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.
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![### Solving Linear Equations
#### Problem Statement
Solve the equation and check your answer:
\[ 0.15t + 0.85(10 - t) = 0.89(10) \]
#### Instructions
- **Step-by-Step Solution:**
1. Distribute the 0.85 on the left-hand side of the equation:
\[ 0.15t + 0.85 \cdot 10 - 0.85t = 0.89 \cdot 10 \]
2. Simplify the equation by combining like terms:
\[ 0.15t + 8.5 - 0.85t = 8.9 \]
3. Combine the terms involving \( t \):
\[ (0.15t - 0.85t) + 8.5 = 8.9 \]
\[ -0.7t + 8.5 = 8.9 \]
4. Isolate \( t \) by subtracting 8.5 from both sides:
\[ -0.7t = 0.4 \]
5. Solve for \( t \) by dividing by -0.7:
\[ t = \frac{0.4}{-0.7} \]
\[ t = -\frac{4}{7} \]
- **Conclusion:**
\[ \text{The solution is } t = -\frac{4}{7}. \]
(Type an integer or a fraction.)
#### Tips for Solving Equations
- Distribute multiplication over addition or subtraction.
- Combine like terms to simplify the equations.
- Perform the same operations on both sides to maintain the equality.
- Isolate the variable by using inverse operations (addition/subtraction, multiplication/division).
### Additional Resources
- **Practice Problems**: Solve similar equations to enhance your understanding.
- **Video Tutorials**: Watch step-by-step solutions for linear equations.
**Note**: This explanation is designed to help students understand and solve similar linear equations systematically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7bd99ef-7092-4177-9c19-951c55d49391%2F38a05690-1ab1-4b44-b86e-ba94f426d9d8%2Fd0gib7p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Linear Equations
#### Problem Statement
Solve the equation and check your answer:
\[ 0.15t + 0.85(10 - t) = 0.89(10) \]
#### Instructions
- **Step-by-Step Solution:**
1. Distribute the 0.85 on the left-hand side of the equation:
\[ 0.15t + 0.85 \cdot 10 - 0.85t = 0.89 \cdot 10 \]
2. Simplify the equation by combining like terms:
\[ 0.15t + 8.5 - 0.85t = 8.9 \]
3. Combine the terms involving \( t \):
\[ (0.15t - 0.85t) + 8.5 = 8.9 \]
\[ -0.7t + 8.5 = 8.9 \]
4. Isolate \( t \) by subtracting 8.5 from both sides:
\[ -0.7t = 0.4 \]
5. Solve for \( t \) by dividing by -0.7:
\[ t = \frac{0.4}{-0.7} \]
\[ t = -\frac{4}{7} \]
- **Conclusion:**
\[ \text{The solution is } t = -\frac{4}{7}. \]
(Type an integer or a fraction.)
#### Tips for Solving Equations
- Distribute multiplication over addition or subtraction.
- Combine like terms to simplify the equations.
- Perform the same operations on both sides to maintain the equality.
- Isolate the variable by using inverse operations (addition/subtraction, multiplication/division).
### Additional Resources
- **Practice Problems**: Solve similar equations to enhance your understanding.
- **Video Tutorials**: Watch step-by-step solutions for linear equations.
**Note**: This explanation is designed to help students understand and solve similar linear equations systematically.
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