What Is The Solution To The Linear Equation? 4 B + 6 = 2 − B + 4 4b + 6 = 2 - B + 4 4 B + 6 = 2 − B + 4 A. B = − 2 B = -2 B = − 2 B. B = 0 B = 0 B = 0 C. B = 4 B = 4 B = 4 D. B = 6 B = 6 B = 6

Mar 9, 2025 by ADMIN 193 views

What is the Solution to the Linear Equation $4b + 6 = 2 - b + 4$?

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 explore the solution to a specific linear equation, $4b + 6 = 2 - b + 4$ , and provide a step-by-step guide on how to solve it.

Understanding the Equation

The given equation is a linear equation in one variable, $b$ . The equation is in the form of $ax + b = c$ , where $a$ , $b$ , and $c$ are constants. In this case, the equation is $4b + 6 = 2 - b + 4$ . Our goal is to isolate the variable $b$ and find its value.

Step 1: Simplify the Equation

To simplify the equation, we need to combine like terms. The equation can be rewritten as $4b + 6 = 2 - b + 4$ . We can start by combining the constants on the right-hand side of the equation.

# Simplify the equation
equation = "4b + 6 = 2 - b + 4"
simplified_equation = "4b + 6 = 6 - b"

Step 2: Isolate the Variable

Now that we have simplified the equation, we need to isolate the variable $b$ . We can do this by adding $b$ to both sides of the equation and then subtracting $6$ from both sides.

# Isolate the variable
simplified_equation = "4b + 6 = 6 - b"
isolated_variable = "5b = 0"

Step 3: Solve for the Variable

Now that we have isolated the variable $b$ , we can solve for its value. We can do this by dividing both sides of the equation by $5$ .

# Solve for the variable
isolated_variable = "5b = 0"
solution = "b = 0"

Conclusion

In conclusion, the solution to the linear equation $4b + 6 = 2 - b + 4$ is $b = 0$ . This can be verified by plugging the value of $b$ back into the original equation.

Final Answer

The final answer is $b = 0$ .

Discussion

The solution to the linear equation $4b + 6 = 2 - b + 4$ is $b = 0$ . This can be verified by plugging the value of $b$ back into the original equation.

Step-by-Step Solution

Here is a step-by-step solution to the linear equation:

Simplify the equation by combining like terms.
Isolate the variable $b$ by adding $b$ to both sides of the equation and then subtracting $6$ from both sides.
Solve for the variable $b$ by dividing both sides of the equation by $5$ .

Common Mistakes

When solving linear equations, it's common to make mistakes such as:

Not simplifying the equation before isolating the variable.
Not isolating the variable correctly.
Not solving for the variable correctly.

Tips and Tricks

Here are some tips and tricks for solving linear equations:

Always simplify the equation before isolating the variable.
Use inverse operations to isolate the variable.
Check your solution by plugging the value of the variable back into the original equation.

Real-World Applications

Linear equations have many real-world applications, such as:

Modeling population growth.
Calculating interest rates.
Determining the cost of goods.

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 always simplify the equation before isolating the variable, and use inverse operations to isolate the variable. With practice and patience, you can become proficient in solving linear equations.

Introduction

Solving linear equations can be a challenging task, especially for students who are new to algebra. However, with practice and patience, anyone can become proficient in solving linear equations. In this article, we will answer some of the most frequently asked questions about 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. In other words, it is an equation in which the variable is not raised to a power greater than 1.

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.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by using inverse operations. This means that you need to add or subtract the same value to both sides of the equation, or multiply or divide both sides of the equation by the same value.

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

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

Not simplifying the equation before isolating the variable.
Not isolating the variable correctly.
Not solving for the variable correctly.
Not checking the solution by plugging the value of the variable back into the original equation.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug the value of the variable back into the original equation and see if it is true. If it is true, then your solution is correct.

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

A: Linear equations have many real-world applications, such as:

Modeling population growth.
Calculating interest rates.
Determining the cost of goods.
Solving problems in physics and engineering.

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

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your solution by plugging the value of the variable back into the original equation.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. This means that you need to add or subtract the same value to both sides of the equation.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is an equation in which the highest power of the variable is 1, while a system of linear equations is a set of two or more linear equations that are solved simultaneously.

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

A: To solve a system of linear equations, you need to use methods such as substitution or elimination to find the values of the variables.

Q: Can I use a graphing calculator to solve linear equations?

A: Yes, you can use a graphing calculator to solve linear equations. However, it's always a good idea to check your solution by plugging the value of the variable back into the original equation.

Conclusion

Additional Resources

If you need additional help with solving linear equations, here are some additional resources that you can use:

Online tutorials and videos
Practice problems and worksheets
Textbooks and study guides
Online communities and forums

Final Tips

Here are some final tips for solving linear equations:

Always simplify the equation before isolating the variable.
Use inverse operations to isolate the variable.
Check your solution by plugging the value of the variable back into the original equation.
Practice, practice, practice!

By following these tips and using the resources outlined in this article, you can become proficient in solving linear equations and tackle even the most challenging problems with ease.