What Do You Need To Do First To The Right Side Of The Equation?A. Distribute The 3 To The $(x+4)$B. Subtract 3C. Divide Both Sides By $(x+4)$D. Subtract 4

What do you need to do first to the right side of the equation?

Understanding the Basics of Algebraic Manipulation

When dealing with algebraic equations, it's essential to understand the order of operations and how to manipulate expressions to isolate the variable. In this article, we'll explore the correct steps to take when presented with an equation that requires simplification.

The Given Equation

Let's consider the equation: $x + 4 = 3(x + 4)$

Our goal is to simplify this equation and isolate the variable $x$. To do this, we need to follow the correct order of operations and apply the appropriate algebraic manipulations.

Option A: Distribute the 3 to the $(x+4)$

One possible approach is to distribute the 3 to the $(x+4)$, which would result in: $x + 4 = 3x + 12$

However, this is not the correct step to take first. Distributing the 3 would indeed simplify the equation, but it would not address the issue of the variable being isolated.

Option B: Subtract 3

Another option is to subtract 3 from both sides of the equation, which would result in: $x + 4 - 3 = 3(x + 4) - 3$

This would simplify the equation, but it would not isolate the variable $x$.

Option C: Divide both sides by $(x+4)$

Dividing both sides of the equation by $(x+4)$ would result in: $\frac{x + 4}{x + 4} = \frac{3(x + 4)}{x + 4}$

This would simplify the equation, but it would not address the issue of the variable being isolated.

Option D: Subtract 4

The correct step to take first is to subtract 4 from both sides of the equation, which would result in: $x = 3(x + 4) - 4$

This would simplify the equation and isolate the variable $x$.

Why Subtract 4 First?

Subtracting 4 first is the correct step because it eliminates the constant term on the left-hand side of the equation, allowing us to focus on the variable $x$. By subtracting 4, we are essentially "moving" the constant term to the right-hand side of the equation, where it can be combined with the other terms.

The Correct Order of Operations

The correct order of operations when dealing with algebraic equations is:

1. Simplify the equation by combining like terms.
2. Isolate the variable by applying inverse operations.
3. Check the solution by plugging it back into the original equation.

Conclusion

In conclusion, the correct step to take first when dealing with the equation $x + 4 = 3(x + 4)$ is to subtract 4 from both sides of the equation. This eliminates the constant term on the left-hand side, allowing us to focus on the variable $x$. By following the correct order of operations and applying the appropriate algebraic manipulations, we can simplify the equation and isolate the variable $x$.

Additional Tips and Tricks

• When dealing with algebraic equations, it's essential to understand the order of operations and how to manipulate expressions to isolate the variable.
• Always simplify the equation by combining like terms before attempting to isolate the variable.
• Use inverse operations to isolate the variable, such as adding or subtracting the same value to both sides of the equation.
• Check the solution by plugging it back into the original equation to ensure that it is correct.

Common Mistakes to Avoid

• Don't forget to simplify the equation by combining like terms before attempting to isolate the variable.
• Avoid applying inverse operations to the wrong side of the equation.
• Don't forget to check the solution by plugging it back into the original equation to ensure that it is correct.

Real-World Applications

Algebraic equations are used in a wide range of real-world applications, including:

• Physics and engineering: Algebraic equations are used to describe the motion of objects and the behavior of physical systems.
• Economics: Algebraic equations are used to model economic systems and make predictions about future trends.
• Computer science: Algebraic equations are used to develop algorithms and solve problems in computer science.

Conclusion

In conclusion, the correct step to take first when dealing with the equation $x + 4 = 3(x + 4)$ is to subtract 4 from both sides of the equation. By following the correct order of operations and applying the appropriate algebraic manipulations, we can simplify the equation and isolate the variable $x$. Remember to always simplify the equation by combining like terms before attempting to isolate the variable, and use inverse operations to isolate the variable.
Frequently Asked Questions (FAQs)

Q: What is the correct order of operations when dealing with algebraic equations?

A: The correct order of operations is:

1. Simplify the equation by combining like terms.
2. Isolate the variable by applying inverse operations.
3. Check the solution by plugging it back into the original equation.

Q: Why is it essential to simplify the equation by combining like terms before attempting to isolate the variable?

A: Simplifying the equation by combining like terms helps to eliminate unnecessary complexity and makes it easier to isolate the variable. It also helps to avoid mistakes and ensures that the solution is correct.

Q: What is the difference between a variable and a constant in an algebraic equation?

A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that remains the same. In the equation $x + 4 = 3(x + 4)$, $x$ is a variable and $4$ is a constant.

Q: How do I know which inverse operation to apply to isolate the variable?

A: To isolate the variable, you need to apply the inverse operation that "reverses" the operation that was applied to the variable. For example, if the variable was multiplied by a value, you need to divide both sides of the equation by that value to isolate the variable.

Q: What is the purpose of checking the solution by plugging it back into the original equation?

A: Checking the solution by plugging it back into the original equation ensures that the solution is correct and that it satisfies the original equation. This helps to avoid mistakes and ensures that the solution is accurate.

Q: Can I use algebraic equations to solve problems in real-world applications?

A: Yes, algebraic equations can be used to solve problems in a wide range of real-world applications, including physics, engineering, economics, and computer science.

Q: How do I know which algebraic operation to apply to solve a problem?

A: To determine which algebraic operation to apply, you need to analyze the problem and identify the variables and constants involved. You can then use algebraic manipulations to isolate the variable and solve the problem.

Q: What are some common mistakes to avoid when working with algebraic equations?

A: Some common mistakes to avoid include:

• Forgetting to simplify the equation by combining like terms
• Applying the wrong inverse operation to isolate the variable
• Forgetting to check the solution by plugging it back into the original equation
• Making mistakes when applying algebraic manipulations

Q: Can I use algebraic equations to solve problems that involve multiple variables?

A: Yes, algebraic equations can be used to solve problems that involve multiple variables. However, you need to be careful to isolate each variable separately and ensure that the solution satisfies the original equation.

Q: How do I know which algebraic equation to use to solve a problem?

A: To determine which algebraic equation to use, you need to analyze the problem and identify the variables and constants involved. You can then use algebraic manipulations to isolate the variable and solve the problem.

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

A: Algebraic equations have a wide range of real-world applications, including:

• Physics and engineering: Algebraic equations are used to describe the motion of objects and the behavior of physical systems.
• Economics: Algebraic equations are used to model economic systems and make predictions about future trends.
• Computer science: Algebraic equations are used to develop algorithms and solve problems in computer science.

Conclusion

In conclusion, algebraic equations are a powerful tool for solving problems in a wide range of real-world applications. By understanding the correct order of operations, simplifying the equation by combining like terms, and applying inverse operations to isolate the variable, you can use algebraic equations to solve problems and make predictions about the world around you.