Solve The Equation: 14 + 9 M = − 13 14 + 9m = -13 14 + 9 M = − 13

Mar 10, 2025 by ADMIN 66 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 and professionals alike. In this article, we will focus on solving a simple linear equation, $14 + 9m = -13$ . We will break down the solution into manageable steps, making it easy to understand and follow.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation and graphical representation.

The Equation to be Solved

The equation we will be solving is $14 + 9m = -13$ . This is a simple linear equation with one variable, $m$ . Our goal is to isolate the variable $m$ and find its value.

Step 1: Subtract 14 from Both Sides

To solve for $m$ , we need to isolate it on one side of the equation. The first step is to subtract 14 from both sides of the equation. This will help us get rid of the constant term on the left-hand side.

14 + 9m = -13
9m = -13 - 14
9m = -27

Step 2: Divide Both Sides by 9

Now that we have $9m = -27$ , we can divide both sides of the equation by 9 to solve for $m$ . This will give us the value of $m$ .

9m = -27
m = -27 / 9
m = -3

The Solution

We have now solved the equation $14 + 9m = -13$ . The value of $m$ is $-3$ . This means that when we substitute $m = -3$ into the original equation, it will be true.

Conclusion

Solving linear equations is an essential skill in mathematics. In this article, we solved the equation $14 + 9m = -13$ using simple algebraic manipulation. We broke down the solution into manageable steps, making it easy to understand and follow. By following these steps, you can solve any linear equation with one variable.

Real-World Applications

Linear equations have numerous real-world applications. For example, they can be used to model population growth, financial transactions, and physical systems. In engineering, linear equations are used to design and optimize systems, such as bridges and buildings. In economics, linear equations are used to model supply and demand curves.

Tips and Tricks

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

Always check your work by plugging the solution back into the original equation.
Use algebraic manipulation to simplify the equation before solving for the variable.
Use graphical representation to visualize the solution and check your work.
Practice, practice, practice! The more you practice solving linear equations, the more comfortable you will become with the process.

Common Mistakes

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

Not checking your work by plugging the solution back into the original equation.
Not using algebraic manipulation to simplify the equation before solving for the variable.
Not using graphical representation to visualize the solution and check your work.
Not practicing regularly to build your skills and confidence.

Conclusion

Introduction

In our previous article, we solved the equation $14 + 9m = -13$ using simple algebraic manipulation. In this article, we will answer some frequently asked questions about solving linear equations. Whether you are a student or a professional, this Q&A guide will help you understand the concepts and techniques involved in solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ 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 on one side of the equation. You can do this by using algebraic manipulation, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation $x + 2 = 5$ is a linear equation, while the equation $x^2 + 4x + 4 = 0$ is a quadratic equation.

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

A: To check your work, plug the solution back into the original equation. If the solution is true, then you have solved the equation correctly.

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

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

Not checking your work by plugging the solution back into the original equation.
Not using algebraic manipulation to simplify the equation before solving for the variable.
Not using graphical representation to visualize the solution and check your work.
Not practicing regularly to build your skills and confidence.

Q: How do I use graphical representation to solve a linear equation?

A: To use graphical representation to solve a linear equation, plot the equation on a coordinate plane and find the point of intersection between the two lines. This point represents the solution to the equation.

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

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

Modeling population growth
Financial transactions
Physical systems
Engineering design and optimization
Economics, such as supply and demand curves

Q: How do I practice solving linear equations?

A: To practice solving linear equations, try the following:

Start with simple equations and gradually move on to more complex ones.
Use online resources, such as worksheets and practice tests.
Work with a partner or join a study group to practice solving equations together.
Use real-world examples to apply the concepts and techniques learned.

Conclusion

Solving linear equations is a fundamental skill in mathematics. By following the steps outlined in this article and practicing regularly, you can become proficient in solving linear equations and apply them to real-world problems. Remember to check your work, use algebraic manipulation, and practice regularly to build your skills and confidence.

Additional Resources

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

Khan Academy: Linear Equations
Mathway: Linear Equations
Wolfram Alpha: Linear Equations
MIT OpenCourseWare: Linear Algebra

Final Tips

Practice regularly to build your skills and confidence.
Use algebraic manipulation to simplify the equation before solving for the variable.
Use graphical representation to visualize the solution and check your work.
Check your work by plugging the solution back into the original equation.

By following these tips and practicing regularly, you will become proficient in solving linear equations and be able to apply them to real-world problems.