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Mar 11, 2025 by ADMIN 117 views

**Solving Linear Equations: A Step-by-Step Guide**

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, and we will provide a step-by-step guide on how to do it.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, r) is 1. It is a simple equation that can be solved using basic algebraic operations.

The Equation

The equation we will be solving is:

4r + 6 = 38

Step 1: Subtract 6 from Both Sides

To solve for r, we need to isolate the variable on one side of the equation. The first step is to subtract 6 from both sides of the equation.

4r + 6 - 6 = 38 - 6

This simplifies to:

4r = 32

Step 2: Divide Both Sides by 4

Now that we have 4r on one side of the equation, we can divide both sides by 4 to solve for r.

(4r) / 4 = 32 / 4

This simplifies to:

r = 8

Conclusion

In this article, we have solved a simple linear equation using basic algebraic operations. We have shown that by following a step-by-step guide, we can easily solve for the variable r. This skill is essential for students to master, as it will help them to solve a wide range of mathematical problems.

Real-World Applications

Solving linear equations has many real-world applications. For example, in finance, linear equations can be used to calculate interest rates, investment returns, and other financial metrics. In science, linear equations can be used to model population growth, chemical reactions, and other phenomena.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

Always follow the order of operations (PEMDAS)
Use inverse operations to isolate the variable
Check your work by plugging the solution back into the original equation

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

Not following the order of operations
Not using inverse operations to isolate the variable
Not checking your work by plugging the solution back into the original equation

Conclusion

Solving linear equations is a fundamental skill that is essential for students to master. By following a step-by-step guide and using basic algebraic operations, we can easily solve for the variable r. This skill has many real-world applications and is a crucial part of mathematics.

Final Answer

The final answer is: 8

Additional Resources

For more information on solving linear equations, check out the following resources:

Khan Academy: Solving Linear Equations
Mathway: Solving Linear Equations
Wolfram Alpha: Solving Linear Equations

References

"Algebra and Trigonometry" by Michael Sullivan
"Mathematics for the Nonmathematician" by Morris Kline
"The Art of Problem Solving" by Richard Rusczyk
Solving Linear Equations: A Q&A Guide =====================================

Introduction

In our previous article, we provided a step-by-step guide on how to solve a simple linear equation. In this article, we will answer some of the most frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, r) is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

The highest power of the variable is 1
The equation is in the form ax + b = c, where a, b, and c are constants
The equation can be solved using basic algebraic operations

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

Simple linear equations: ax + b = c
Linear equations with fractions: ax/b + c = d
Linear equations with decimals: ax.5 + b = c

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

Multiply both sides of the equation by the least common multiple (LCM) of the denominators
Simplify the equation
Solve for the variable

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, follow these steps:

Multiply both sides of the equation by 10 to eliminate the decimal
Simplify the equation
Solve for the variable

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

Not following the order of operations (PEMDAS)
Not using inverse operations to isolate the variable
Not checking your work by plugging the solution back into the original equation

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, follow these steps:

Plug the solution back into the original equation
Simplify the equation
Verify that the solution is true

Q: What are some real-world applications of linear equations?

A: Some real-world applications of linear equations include:

Finance: calculating interest rates, investment returns, and other financial metrics
Science: modeling population growth, chemical reactions, and other phenomena
Engineering: designing and building structures, such as bridges and buildings

Q: How can I practice solving linear equations?

A: There are many resources available to help you practice solving linear equations, including:

Online practice problems and quizzes
Math textbooks and workbooks
Online math courses and tutorials

Conclusion

Final Answer

The final answer is: 8

Additional Resources

For more information on solving linear equations, check out the following resources:

Khan Academy: Solving Linear Equations
Mathway: Solving Linear Equations
Wolfram Alpha: Solving Linear Equations

References

"Algebra and Trigonometry" by Michael Sullivan
"Mathematics for the Nonmathematician" by Morris Kline
"The Art of Problem Solving" by Richard Rusczyk