What Value Of $x$ Makes The Following Equation True?$\frac{x+6}{2}=9$A. 1 B. 5 C. 12 D. 24

Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics that involves finding the value of a variable that makes an equation true. In this article, we will focus on solving a simple linear equation involving a variable $x$. The equation is given as $\frac{x+6}{2}=9$. Our goal is to find the value of $x$ that makes this equation true.

Understanding the Equation

The given equation is a linear equation, which means it is an equation in which the highest power of the variable is 1. In this case, the variable is $x$, and the equation is $\frac{x+6}{2}=9$. To solve for $x$, we need to isolate the variable on one side of the equation.

Isolating the Variable

To isolate the variable $x$, we can start by multiplying both sides of the equation by 2. This will eliminate the fraction and make it easier to solve for $x$. The equation becomes:

$$x+6=18$$

Solving for $x$

Now that we have eliminated the fraction, we can solve for $x$ by subtracting 6 from both sides of the equation. This will give us the value of $x$ that makes the equation true.

$$x=18-6$$

$$x=12$$

Conclusion

In this article, we have solved a simple linear equation involving a variable $x$. The equation was $\frac{x+6}{2}=9$, and we found that the value of $x$ that makes this equation true is $x=12$. This is a fundamental concept in mathematics that is used to solve a wide range of problems.

Importance of Solving Linear Equations

Solving linear equations is an essential skill in mathematics that has numerous applications in real-life situations. It is used in a wide range of fields, including science, engineering, economics, and finance. In science, linear equations are used to model the behavior of physical systems, while in engineering, they are used to design and optimize systems. In economics and finance, linear equations are used to model the behavior of economic systems and make predictions about future trends.

Real-World Applications of Solving Linear Equations

Solving linear equations has numerous real-world applications. In science, linear equations are used to model the behavior of physical systems, such as the motion of objects under the influence of gravity or the flow of fluids through pipes. In engineering, linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits. In economics and finance, linear equations are used to model the behavior of economic systems and make predictions about future trends.

Tips for Solving Linear Equations

Solving linear equations can be a challenging task, but with practice and patience, it can become second nature. Here are some tips for solving linear equations:

• Read the equation carefully: Before starting to solve the equation, read it carefully to make sure you understand what is being asked.
• Use inverse operations: To solve for the variable, use inverse operations to isolate the variable on one side of the equation.
• Check your work: Once you have solved the equation, check your work by plugging the solution back into the original equation.
• Practice, practice, practice: The more you practice solving linear equations, the more comfortable you will become with the process.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that has numerous applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease and confidence. Remember to read the equation carefully, use inverse operations, check your work, and practice, practice, practice. With practice and patience, you will become proficient in solving linear equations and be able to apply this skill to a wide range of problems.

Final Answer

The final answer is $\boxed{12}$.

Introduction

Solving linear equations is a fundamental concept in mathematics that has numerous applications in real-life situations. In our previous article, we discussed how to solve a simple linear equation involving a variable $x$. In this article, we will answer some frequently asked questions (FAQs) 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 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 on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

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. Quadratic equations are more complex and require more advanced algebraic techniques to solve.

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

A: Yes, you can use a calculator to solve linear equations. However, it is always a good idea to check 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, plug the solution back into the original equation and make sure it is true. If the solution is not true, you need to go back and recheck your work.

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

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

• Not reading the equation carefully: Make sure you understand what is being asked before starting to solve the equation.
• Not using inverse operations: Use inverse operations to isolate the variable on one side of the equation.
• Not checking your work: Always check your work by plugging the solution back into the original equation.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through a series of problems, either on your own or with the help of a tutor or teacher. You can also use online resources, such as worksheets and practice tests, to help you practice.

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

A: Solving linear equations has numerous real-world applications, including:

• Science: Linear equations are used to model the behavior of physical systems, such as the motion of objects under the influence of gravity or the flow of fluids through pipes.
• Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
• Economics and finance: Linear equations are used to model the behavior of economic systems and make predictions about future trends.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that has numerous applications in real-life situations. By following the steps outlined in this article, you can answer frequently asked questions about solving linear equations and become proficient in solving these types of equations.

Final Answer

The final answer is $\boxed{12}$.