Solve The Equation: ${ \frac{3}{4} X - 7 = \frac{1}{2} X }$A. { X = 20$}$B. { X = 32$}$C. { X = 24$}$D. { X = 28$}$

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, which is a simple algebraic equation involving one variable. We will use the equation $\frac{3}{4} x - 7 = \frac{1}{2} x$ as an example to demonstrate the step-by-step process of solving linear equations.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable (usually x) 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 to be Solved

The equation we will be solving is $\frac{3}{4} x - 7 = \frac{1}{2} x$. This equation involves fractions, which can make it more challenging to solve. However, with the right approach, we can simplify the equation and solve for the value of $x$.

Step 1: Add 7 to Both Sides

To begin solving the equation, we need to isolate the term involving $x$. We can do this by adding 7 to both sides of the equation. This will eliminate the constant term on the left-hand side of the equation.

$\frac{3}{4} x - 7 + 7 = \frac{1}{2} x + 7$

Simplifying the left-hand side of the equation, we get:

$\frac{3}{4} x = \frac{1}{2} x + 7$

Step 2: Subtract $\frac{1}{2} x$ from Both Sides

Next, we need to eliminate the term involving $x$ on the right-hand side of the equation. We can do this by subtracting $\frac{1}{2} x$ from both sides of the equation.

$\frac{3}{4} x - \frac{1}{2} x = \frac{1}{2} x + 7 - \frac{1}{2} x$

Simplifying the left-hand side of the equation, we get:

$\frac{1}{4} x = 7$

Step 3: Multiply Both Sides by 4

To solve for the value of $x$, we need to isolate $x$ on one side of the equation. We can do this by multiplying both sides of the equation by 4.

$\frac{1}{4} x \times 4 = 7 \times 4$

Simplifying the equation, we get:

$x = 28$

Conclusion

In this article, we solved the linear equation $\frac{3}{4} x - 7 = \frac{1}{2} x$ using the step-by-step process of adding 7 to both sides, subtracting $\frac{1}{2} x$ from both sides, and multiplying both sides by 4. We found that the value of $x$ is 28. This equation is a simple example of a linear equation, and solving it requires careful attention to detail and a solid understanding of algebraic manipulation.

Answer

The correct answer is:

• D. $x = 28$

Discussion

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we demonstrated the step-by-step process of solving a linear equation involving fractions. We hope that this article has provided a clear and concise guide to solving linear equations, and that it has helped to build your confidence in solving these types of equations.

Additional Resources

If you are struggling to solve linear equations, there are many additional resources available to help you. Some of these resources include:

• Online tutorials and videos
• Practice problems and worksheets
• Algebra textbooks and study guides
• Online communities and forums

Introduction

In our previous article, we discussed the step-by-step process of solving linear equations. However, we understand that sometimes, it's not enough to just read about a concept - you need to see it in action, and have your questions answered. That's why we've put together this Q&A guide, where we'll answer some of the most common 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 (usually x) 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 know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

• The equation can be written in the form $ax + b = c$.
• The highest power of the variable (usually x) is 1.
• The equation does not involve any exponents or roots.

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

• Simple linear equations: Equations that can be written in the form $ax + b = c$.
• Linear equations with fractions: Equations that involve fractions, such as $\frac{3}{4} x - 7 = \frac{1}{2} x$.
• Linear equations with decimals: Equations that involve decimals, such as $2.5x + 3 = 7$.

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

A: To solve a linear equation with fractions, follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
2. Simplify the equation by combining like terms.
3. Isolate the variable (usually x) on one side of the equation.

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

A: To solve a linear equation with decimals, follow these steps:

1. Multiply both sides of the equation by 10 to eliminate the decimals.
2. Simplify the equation by combining like terms.
3. Isolate the variable (usually x) on one side of the 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 following the order of operations (PEMDAS).
• Not simplifying the equation before solving for the variable.
• Not checking the solution to make sure it is correct.

Q: How can I practice solving linear equations?

A: There are many ways to practice solving linear equations, including:

• Using online resources, such as Khan Academy or Mathway.
• Working with a tutor or teacher.
• Practicing with worksheets or practice problems.
• Using a calculator to check your solutions.

Conclusion

We hope that this Q&A guide has been helpful in answering some of the most common questions about solving linear equations. Remember to always follow the order of operations, simplify the equation before solving for the variable, and check your solution to make sure it is correct. With practice and patience, you'll become a pro at solving linear equations in no time!

Additional Resources

If you're looking for more practice or want to learn more about linear equations, check out these additional resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Algebra textbooks and study guides
• Online communities and forums

We hope that this article has been helpful in providing a clear and concise guide to solving linear equations. If you have any questions or need further assistance, please don't hesitate to ask.