Solve For $x$:$\[ \frac{2(x-12)}{3} = 0 \\]

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Introduction

Solving for $x$ in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving for $x$ in the equation $\frac{2(x-12)}{3} = 0$. This equation involves fractions, and we will use algebraic techniques to simplify and solve for $x$.

Understanding the Equation

The given equation is $\frac{2(x-12)}{3} = 0$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The equation involves a fraction, and we will start by simplifying the fraction.

Simplifying the Fraction

To simplify the fraction, we can multiply both sides of the equation by the denominator, which is $3$. This will eliminate the fraction and make it easier to solve for $x$.

$\frac{2(x-12)}{3} = 0$

Multiplying both sides by $3$:

$2(x-12) = 0 \times 3$

$2(x-12) = 0$

Expanding and Simplifying

Now that we have eliminated the fraction, we can expand and simplify the equation. We will start by distributing the $2$ to the terms inside the parentheses.

$2(x-12) = 0$

Expanding the equation:

$2x - 24 = 0$

Isolating the Variable

Now that we have simplified the equation, we can isolate the variable $x$ by adding $24$ to both sides of the equation.

$2x - 24 = 0$

Adding $24$ to both sides:

$2x = 24$

Solving for $x$

Finally, we can solve for $x$ by dividing both sides of the equation by $2$.

$2x = 24$

Dividing both sides by $2$:

$x = \frac{24}{2}$

$x = 12$

Conclusion

In this article, we solved for $x$ in the equation $\frac{2(x-12)}{3} = 0$. We started by simplifying the fraction, then expanded and simplified the equation, isolated the variable, and finally solved for $x$. The solution to the equation is $x = 12$.

Tips and Tricks

• When solving for $x$, it is essential to isolate the variable on one side of the equation.
• Use algebraic techniques such as multiplying, dividing, adding, and subtracting to simplify the equation.
• Be careful when working with fractions, and make sure to eliminate them before solving for $x$.
• Check your solution by plugging it back into the original equation.

Common Mistakes

• Failing to isolate the variable on one side of the equation.
• Not eliminating fractions before solving for $x$.
• Not checking the solution by plugging it back into the original equation.

Real-World Applications

Solving for $x$ is a fundamental concept in mathematics, and it has many real-world applications. For example, in physics, solving for $x$ can help us determine the position of an object at a given time. In engineering, solving for $x$ can help us design and optimize systems. In finance, solving for $x$ can help us calculate interest rates and investment returns.

Final Thoughts

Solving for $x$ is a critical skill in mathematics, and it requires practice and patience. By following the steps outlined in this article, you can develop your skills and become proficient in solving for $x$. Remember to always isolate the variable, eliminate fractions, and check your solution. With practice and dedication, you can master the art of solving for $x$.

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Introduction

In our previous article, we solved for $x$ in the equation $\frac{2(x-12)}{3} = 0$. We covered the steps to simplify the fraction, expand and simplify the equation, isolate the variable, and finally solve for $x$. In this article, we will answer some frequently asked questions (FAQs) related to solving for $x$.

Q&A

Q: What is the first step in solving for $x$?

A: The first step in solving for $x$ is to simplify the equation by eliminating any fractions. This can be done by multiplying both sides of the equation by the denominator.

Q: How do I know if I have isolated the variable?

A: You have isolated the variable when it is on one side of the equation, and the other side of the equation is a constant or a numerical value.

Q: What if the equation has multiple variables?

A: If the equation has multiple variables, you will need to use algebraic techniques such as substitution or elimination to solve for the variables.

Q: Can I use a calculator to solve for $x$?

A: Yes, you can use a calculator to solve for $x$, but it is essential to understand the steps involved in solving for $x$ so that you can verify the solution.

Q: What if I get stuck while solving for $x$?

A: If you get stuck while solving for $x$, try breaking down the problem into smaller steps, and use algebraic techniques such as factoring or simplifying to make the equation more manageable.

Q: How do I check my solution?

A: To check your solution, plug the value of $x$ back into the original equation and verify that it is true.

Q: What are some common mistakes to avoid when solving for $x$?

A: Some common mistakes to avoid when solving for $x$ include:

• Failing to isolate the variable on one side of the equation
• Not eliminating fractions before solving for $x$
• Not checking the solution by plugging it back into the original equation

Q: Can I use solving for $x$ in real-world applications?

A: Yes, solving for $x$ has many real-world applications, including physics, engineering, and finance.

Tips and Tricks

• Always simplify the equation before solving for $x$.
• Use algebraic techniques such as substitution or elimination to solve for multiple variables.
• Verify your solution by plugging it back into the original equation.
• Practice, practice, practice! Solving for $x$ requires practice and patience.

Common Mistakes

• Failing to isolate the variable on one side of the equation.
• Not eliminating fractions before solving for $x$.
• Not checking the solution by plugging it back into the original equation.

Real-World Applications

Solving for $x$ has many real-world applications, including:

• Physics: Solving for $x$ can help us determine the position of an object at a given time.
• Engineering: Solving for $x$ can help us design and optimize systems.
• Finance: Solving for $x$ can help us calculate interest rates and investment returns.

Final Thoughts

Solving for $x$ is a critical skill in mathematics, and it requires practice and patience. By following the steps outlined in this article and practicing regularly, you can develop your skills and become proficient in solving for $x. Remember to always simplify the equation, isolate the variable, and check your solution. With practice and dedication, you can master the art of solving for $x.