Solve This Equation. 2 X − 3 X 2 = 4 2x - \frac{3x}{2} = 4 2 X − 2 3 X ​ = 4

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Introduction to Solving Equations

Solving equations is a fundamental concept in mathematics, and it is essential to understand how to approach and solve various types of equations. In this article, we will focus on solving a linear equation that involves fractions. The equation we will be solving is $2x - \frac{3x}{2} = 4$. This equation involves a variable $x$ and fractions, making it a bit more challenging to solve.

Understanding the Equation

Before we start solving the equation, let's understand what it means. The equation $2x - \frac{3x}{2} = 4$ states that the product of $2$ and $x$ minus the product of $\frac{3}{2}$ and $x$ is equal to $4$. In other words, we have a linear equation that involves a variable $x$ and fractions.

Step 1: Simplify the Equation

To solve the equation, we need to simplify it first. We can start by combining the like terms on the left-hand side of the equation. The like terms are the terms that involve the variable $x$. We can combine the terms as follows:

$2x - \frac{3x}{2} = \frac{4x}{2} - \frac{3x}{2}$

Now, we can simplify the equation by combining the fractions:

$\frac{4x}{2} - \frac{3x}{2} = \frac{4x - 3x}{2}$

Step 2: Simplify the Fraction

Now that we have simplified the equation, we can simplify the fraction on the left-hand side. We can do this by dividing the numerator and denominator by their greatest common divisor, which is $1$. This will give us:

$\frac{4x - 3x}{2} = \frac{x}{2}$

Step 3: Solve for x

Now that we have simplified the equation, we can solve for $x$. We can do this by multiplying both sides of the equation by $2$ to eliminate the fraction:

$\frac{x}{2} = 4$

Multiplying both sides by $2$ gives us:

$x = 8$

Conclusion

In this article, we solved the equation $2x - \frac{3x}{2} = 4$ by simplifying it and then solving for $x$. We started by combining the like terms on the left-hand side of the equation and then simplified the fraction. Finally, we solved for $x$ by multiplying both sides of the equation by $2$. The solution to the equation is $x = 8$.

Tips and Tricks

• When solving equations that involve fractions, it's essential to simplify the equation first.
• Use the distributive property to combine like terms.
• Simplify fractions by dividing the numerator and denominator by their greatest common divisor.
• Solve for the variable by isolating it on one side of the equation.

Real-World Applications

Solving equations is a fundamental concept in mathematics, and it has many real-world applications. Here are a few examples:

• Physics: Solving equations is essential in physics to describe the motion of objects. For example, the equation $s = ut + \frac{1}{2}at^2$ describes the position of an object as a function of time.
• Engineering: Solving equations is essential in engineering to design and optimize systems. For example, the equation $F = ma$ describes the force exerted on an object as a function of its mass and acceleration.
• Economics: Solving equations is essential in economics to model and analyze economic systems. For example, the equation $C = a + bY$ describes the consumption of a good as a function of its price and income.

Final Thoughts

Solving equations is a fundamental concept in mathematics, and it has many real-world applications. In this article, we solved the equation $2x - \frac{3x}{2} = 4$ by simplifying it and then solving for $x$. We started by combining the like terms on the left-hand side of the equation and then simplified the fraction. Finally, we solved for $x$ by multiplying both sides of the equation by $2$. The solution to the equation is $x = 8$. We hope this article has provided you with a better understanding of how to solve equations and has inspired you to explore the many real-world applications of mathematics.

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Introduction

In our previous article, we solved the equation $2x - \frac{3x}{2} = 4$ by simplifying it and then solving for $x$. We received many questions from our readers, and we are excited to provide answers to them in this Q&A article.

Q: What is the first step in solving the equation $2x - \frac{3x}{2} = 4$?

A: The first step in solving the equation $2x - \frac{3x}{2} = 4$ is to simplify the equation by combining the like terms on the left-hand side.

Q: How do I simplify the equation $2x - \frac{3x}{2} = 4$?

A: To simplify the equation $2x - \frac{3x}{2} = 4$, you can start by combining the like terms on the left-hand side. The like terms are the terms that involve the variable $x$. You can combine the terms as follows:

$2x - \frac{3x}{2} = \frac{4x}{2} - \frac{3x}{2}$

Now, you can simplify the equation by combining the fractions:

$\frac{4x}{2} - \frac{3x}{2} = \frac{4x - 3x}{2}$

Q: What is the next step in solving the equation $2x - \frac{3x}{2} = 4$?

A: The next step in solving the equation $2x - \frac{3x}{2} = 4$ is to simplify the fraction on the left-hand side. You can do this by dividing the numerator and denominator by their greatest common divisor, which is $1$. This will give you:

$\frac{4x - 3x}{2} = \frac{x}{2}$

Q: How do I solve for $x$ in the equation $2x - \frac{3x}{2} = 4$?

A: To solve for $x$ in the equation $2x - \frac{3x}{2} = 4$, you can multiply both sides of the equation by $2$ to eliminate the fraction:

$\frac{x}{2} = 4$

Multiplying both sides by $2$ gives you:

$x = 8$

Q: What are some common mistakes to avoid when solving the equation $2x - \frac{3x}{2} = 4$?

A: Some common mistakes to avoid when solving the equation $2x - \frac{3x}{2} = 4$ include:

• Not simplifying the equation before solving for $x$
• Not combining like terms on the left-hand side
• Not eliminating the fraction by multiplying both sides by $2$

Q: How can I apply the concept of solving equations to real-world problems?

A: The concept of solving equations can be applied to many real-world problems, including:

• Physics: Solving equations is essential in physics to describe the motion of objects. For example, the equation $s = ut + \frac{1}{2}at^2$ describes the position of an object as a function of time.
• Engineering: Solving equations is essential in engineering to design and optimize systems. For example, the equation $F = ma$ describes the force exerted on an object as a function of its mass and acceleration.
• Economics: Solving equations is essential in economics to model and analyze economic systems. For example, the equation $C = a + bY$ describes the consumption of a good as a function of its price and income.

Q: What are some additional resources for learning how to solve equations?

A: Some additional resources for learning how to solve equations include:

• Textbooks: There are many textbooks available that cover the topic of solving equations, including "Algebra" by Michael Artin and "Calculus" by Michael Spivak.
• Online resources: There are many online resources available that provide tutorials and examples on how to solve equations, including Khan Academy and MIT OpenCourseWare.
• Practice problems: Practice problems are an essential part of learning how to solve equations. You can find practice problems in textbooks, online resources, and practice problem books.

Conclusion

In this Q&A article, we provided answers to many questions from our readers about solving the equation $2x - \frac{3x}{2} = 4$. We hope that this article has provided you with a better understanding of how to solve equations and has inspired you to explore the many real-world applications of mathematics.