Evaluate the rational expression for the given values of the variables. 6y+11 2y-z 6y + 11 2y-z for y = 4, z = 1 (Type an integer or a simplified fraction.) EEE
Evaluate the rational expression for the given values of the variables. 6y+11 2y-z 6y + 11 2y-z for y = 4, z = 1 (Type an integer or a simplified fraction.) EEE
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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Question
![### Evaluating Rational Expressions
**Problem Statement**
Evaluate the rational expression for the given values of the variables:
\[
\frac{6y + 11}{2y - z}
\]
Given: \( y = 4 \), \( z = 1 \)
**Solution**
To solve the expression \(\frac{6y + 11}{2y - z}\) when \( y = 4 \) and \( z = 1 \), substitute the values into the expression:
1. Substitute \( y = 4 \) and \( z = 1 \) into the expression:
\[
\frac{6(4) + 11}{2(4) - 1}
\]
2. Simplify the numerator:
\[
6 \times 4 + 11 = 24 + 11 = 35
\]
3. Simplify the denominator:
\[
2 \times 4 - 1 = 8 - 1 = 7
\]
4. Calculate the expression:
\[
\frac{35}{7} = 5
\]
The value of the expression is 5.
**Interactive Component**
Enter the evaluated expression: \(\frac{6y + 11}{2y - z} = \Box\)
*(Type an integer or a simplified fraction.)*
This exercise helps to understand how to evaluate rational expressions by substituting the given values and simplifying the expression step by step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19772496-b599-484e-9a18-05f191d4af79%2Fbd62be06-002b-480d-a356-aee1c50f3a62%2Fhbfj1u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Rational Expressions
**Problem Statement**
Evaluate the rational expression for the given values of the variables:
\[
\frac{6y + 11}{2y - z}
\]
Given: \( y = 4 \), \( z = 1 \)
**Solution**
To solve the expression \(\frac{6y + 11}{2y - z}\) when \( y = 4 \) and \( z = 1 \), substitute the values into the expression:
1. Substitute \( y = 4 \) and \( z = 1 \) into the expression:
\[
\frac{6(4) + 11}{2(4) - 1}
\]
2. Simplify the numerator:
\[
6 \times 4 + 11 = 24 + 11 = 35
\]
3. Simplify the denominator:
\[
2 \times 4 - 1 = 8 - 1 = 7
\]
4. Calculate the expression:
\[
\frac{35}{7} = 5
\]
The value of the expression is 5.
**Interactive Component**
Enter the evaluated expression: \(\frac{6y + 11}{2y - z} = \Box\)
*(Type an integer or a simplified fraction.)*
This exercise helps to understand how to evaluate rational expressions by substituting the given values and simplifying the expression step by step.
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