### Solving Linear Equations#### Problem StatementSolve 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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Solve the equation and check your answer 0.15t + 0.85(10 -t) = 0.89(10)

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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Concept explainers

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.

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