Solve The Equation:${ -9x + 6 = -x + 4 }$Show Your Work.

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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 specific linear equation, step by step, to help readers understand the process and build their confidence in solving similar equations.

The Equation

The equation we will be solving is:

−9x+6=−x+4-9x + 6 = -x + 4

Step 1: Write Down the Equation

The first step in solving a linear equation is to write it down clearly. In this case, our equation is:

−9x+6=−x+4-9x + 6 = -x + 4

Step 2: Add or Subtract the Same Value to Both Sides

To isolate the variable (x), we need to get rid of the constant term on the same side as the variable. In this case, we can add 9x to both sides of the equation to get:

−9x+9x+6=−x+9x+4-9x + 9x + 6 = -x + 9x + 4

This simplifies to:

6=8x+46 = 8x + 4

Step 3: Subtract the Same Value from Both Sides

Now, we need to get rid of the constant term on the same side as the variable. We can subtract 4 from both sides of the equation to get:

6−4=8x+4−46 - 4 = 8x + 4 - 4

This simplifies to:

2=8x2 = 8x

Step 4: Divide Both Sides by the Coefficient

Finally, we need to isolate the variable by dividing both sides of the equation by the coefficient of the variable. In this case, we can divide both sides by 8 to get:

28=8x8\frac{2}{8} = \frac{8x}{8}

This simplifies to:

14=x\frac{1}{4} = x

Conclusion

In this article, we have solved a linear equation step by step, using basic algebraic operations. By following these steps, readers should be able to solve similar equations with confidence. Remember, solving linear equations is a crucial skill in mathematics, and practice is key to mastering it.

Tips and Tricks

  • Always write down the equation clearly before starting to solve it.
  • Use addition and subtraction to isolate the variable.
  • Use division to isolate the variable.
  • Check your answer by plugging it back into the original equation.

Real-World Applications

Linear equations have numerous 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

  • Not writing down the equation clearly before starting to solve it.
  • Not using addition and subtraction to isolate the variable.
  • Not using division to isolate the variable.
  • Not checking the answer by plugging it back into the original equation.

Solving Linear Equations: A Summary

Solving linear equations is a crucial skill in mathematics, and practice is key to mastering it. By following the steps outlined in this article, readers should be able to solve similar equations with confidence. Remember to always write down the equation clearly, use addition and subtraction to isolate the variable, use division to isolate the variable, and check your answer by plugging it back into the original equation.

Frequently Asked Questions

  • Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.
  • Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable by using addition and subtraction to get rid of the constant term on the same side as the variable, and then use division to isolate the variable.
  • Q: What are some real-world applications of linear equations? A: Linear equations have numerous real-world applications, including physics, engineering, and economics.

Conclusion

Introduction

In our previous article, we covered the basics of solving linear equations, including step-by-step instructions and real-world applications. However, we know that sometimes, the best way to learn is through asking questions and getting answers. In this article, we will provide a Q&A guide to help readers who are struggling with 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. For example, the equation 2x + 3 = 5 is a linear equation because the highest power of x is 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by using addition and subtraction to get rid of the constant term on the same side as the variable, and then use division to isolate the variable. For example, to solve the equation 2x + 3 = 5, you would first subtract 3 from both sides to get 2x = 2, and then divide both sides by 2 to get x = 1.

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

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

  • Not writing down the equation clearly before starting to solve it.
  • Not using addition and subtraction to isolate the variable.
  • Not using division to isolate the variable.
  • Not checking the answer by plugging it back into the original equation.

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

A: To check your answer when solving a linear equation, you need to plug the solution back into the original equation and make sure it is true. For example, if you solve the equation 2x + 3 = 5 and get x = 1, you would plug x = 1 back into the original equation to get 2(1) + 3 = 5, which is true.

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

A: Linear equations have numerous 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 do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms and eliminate any unnecessary variables. For example, the equation 2x + 3 + 2x - 2 = 5 can be simplified by combining the like terms 2x and 2x to get 4x + 1 = 5.

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

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

A: To solve a system of linear equations, you need to use substitution or elimination to find the values of the variables. For example, the system of equations x + y = 3 and 2x - 2y = -2 can be solved by using substitution to get x = 1 and y = 2.

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics, and practice is key to mastering it. By following the steps outlined in this article, readers should be able to solve similar equations with confidence. Remember to always write down the equation clearly, use addition and subtraction to isolate the variable, use division to isolate the variable, and check your answer by plugging it back into the original equation.

Frequently Asked Questions

  • Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.
  • Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable by using addition and subtraction to get rid of the constant term on the same side as the variable, and then use division to isolate the variable.
  • Q: What are some real-world applications of linear equations? A: Linear equations have numerous real-world applications, including physics, engineering, and economics.

Additional Resources

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

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics, and practice is key to mastering it. By following the steps outlined in this article, readers should be able to solve similar equations with confidence. Remember to always write down the equation clearly, use addition and subtraction to isolate the variable, use division to isolate the variable, and check your answer by plugging it back into the original equation.