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
![**Objective:** Translate the equation into a verbal sentence and solve it.
**Equation:** \(5(x - y) = 3y + 12\)
**Verbal Sentence:** Five times the difference between \(x\) and \(y\) is equal to three times \(y\) plus twelve.
**Solution:**
1. Distribute the 5:
\[
5x - 5y = 3y + 12
\]
2. Add \(5y\) to both sides:
\[
5x = 8y + 12
\]
3. Solve for \(x\) in terms of \(y\):
\[
x = \frac{8y + 12}{5}
\]
Here, we have expressed \(x\) in terms of \(y\). Additional steps can involve specific values or conditions given for either variable to find their respective solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb74725b5-bc4f-4bb1-afd9-bc707d803ac2%2F63fc1832-2ae4-471e-b766-207625447ce8%2Fvfv5w8p.jpeg&w=3840&q=75)
Transcribed Image Text:**Objective:** Translate the equation into a verbal sentence and solve it.
**Equation:** \(5(x - y) = 3y + 12\)
**Verbal Sentence:** Five times the difference between \(x\) and \(y\) is equal to three times \(y\) plus twelve.
**Solution:**
1. Distribute the 5:
\[
5x - 5y = 3y + 12
\]
2. Add \(5y\) to both sides:
\[
5x = 8y + 12
\]
3. Solve for \(x\) in terms of \(y\):
\[
x = \frac{8y + 12}{5}
\]
Here, we have expressed \(x\) in terms of \(y\). Additional steps can involve specific values or conditions given for either variable to find their respective solutions.
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