Solve For \[$ X \$\]:$\[ 3x + 7 - 9 = 0 \\]

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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 of the form 3x + 7 - 9 = 0. We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

Understanding the Equation

The given equation is 3x + 7 - 9 = 0. To solve for x, we need to isolate the variable x on one side of the equation. The first step is to simplify the equation by combining like terms.

Simplifying the Equation

The equation 3x + 7 - 9 = 0 can be simplified by combining the constants 7 and -9. This gives us:

3x - 2 = 0

Isolating the Variable

Now that we have simplified the equation, we need to isolate the variable x. To do this, we can add 2 to both sides of the equation, which will eliminate the constant term.

3x - 2 + 2 = 0 + 2

This simplifies to:

3x = 2

Solving for x

Now that we have isolated the variable x, we can solve for its value. To do this, we can divide both sides of the equation by 3, which will give us the value of x.

3x / 3 = 2 / 3

This simplifies to:

x = 2/3

Conclusion

Solving linear equations is a straightforward process that requires careful attention to detail. By following the steps outlined in this article, readers should be able to solve simple linear equations like 3x + 7 - 9 = 0. Remember to simplify the equation, isolate the variable, and solve for its value.

Tips and Tricks

  • Always start by simplifying the equation to make it easier to solve.
  • Use inverse operations 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:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes to Avoid

  • Failing to simplify the equation before solving for x.
  • Not using inverse operations to isolate the variable.
  • Not checking the solution by plugging it back into the original equation.

Additional Resources

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

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

Final Thoughts

Solving linear equations is a fundamental skill that is essential for success in mathematics and many other fields. By following the steps outlined in this article, readers should be able to solve simple linear equations with ease. Remember to simplify the equation, isolate the variable, and solve for its value. With practice and patience, you will become a master of solving linear equations in no time!

Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and sometimes, it's helpful to have a refresher or to clarify any doubts. That's why we've put together this Q&A guide to help you tackle any questions you may have 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 (usually x) is 1. In other words, it's an equation that can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, but 2x and 3y are not.

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, 2x + 3 = 5 is a linear equation, while x^2 + 2x + 1 = 0 is a quadratic equation.

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

A: To solve a linear equation with fractions, you need to get rid of the fractions by multiplying both sides of the equation by the denominator. For example, if you have the equation 1/2x + 3 = 5, you can multiply both sides by 2 to get rid of the fraction.

Q: What is the inverse operation of addition?

A: The inverse operation of addition is subtraction. In other words, if you have an equation like x + 3 = 5, you can subtract 3 from both sides to get x = 2.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug it back into the original equation and see if it's true. For example, if you have the equation x + 2 = 5 and you think the solution is x = 3, you can plug x = 3 back into the equation to see if it's 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 simplify the equation before solving for x
  • Not using inverse operations to isolate the variable
  • Not checking the solution by plugging it back into the original equation
  • Making errors when multiplying or dividing both sides of the equation

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

A: To solve a linear equation with decimals, you can use the same steps as you would for solving a linear equation with fractions. For example, if you have the equation 0.5x + 3 = 5, you can multiply both sides by 2 to get rid of the decimal.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one variable, while a system of linear equations is a set of two or more equations with the same variables. For example, the equation x + 2 = 5 is a linear equation, while the system of equations x + 2 = 5 and 2x - 3 = 7 is a system of linear equations.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to find the values of the variables that satisfy all of the equations in the system. You can use substitution or elimination to solve a system of linear equations.

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

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

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through examples and exercises in a textbook or online resource. You can also try solving linear equations on your own by creating your own problems and solutions.

Q: What are some online resources for learning about linear equations?

A: Some online resources for learning about linear equations include:

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

Q: How can I get help if I'm struggling with linear equations?

A: If you're struggling with linear equations, you can try:

  • Asking a teacher or tutor for help
  • Working with a study group or classmate
  • Using online resources, such as video tutorials or practice problems
  • Seeking help from a math tutor or online tutor