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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Solve the Literal Equation**
**Problem Statement:**
Solve the literal equation \( cy + 4 = d - 9y \) for \( y \).
**Solution Format:**
\( y = \) [Answer Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06b145d7-43b7-4957-a124-06d6435c3e80%2F5ed2a92e-f6f2-4e31-8775-7c09ffddc0f5%2F0ia9iak_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the Literal Equation**
**Problem Statement:**
Solve the literal equation \( cy + 4 = d - 9y \) for \( y \).
**Solution Format:**
\( y = \) [Answer Box]
![**Educational Content: Solving Literal Equations**
In this lesson, we'll explore how to solve the literal equation for a specified variable.
**Problem Statement:**
Solve the literal equation \(cy + 4 = d - 9y\) for \(y\).
**Steps to Solve the Equation:**
1. **Combine like terms:** Move all terms involving \(y\) to one side of the equation.
- Add \(9y\) to both sides to isolate \(y\) terms on the left:
\[
cy + 9y + 4 = d
\]
2. **Factor out \(y\) from the terms on the left side:**
- Combine the \(y\) terms:
\[
(c + 9)y + 4 = d
\]
3. **Isolate \(y\):**
- Subtract 4 from both sides:
\[
(c + 9)y = d - 4
\]
4. **Solve for \(y\):**
- Divide both sides by \((c + 9)\):
\[
y = \frac{d - 4}{c + 9}
\]
By following these steps, you can solve the equation for \(y\) in terms of \(c\) and \(d\). This technique is useful for understanding how different variables relate to each other in algebraic expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06b145d7-43b7-4957-a124-06d6435c3e80%2F5ed2a92e-f6f2-4e31-8775-7c09ffddc0f5%2F2jh4vb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Solving Literal Equations**
In this lesson, we'll explore how to solve the literal equation for a specified variable.
**Problem Statement:**
Solve the literal equation \(cy + 4 = d - 9y\) for \(y\).
**Steps to Solve the Equation:**
1. **Combine like terms:** Move all terms involving \(y\) to one side of the equation.
- Add \(9y\) to both sides to isolate \(y\) terms on the left:
\[
cy + 9y + 4 = d
\]
2. **Factor out \(y\) from the terms on the left side:**
- Combine the \(y\) terms:
\[
(c + 9)y + 4 = d
\]
3. **Isolate \(y\):**
- Subtract 4 from both sides:
\[
(c + 9)y = d - 4
\]
4. **Solve for \(y\):**
- Divide both sides by \((c + 9)\):
\[
y = \frac{d - 4}{c + 9}
\]
By following these steps, you can solve the equation for \(y\) in terms of \(c\) and \(d\). This technique is useful for understanding how different variables relate to each other in algebraic expressions.
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