Solve $7x - 5x - 3 = X + 4$.A) $x = -10$ B) $x = 6$ C) $x = -8$ D) $x = 7$

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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, 7x−5x−3=x+47x - 5x - 3 = x + 4, and provide a step-by-step guide on how to arrive at the solution.

Understanding the Equation

Before we dive into solving the equation, let's break it down and understand what it represents. The equation 7x−5x−3=x+47x - 5x - 3 = x + 4 is a linear equation, which means it is an equation in which the highest power of the variable (in this case, xx) is 1.

Step 1: Simplify the Equation

The first step in solving the equation is to simplify it by combining like terms. In this case, we can combine the 7x7x and −5x-5x terms to get 2x2x. The equation now becomes:

2x−3=x+42x - 3 = x + 4

Step 2: Isolate the Variable

The next step is to isolate the variable xx on one side of the equation. To do this, we can add 3 to both sides of the equation to get:

2x=x+72x = x + 7

Step 3: Subtract the Variable

Now, we can subtract xx from both sides of the equation to get:

x=7x = 7

Conclusion

In conclusion, the solution to the equation 7x−5x−3=x+47x - 5x - 3 = x + 4 is x=7x = 7. This is the value of xx that satisfies the equation.

Answer Key

A) x=−10x = -10 B) x=6x = 6 C) x=−8x = -8 D) x=7x = 7

The correct answer is D) x=7x = 7.

Tips and Tricks

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

  • Combine like terms: When simplifying an equation, combine like terms to make it easier to solve.
  • Isolate the variable: To solve for the variable, isolate it on one side of the equation.
  • Check your work: Once you think you have the solution, check your work by plugging the value 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.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations with ease. Remember to combine like terms, isolate the variable, and check your work to ensure that you have the correct solution. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.

Additional Resources

If you need additional help or resources to solve linear equations, here are some additional resources:

  • Online tutorials: Websites such as Khan Academy and Mathway offer interactive tutorials and practice problems to help you learn how to solve linear equations.
  • Textbooks: There are many textbooks available that provide detailed explanations and examples of how to solve linear equations.
  • Practice problems: Websites such as IXL and Math Open Reference offer practice problems to help you reinforce your understanding of linear equations.

Final Thoughts

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 simplify a linear equation?

A: To simplify a linear equation, combine like terms by adding or subtracting the coefficients of the same variable. For example, in the equation 2x + 3x = 5x, the like terms are 2x and 3x, which can be combined to get 5x.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, add or subtract the same value to both sides of the equation. For example, in the equation x + 2 = 5, subtract 2 from both sides to get x = 3.

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 + 2 = 5 is a linear equation, while the equation 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, multiply both sides of the equation by the least common multiple (LCM) of the denominators. For example, in the equation 1/2x + 1/3 = 2, multiply both sides by 6 to get 3x + 2 = 12.

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 value back into the original equation.

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

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

  • Not combining like terms: Failing to combine like terms can make the equation more difficult to solve.
  • Not isolating the variable: Failing to isolate the variable can make it difficult to find the solution.
  • Not checking your work: Failing to check your work can lead to incorrect solutions.

Q: How can I practice solving linear equations?

A: There are many ways to practice solving linear equations, including:

  • Using online resources: Websites such as Khan Academy and Mathway offer interactive tutorials and practice problems.
  • Using textbooks: Textbooks provide detailed explanations and examples of how to solve linear equations.
  • Using practice problems: Websites such as IXL and Math Open Reference offer practice problems to help you reinforce your understanding 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.

Conclusion

In conclusion, solving linear equations is a fundamental skill that is used in many areas of mathematics and science. By following the steps outlined in this article, you can solve linear equations with ease. Remember to combine like terms, isolate the variable, and check your work to ensure that you have the correct solution. With practice and patience, you will become proficient in solving linear equations and be able to apply them to real-world problems.