Solve: { -8b + 54 = B$} P R O V I D E Y O U R A N S W E R B E L O W : Provide Your Answer Below: P Ro V I D Eyo U R An S W Er B E L O W : { B =\$}

Mar 7, 2025 by ADMIN 147 views

**Solving Linear Equations: A Step-by-Step Guide**

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, ${-8b + 54 = b}$ . We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at what it represents. The equation ${-8b + 54 = b}$ is a linear equation in one variable, which means it has only one unknown value, denoted by the variable ${b}$ . The equation is in the form of ${ax + b = c}$ , where ${a}$ , ${b}$ , and ${c}$ are constants.

Step 1: Isolate the Variable

To solve the equation, we need to isolate the variable ${b}$ . This means we need to get ${b}$ by itself on one side of the equation. To do this, we can start by adding ${8b}$ to both sides of the equation. This will eliminate the negative term and allow us to simplify the equation.

-8b + 54 = b
-8b + 8b + 54 = b + 8b
54 = 9b

Step 2: Solve for the Variable

Now that we have isolated the variable, we can solve for ${b}$ . To do this, we need to divide both sides of the equation by the coefficient of ${b}$ , which is ${9}$ .

54 = 9b
54 / 9 = b
6 = b

Conclusion

In this article, we solved the linear equation ${-8b + 54 = b}$ using a step-by-step approach. We isolated the variable ${b}$ by adding ${8b}$ to both sides of the equation and then solved for ${b}$ by dividing both sides by the coefficient of ${b}$ . The final solution is ${b = 6}$ .

Final Answer

The final answer is: $b = 6$

Additional Tips and Resources

To practice solving linear equations, try using online resources such as Khan Academy or Mathway.
For more advanced topics in linear equations, check out the following resources:
- Linear Equations in Two Variables: A Guide to Solving Systems of Equations
- Linear Equations in Three Variables: A Guide to Solving Systems of Equations
- Linear Equations with Fractions: A Guide to Solving Equations with Rational Coefficients
  Solving Linear Equations: Q&A =============================

Introduction

In our previous article, we solved the linear equation ${-8b + 54 = b}$ using a step-by-step approach. In this article, we will answer some common questions related to solving linear equations. Whether you're a student or a professional, this Q&A article will provide you with the information you need to tackle linear equations with confidence.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it's an equation that can be written in the form of ${ax + b = c}$ , where ${a}$ , ${b}$ , and ${c}$ are constants.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

The highest power of the variable(s) is 1.
The equation can be written in the form of ${ax + b = c}$ .
The equation has only one unknown value.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example:

Linear equation: ${2x + 3 = 5}$
Quadratic equation: ${x^2 + 4x + 4 = 0}$

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
Simplify the equation by canceling out any common factors.
Solve for the variable using the usual methods.

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

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the underlying math concepts and be able to solve equations by hand. This will help you to:

Check your calculator's accuracy.
Understand the solution process.
Apply the concepts to more complex equations.

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

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

Not isolating the variable.
Not simplifying the equation.
Not checking the solution.
Not using the correct order of operations.

Conclusion

In this Q&A article, we answered some common questions related to solving linear equations. Whether you're a student or a professional, this article will provide you with the information you need to tackle linear equations with confidence. Remember to practice solving linear equations regularly to build your skills and confidence.

Additional Tips and Resources

To practice solving linear equations, try using online resources such as Khan Academy or Mathway.
For more advanced topics in linear equations, check out the following resources:
- Linear Equations in Two Variables: A Guide to Solving Systems of Equations
- Linear Equations in Three Variables: A Guide to Solving Systems of Equations
- Linear Equations with Fractions: A Guide to Solving Equations with Rational Coefficients