Solve The Equation: \[$-8k = -56\$\]A. \[$k = -48\$\] B. \[$k = 7\$\] C. \[$k = -7\$\] D. \[$k = -64\$\]

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 simple linear equation, ${-8k = -56}$, and explore the different methods and techniques used to find the value of the variable k.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It 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.

Solving the Equation: ${-8k = -56}$

To solve the equation ${-8k = -56}$, we need to isolate the variable k. We can do this by dividing both sides of the equation by -8.

Step 1: Divide Both Sides by -8

When we divide both sides of the equation by -8, we get:

${-8k / -8 = -56 / -8}$

This simplifies to:

k = 7

Step 2: Check the Solution

To verify that k = 7 is the correct solution, we can substitute this value back into the original equation:

${-8(7) = -56}$

Expanding the left-hand side, we get:

${-56 = -56}$

This shows that k = 7 is indeed the correct solution.

Answer Options

Now that we have solved the equation, let's take a look at the answer options:

A. k = -48 B. k = 7 C. k = -7 D. k = -64

Based on our solution, we can see that option B, k = 7, is the correct answer.

Conclusion

Solving linear equations is an essential skill for students to master. By following the steps outlined in this article, we can solve equations like ${-8k = -56}$ and find the value of the variable k. Remember to always check your solution by substituting the value back into the original equation.

Tips and Tricks

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

• Always start by isolating the variable on one side of the equation.
• Use inverse operations to eliminate any coefficients or constants.
• Check your solution by substituting the value back into the original equation.
• Practice, practice, practice! The more you practice solving linear equations, the more comfortable you will become with the different methods and techniques.

Common Mistakes

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

• Not isolating the variable on one side of the equation.
• Not using inverse operations to eliminate coefficients or constants.
• Not checking the solution by substituting the value back into the original equation.
• Not practicing regularly to build your skills and confidence.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

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Introduction

In our previous article, we explored the concept of linear equations and how to solve them using algebraic manipulation. 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(s) is 1. It 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 need to isolate the variable on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

Q: What is an inverse operation?

A: An inverse operation is an operation that "reverses" another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to identify the operation that is being performed on the variable, and then perform the inverse operation to isolate the variable.

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.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula to solve a quadratic equation, you need to plug in the values of a, b, and c into the formula, and then simplify the expression.

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 inverse operations to eliminate coefficients or constants
• Not checking the solution by substituting the value back into the original equation
• Not practicing regularly to build your skills and confidence

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through example problems, using online resources, or taking practice quizzes.

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 under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

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 and understand the concepts behind them. Remember to always check your solution by substituting the value back into the original equation, and practice regularly to build your skills and confidence.

Additional Resources

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: 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 need to isolate the variable on one side of the equation using inverse operations.
• Q: What is an inverse operation? A: An inverse operation is an operation that "reverses" another operation.
• Q: How do I use inverse operations to solve a linear equation? A: To use inverse operations to solve a linear equation, you need to identify the operation that is being performed on the variable, and then perform the inverse operation to isolate the variable.