What Are The Possible Steps Involved In Solving The Equation Shown? Select Three Options.$\[3.5 + 1.2(6.3 - 7x) = 9.38\\]A. Distribute 1.2 To 6.3 And \[$-7x\$\].B. Add 3.5 And 1.2.C. Combine 6.3 And \[$-7x\$\].D. Combine 3.5

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Understanding the Equation

The given equation is a linear equation involving variables and constants. To solve it, we need to follow a series of steps that will help us isolate the variable and find its value. The equation is:

3.5+1.2(6.3−7x)=9.38{3.5 + 1.2(6.3 - 7x) = 9.38}

Step 1: Distribute 1.2 to 6.3 and -7x

The first step in solving this equation is to distribute the coefficient 1.2 to the terms inside the parentheses. This means we need to multiply 1.2 by 6.3 and -7x.

1.2(6.3−7x)=1.2(6.3)−1.2(7x){1.2(6.3 - 7x) = 1.2(6.3) - 1.2(7x)}

1.2(6.3−7x)=7.56−8.4x{1.2(6.3 - 7x) = 7.56 - 8.4x}

Step 2: Rewrite the Equation

Now that we have distributed the coefficient, we can rewrite the original equation with the new expression.

3.5+7.56−8.4x=9.38{3.5 + 7.56 - 8.4x = 9.38}

Step 3: Combine Like Terms

The next step is to combine like terms on the left-hand side of the equation. In this case, we can combine the constants 3.5 and 7.56.

11.06−8.4x=9.38{11.06 - 8.4x = 9.38}

Step 4: Isolate the Variable

To isolate the variable x, we need to get all the terms involving x on one side of the equation. We can do this by subtracting 11.06 from both sides of the equation.

−8.4x=−1.68{-8.4x = -1.68}

Step 5: Solve for x

Finally, we can solve for x by dividing both sides of the equation by -8.4.

x=−1.68−8.4{x = \frac{-1.68}{-8.4}}

x=0.2{x = 0.2}

Conclusion

In conclusion, the possible steps involved in solving the equation are:

  • Distribute 1.2 to 6.3 and -7x
  • Rewrite the equation with the new expression
  • Combine like terms on the left-hand side of the equation
  • Isolate the variable x by subtracting 11.06 from both sides of the equation
  • Solve for x by dividing both sides of the equation by -8.4

The correct options are:

A. Distribute 1.2 to 6.3 and -7x B. Rewrite the equation with the new expression C. Combine like terms on the left-hand side of the equation

The other options are not correct because:

  • Option D is incorrect because we need to combine 3.5 and 1.2(6.3 - 7x) first.
  • Option C is incorrect because we need to distribute 1.2 to 6.3 and -7x first.

Frequently Asked Questions

  • What is the first step in solving the equation? The first step in solving the equation is to distribute 1.2 to 6.3 and -7x.
  • What is the final value of x? The final value of x is 0.2.
  • What are the possible steps involved in solving the equation? The possible steps involved in solving the equation are:
  • Distribute 1.2 to 6.3 and -7x
  • Rewrite the equation with the new expression
  • Combine like terms on the left-hand side of the equation
  • Isolate the variable x by subtracting 11.06 from both sides of the equation
  • Solve for x by dividing both sides of the equation by -8.4

Introduction

Solving linear equations can be a challenging task, especially for those who are new to algebra. However, with the right approach and a clear understanding of the steps involved, it can be a manageable and even enjoyable process. In this article, we will answer some of the most frequently asked questions about solving linear equations, providing you with a better understanding of the subject and helping you to become more confident in your ability to solve these types of 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. It can be written in the form ax + b = c, where a, b, and c are constants.

Q: What are the steps involved in solving a linear equation?

A: The steps involved in solving a linear equation are:

  1. Distribute any coefficients to the terms inside the parentheses.
  2. Combine like terms on the left-hand side of the equation.
  3. Isolate the variable by adding or subtracting the same value to both sides of the equation.
  4. Solve for the variable by dividing both sides of the equation by the coefficient of 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 2x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I know which order to perform the operations in when solving a linear equation?

A: When solving a linear equation, it is generally best to perform the operations in the following order:

  1. Distribute any coefficients to the terms inside the parentheses.
  2. Combine like terms on the left-hand side of the equation.
  3. Isolate the variable by adding or subtracting the same value to both sides of the equation.
  4. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

Q: What is the importance of following the order of operations when solving a linear equation?

A: Following the order of operations is crucial when solving a linear equation because it ensures that the equation is solved correctly and that the solution is accurate. If the operations are not performed in the correct order, the solution may be incorrect, which can lead to errors in further calculations.

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

A: Yes, you can use a calculator to solve a linear equation. However, it is generally best to solve the equation by hand, as this will help you to understand the steps involved and to develop your problem-solving skills.

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

A: Some common mistakes to avoid when solving a linear equation include:

  • Not distributing coefficients to terms inside parentheses
  • Not combining like terms on the left-hand side of the equation
  • Not isolating the variable by adding or subtracting the same value to both sides of the equation
  • Not solving for the variable by dividing both sides of the equation by the coefficient of the variable

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 develop your skills.

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 the influence of forces.
  • 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 to make predictions about future economic trends.
  • Computer Science: Linear equations are used in computer graphics and game development to create realistic simulations and animations.

Conclusion

Solving linear equations is an important skill that has many real-world applications. By following the steps involved in solving a linear equation and avoiding common mistakes, you can develop your problem-solving skills and become more confident in your ability to solve these types of equations. Remember to practice regularly and to seek help when you need it, and you will be well on your way to becoming proficient in solving linear equations.