Solve The Equation:${ \begin{array}{l} x - 21 = 6 \ x = \ \end{array} }$

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, step by step, to help you understand the concept better. We will use the equation $x - 21 = 6$ as an example and guide you through the process of solving it.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It is a simple equation that can be solved using basic algebraic operations. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

The Equation to be Solved

The equation we will be solving is $x - 21 = 6$. This is a simple linear equation, and we will use the following steps to solve it.

Step 1: Add 21 to Both Sides of the Equation

To solve the equation, we need to isolate the variable $x$. We can do this by adding 21 to both sides of the equation. This will eliminate the negative term on the left side of the equation.

x - 21 + 21 = 6 + 21

By adding 21 to both sides of the equation, we get:

x = 27

Step 2: Simplify the Equation

Now that we have added 21 to both sides of the equation, we can simplify the equation by combining like terms.

x = 27

This is the simplified equation, and we can see that the variable $x$ is equal to 27.

Step 3: Check the Solution

To make sure that our solution is correct, we can plug it back into the original equation and check if it is true.

x - 21 = 6
27 - 21 = 6
6 = 6

As we can see, the solution $x = 27$ satisfies the original equation, and we can be confident that it is the correct solution.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. In this article, we have used the equation $x - 21 = 6$ as an example and guided you through the process of solving it. We have shown you how to add 21 to both sides of the equation, simplify the equation, and check the solution. By following these steps, you can solve linear equations with ease.

Tips and Tricks

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

• Make sure to add or subtract the same value from both sides of the equation.
• Use inverse operations to eliminate the variable.
• Check the solution by plugging it back into the original equation.
• Use a calculator or a computer program to check your solution.

Common Mistakes

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

• Adding or subtracting the wrong value from both sides of the equation.
• Not using inverse operations to eliminate the variable.
• Not checking the solution by plugging it back into the original equation.
• Not using a calculator or a computer program to check your solution.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems.
• Computer Science: Linear equations are used to solve problems in computer science.

Conclusion

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Introduction

In our previous article, we discussed how to solve linear equations step by step. 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 concept of solving linear equations better.

Q: What is a linear equation?

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

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by adding or subtracting the same value from both sides of the equation. You can also use inverse operations to eliminate the variable.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation x - 21 = 6 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I check if my solution is correct?

A: To check if your solution is correct, you need to plug it back into the original equation and see if it is true. If the solution satisfies the original equation, then it is the correct solution.

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

A: Some common mistakes to avoid when solving linear equations include adding or subtracting the wrong value from both sides of the equation, not using inverse operations to eliminate the variable, and not checking the solution by plugging it back into the original equation.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to identify the operation that was used to create the equation and then use the inverse operation to eliminate the variable. For example, if the equation is 2x + 3 = 5, you can use the inverse operation of subtraction to eliminate the constant term.

Q: Can I use a calculator or a computer program to solve linear equations?

A: Yes, you can use a calculator or a computer program to solve linear equations. In fact, using a calculator or a computer program can be a great way to check your solution and ensure that it is correct.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to a wide range of real-world problems, including physics, engineering, economics, and computer science. For example, you can use linear equations to model the motion of objects, design and optimize systems, and solve problems in computer science.

Q: What are some examples of linear equations in real-world problems?

A: Some examples of linear equations in real-world problems include:

• Modeling the motion of objects in physics
• Designing and optimizing systems in engineering
• Solving problems in computer science
• Modeling economic systems in economics

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. In this Q&A guide, we have answered some frequently asked questions about solving linear equations. Whether you are a student or a professional, this guide will help you understand the concept of solving linear equations better.

Tips and Tricks

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

• Make sure to add or subtract the same value from both sides of the equation.
• Use inverse operations to eliminate the variable.
• Check the solution by plugging it back into the original equation.
• Use a calculator or a computer program to check your solution.

Common Mistakes

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

• Adding or subtracting the wrong value from both sides of the equation.
• Not using inverse operations to eliminate the variable.
• Not checking the solution by plugging it back into the original equation.
• Not using a calculator or a computer program to check your solution.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems.
• Computer Science: Linear equations are used to solve problems in computer science.