Solve The Equation:${ 1.25 = 0.75 + R }$Find { R $}$: ${ R = }$

Mar 11, 2025 by ADMIN 67 views

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

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, and we will use the equation $1.25 = 0.75 + r$ as an example. We will break down the solution step by step, and we will provide a clear and concise explanation of each step.

Understanding the Equation

The equation $1.25 = 0.75 + r$ is a linear equation, which means that it can be written in the form $ax = b$ , where $a$ and $b$ are constants, and $x$ is the variable. In this case, the equation can be rewritten as $1.25 - 0.75 = r$ , which simplifies to $0.5 = r$ .

Solving the Equation

To solve the equation, we need to isolate the variable $r$ . We can do this by subtracting $0.75$ from both sides of the equation. This will give us $1.25 - 0.75 = r$ , which simplifies to $0.5 = r$ .

Checking the Solution

To check our solution, we can plug it back into the original equation. If our solution is correct, then the equation should be true. In this case, we can plug in $r = 0.5$ and check that the equation is true.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, we can solve even the most complex linear equations. Remember to always check your solution by plugging it back into the original equation.

Tips and Tricks

Always read the equation carefully and make sure you understand what it is asking for.
Use algebraic manipulations to isolate the variable.
Check your solution by plugging it back into the original equation.

Real-World Applications

Linear equations have many real-world applications, including:

Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.

Common Mistakes

Failing to read the equation carefully and understand what it is asking for.
Not using algebraic manipulations to isolate the variable.
Not checking the solution by plugging it back into the original equation.

Conclusion

Final Thoughts

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. By following the steps outlined in this article, we can solve even the most complex linear equations. Remember to always check your solution by plugging it back into the original equation.

References

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will provide a Q&A guide to help you understand and solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form ax = b, where a and b are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my solution?

A: To check your solution, plug it back into the original equation and make sure it is true. If your solution is correct, then the equation should be true.

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

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

Failing to read the equation carefully and understand what it is asking for.
Not using algebraic manipulations to isolate the variable.
Not checking the solution by plugging it back into the original equation.

Q: How do I use algebraic manipulations to solve linear equations?

A: Algebraic manipulations are a set of rules that allow you to simplify and solve linear equations. Some common algebraic manipulations include:

Adding or subtracting the same value to both sides of the equation.
Multiplying or dividing both sides of the equation by the same value.
Using inverse operations to isolate the variable.

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

A: Linear equations have many real-world applications, including:

Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.

Q: How do I use technology to solve linear equations?

A: Technology can be a powerful tool for solving linear equations. Some common tools include:

Graphing calculators: These can be used to graph linear equations and find their solutions.
Computer algebra systems: These can be used to solve linear equations and other mathematical problems.
Online resources: There are many online resources available that can help you solve linear equations, including video tutorials and practice problems.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve even the most complex linear equations. Remember to always check your solution by plugging it back into the original equation.