Solve: \[$-18b = 32\$\].

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 focus on solving a specific type of linear equation, namely the equation ${-18b = 32}$. We will break down the solution process into manageable steps, making it easy for readers to understand and follow along.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ${ax + b = c}$, where ${a}$, ${b}$, and ${c}$ are constants, and ${x}$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation ${-18b = 32}$

The equation ${-18b = 32}$ is a linear equation in one variable, ${b}$. To solve for ${b}$, we need to isolate the variable on one side of the equation. In this case, we can start by dividing both sides of the equation by ${-18}$.

Step 1: Divide Both Sides by ${-18}$

To solve for ${b}$, we need to get rid of the coefficient ${-18}$ that is multiplied by the variable ${b}$. We can do this by dividing both sides of the equation by ${-18}$. This will give us:

${-18b \div -18 = 32 \div -18}$

Using the rule that ${\frac{-a}{-b} = \frac{a}{b}}$, we can simplify the left-hand side of the equation:

${b = -\frac{32}{18}}$

Step 2: Simplify the Fraction

The fraction ${-\frac{32}{18}}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us:

${b = -\frac{16}{9}}$

Conclusion

In this article, we solved the linear equation ${-18b = 32}$ by dividing both sides of the equation by ${-18}$ and simplifying the resulting fraction. The solution to the equation is ${b = -\frac{16}{9}}$. We hope that this step-by-step guide has helped readers understand how to solve linear equations and has provided a useful resource for students and teachers alike.

Additional Resources

For more information on solving linear equations, we recommend the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.

Q: How do I solve a linear equation? A: To solve a linear equation, you can use various methods, including algebraic manipulation, graphing, and substitution.

Q: What is the solution to the equation ${-18b = 32}$? A: The solution to the equation ${-18b = 32}$ is ${b = -\frac{16}{9}}$.

Related Topics

• Solving Quadratic Equations
• Solving Systems of Linear Equations
• Graphing Linear Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable(s) is 1.
• Variable: A letter or symbol that represents a value that can change.
• Coefficient: A number that is multiplied by a variable.
• Fraction: A way of expressing a part of a whole as a ratio of two numbers.
  Solving Linear Equations: A Q&A Guide =====================================

Introduction

In our previous article, we solved the linear equation ${-18b = 32}$ using a step-by-step approach. In this article, we will provide a Q&A guide to help readers understand the concepts and methods involved in solving linear equations.

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 is an equation that can be written in the form ${ax + b = c}$, where ${a}$, ${b}$, and ${c}$ are constants, and ${x}$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use various methods, including algebraic manipulation, graphing, and substitution. The most common method is to isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by the same 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, the equation ${x^2 + 4x + 4 = 0}$ is a quadratic equation, while the equation ${2x + 3 = 5}$ is a linear equation.

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

A: To solve a linear equation with fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators. This will eliminate the fractions and allow you to solve the equation using the methods mentioned earlier.

Q: What is the solution to the equation ${-18b = 32}$?

A: The solution to the equation ${-18b = 32}$ is ${b = -\frac{16}{9}}$.

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the slope-intercept form of the equation, which is ${y = mx + b}$, where ${m}$ is the slope and ${b}$ is the y-intercept. You can plot the y-intercept on the graph and then use the slope to determine the direction and steepness of the line.

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

A: A linear equation is a single equation with one variable, while a system of linear equations is a set of two or more linear equations with the same variables. To solve a system of linear equations, you can use methods such as substitution, elimination, or graphing.

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

A: To solve a system of linear equations, you can use methods such as substitution, elimination, or graphing. The most common method is to use the substitution method, which involves solving one equation for one variable and then substituting that expression into the other equation.

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

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

• Not isolating the variable on one side of the equation
• Not using the correct order of operations
• Not checking the solution for extraneous solutions
• Not using the correct method for solving the equation

Conclusion

In this article, we provided a Q&A guide to help readers understand the concepts and methods involved in solving linear equations. We hope that this guide has been helpful in answering your questions and providing a better understanding of linear equations.

Additional Resources

For more information on solving linear equations, we recommend the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.

Q: How do I solve a linear equation? A: To solve a linear equation, you can use various methods, including algebraic manipulation, graphing, and substitution.

Q: What is the solution to the equation ${-18b = 32}$? A: The solution to the equation ${-18b = 32}$ is ${b = -\frac{16}{9}}$.

Related Topics

• Solving Quadratic Equations
• Solving Systems of Linear Equations
• Graphing Linear Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable(s) is 1.
• Variable: A letter or symbol that represents a value that can change.
• Coefficient: A number that is multiplied by a variable.
• Fraction: A way of expressing a part of a whole as a ratio of two numbers.