Solve $3kx + 24 = 9kx$ For $x$.A. $x = -\frac{2}{k}$ B. $x = \frac{2}{k}$ C. $x = \frac{4}{k}$ D. $x = -\frac{4}{k}$

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 linear equation, $3kx + 24 = 9kx$, for the variable $x$. We will break down the solution step by step, using algebraic manipulations to isolate the variable.

Understanding the Equation

The given equation is $3kx + 24 = 9kx$. Our goal is to solve for $x$, which means we need to isolate $x$ on one side of the equation. To do this, we will use various algebraic techniques, such as subtracting, adding, multiplying, and dividing.

Step 1: Subtract $3kx$ from Both Sides

Our first step is to get rid of the $3kx$ term on the left-hand side of the equation. We can do this by subtracting $3kx$ from both sides of the equation:

$$3kx + 24 = 9kx$$

Subtracting $3kx$ from both sides gives us:

$$24 = 6kx$$

Step 2: Divide Both Sides by $6k$

Now that we have $6kx$ on the right-hand side, we can divide both sides of the equation by $6k$ to isolate $x$:

$$\frac{24}{6k} = x$$

Simplifying the left-hand side gives us:

$$\frac{4}{k} = x$$

Conclusion

We have successfully solved the linear equation $3kx + 24 = 9kx$ for the variable $x$. The solution is $x = \frac{4}{k}$. This result can be verified by plugging it back into the original equation.

Answer

The correct answer is:

• C. $x = \frac{4}{k}$

Why This Matters

Solving linear equations is a fundamental skill in mathematics, and it has numerous applications in various fields, such as physics, engineering, and economics. By mastering this skill, students can solve a wide range of problems, from simple algebraic equations to complex systems of equations.

Real-World Applications

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

• Physics: Linear equations are used to describe the motion of objects, including the trajectory of projectiles and the motion of particles in a magnetic field.
• 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, including the behavior of supply and demand.

Tips and Tricks

Here are some tips and tricks for solving linear equations:

• Use algebraic manipulations: Linear equations can be solved using various algebraic techniques, such as subtracting, adding, multiplying, and dividing.
• Isolate the variable: The goal of solving a linear equation is to isolate the variable on one side of the equation.
• Check your work: Always plug your solution back into the original equation to verify that it is correct.

Conclusion

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Introduction

In our previous article, we solved the linear equation $3kx + 24 = 9kx$ for the variable $x$. In this article, we will provide a Q&A guide to help students understand the concepts and techniques 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: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

1. Isolate the variable: The goal of solving a linear equation is to isolate the variable on one side of the equation.
2. Use algebraic manipulations: Linear equations can be solved using various algebraic techniques, such as subtracting, adding, multiplying, and dividing.
3. Check your work: Always plug your solution back into the original equation to verify that it is correct.

Q: How do I isolate the variable?

A: To isolate the variable, you need to get rid of the constant term on the same side of the equation as the variable. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What are some common algebraic manipulations used to solve linear equations?

A: Some common algebraic manipulations used to solve linear equations include:

• Subtracting: Subtracting the same value from both sides of the equation to get rid of a constant term.
• Adding: Adding the same value to both sides of the equation to get rid of a constant term.
• Multiplying: Multiplying both sides of the equation by a non-zero value to get rid of a fraction.
• Dividing: Dividing both sides of the equation by a non-zero value to get rid of a fraction.

Q: How do I check my work?

A: To check your work, you need to plug your solution back into the original equation and verify that it is true. If the solution is correct, the equation should be true. If the solution is incorrect, the equation should be false.

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: Failing to isolate the variable on one side of the equation.
• Not using algebraic manipulations: Failing to use algebraic techniques, such as subtracting, adding, multiplying, and dividing, to solve the equation.
• Not checking your work: Failing to plug your solution back into the original equation to verify that it is correct.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to a wide range of real-world problems, including:

• Physics: Linear equations are used to describe the motion of objects, including the trajectory of projectiles and the motion of particles in a magnetic field.
• 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, including the behavior of supply and demand.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it has numerous applications in various fields. By mastering this skill, students can solve a wide range of problems, from simple algebraic equations to complex systems of equations. In this article, we provided a Q&A guide to help students understand the concepts and techniques involved in solving linear equations.