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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![### Algebraic Inequality Problem
**Problem Statement:**
Solve for \( y \):
\[ 5(y - 2) + 1 \leq 7y + 8 \]
**Solution:**
1. First, distribute the 5 on the left-hand side:
\[ 5y - 10 + 1 \leq 7y + 8 \]
2. Combine like terms on the left-hand side:
\[ 5y - 9 \leq 7y + 8 \]
3. Subtract 7y from both sides to get all y terms on one side:
\[ 5y - 7y - 9 \leq 8 \]
4. This simplifies to:
\[ -2y - 9 \leq 8 \]
5. Add 9 to both sides to isolate the y term:
\[ -2y \leq 17 \]
6. Finally, divide by -2, remembering to reverse the inequality sign because we are dividing by a negative number:
\[ y \geq -\frac{17}{2} \]
**Answer:**
\[ y \geq -\frac{17}{2} \]
This inequality indicates that the values of \( y \) must be greater than or equal to \( -\frac{17}{2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1b1525-9f55-427c-9418-433680b9f4b9%2F1e6bb0ec-efe2-4b16-9940-edec6cc77ef1%2F3uvoi2v_processed.png&w=3840&q=75)
Transcribed Image Text:### Algebraic Inequality Problem
**Problem Statement:**
Solve for \( y \):
\[ 5(y - 2) + 1 \leq 7y + 8 \]
**Solution:**
1. First, distribute the 5 on the left-hand side:
\[ 5y - 10 + 1 \leq 7y + 8 \]
2. Combine like terms on the left-hand side:
\[ 5y - 9 \leq 7y + 8 \]
3. Subtract 7y from both sides to get all y terms on one side:
\[ 5y - 7y - 9 \leq 8 \]
4. This simplifies to:
\[ -2y - 9 \leq 8 \]
5. Add 9 to both sides to isolate the y term:
\[ -2y \leq 17 \]
6. Finally, divide by -2, remembering to reverse the inequality sign because we are dividing by a negative number:
\[ y \geq -\frac{17}{2} \]
**Answer:**
\[ y \geq -\frac{17}{2} \]
This inequality indicates that the values of \( y \) must be greater than or equal to \( -\frac{17}{2} \).
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