What Is The First Step To Solving The Equation − 2 ( 3 X + 8 ) − 2 = 10 -2(3x + 8) - 2 = 10 − 2 ( 3 X + 8 ) − 2 = 10 ?A. Combine Like Terms. B. Distribute The -2. C. Add 3 X + 8 3x + 8 3 X + 8 . D. None Of These Choices Are Correct.

Understanding the Basics of Linear Equations

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 understand the process and identify the first step in solving it.

The Equation: $-2(3x + 8) - 2 = 10$

The given equation is $-2(3x + 8) - 2 = 10$. To solve this equation, we need to follow a series of steps that will help us isolate the variable $x$. But before we dive into the solution, let's analyze the equation and identify the first step.

Analyzing the Equation

The equation $-2(3x + 8) - 2 = 10$ contains a few key elements that we need to understand:

• The equation is a linear equation, meaning it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.
• The equation contains a negative sign in front of the parentheses, indicating that we need to distribute the negative sign to the terms inside the parentheses.
• The equation also contains a constant term, $-2$, which needs to be isolated.

The First Step: Distributing the Negative Sign

The first step in solving the equation $-2(3x + 8) - 2 = 10$ is to distribute the negative sign to the terms inside the parentheses. This means that we need to multiply the negative sign by each term inside the parentheses.

Distributing the Negative Sign

To distribute the negative sign, we need to multiply the negative sign by each term inside the parentheses:

$$-2(3x + 8) = -6x - 16$$

Now, the equation becomes:

$$-6x - 16 - 2 = 10$$

Simplifying the Equation

The next step is to simplify the equation by combining like terms. We can combine the constant terms $-16$ and $-2$ to get:

$$-6x - 18 = 10$$

Conclusion

In conclusion, the first step in solving the equation $-2(3x + 8) - 2 = 10$ is to distribute the negative sign to the terms inside the parentheses. This step is crucial in simplifying the equation and making it easier to solve.

Answer

The correct answer is B. Distribute the -2.

Additional Tips and Tricks

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

• Always start by simplifying the equation by combining like terms.
• Use the distributive property to distribute negative signs and coefficients.
• Isolate the variable by adding or subtracting the same value to both sides of the equation.
• Use inverse operations to solve for the variable.

By following these tips and tricks, you can become proficient in solving linear equations and tackle even the most challenging problems with confidence.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

• Failing to distribute negative signs and coefficients.
• Not combining like terms.
• Not isolating the variable.
• Not using inverse operations to solve for the variable.

By avoiding these common mistakes, you can ensure that you are solving linear equations correctly and efficiently.

Conclusion

$$

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about solving linear equations. Whether you are a student struggling to understand the concept or a teacher looking for ways to explain it to your students, this article is for you.

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 is the first step in solving a linear equation?

A: The first step in solving a linear equation is to simplify the equation by combining like terms. This involves adding or subtracting the same value to both sides of the equation.

Q: How do I distribute a negative sign in a linear equation?

A: To distribute a negative sign in a linear equation, you need to multiply the negative sign by each term inside the parentheses. For example, if you have the equation -2(3x + 8), you would multiply the negative sign by each term inside the parentheses to get -6x - 16.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that allows you to distribute a coefficient (a number that is multiplied by a variable) to each term inside the parentheses. For example, if you have the equation 2(3x + 4), you can use the distributive property to get 6x + 8.

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

A: To isolate the variable in a linear equation, you need to use inverse operations to get the variable by itself on one side of the equation. For example, if you have the equation 2x + 3 = 5, you can 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:

• Failing to distribute negative signs and coefficients.
• Not combining like terms.
• Not isolating the variable.
• Not using inverse operations to solve for the variable.

Q: How can I practice solving linear equations?

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

• Using online resources such as Khan Academy or Mathway.
• Working with a tutor or teacher.
• Practicing with worksheets or online exercises.
• Solving real-world problems that involve 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.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems and make predictions.
• Computer Science: Linear equations are used in algorithms and data analysis.

Conclusion

In conclusion, solving linear equations is a crucial skill that has many real-world applications. By understanding the basics of linear equations and practicing with exercises and real-world problems, you can become proficient in solving linear equations and tackle even the most challenging problems with confidence.