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