An Equation Is Given:$\frac{3}{4} X = 39$What Is The Value Of $x$?

Introduction

In mathematics, equations are a fundamental concept that help us solve for unknown values. Given an equation, we can use various techniques to isolate the variable and find its value. In this article, we will focus on solving a simple linear equation, $\frac{3}{4} x = 39$, to determine the value of $x$. We will break down the solution step by step, using algebraic manipulations to isolate the variable.

Understanding the Equation

The given equation is $\frac{3}{4} x = 39$. This is a linear equation, where the variable $x$ is multiplied by a fraction, $\frac{3}{4}$. Our goal is to solve for $x$, which means we need to isolate the variable on one side of the equation.

Step 1: Multiply Both Sides by the Reciprocal of the Fraction

To isolate the variable, we can multiply both sides of the equation by the reciprocal of the fraction, which is $\frac{4}{3}$. This will cancel out the fraction on the left-hand side of the equation.

$\frac{3}{4} x = 39$

$\frac{4}{3} \times \frac{3}{4} x = \frac{4}{3} \times 39$

$x = 52$

Conclusion

By multiplying both sides of the equation by the reciprocal of the fraction, we were able to isolate the variable $x$. The value of $x$ is $52$. This solution demonstrates the importance of algebraic manipulations in solving linear equations.

Real-World Applications

Solving linear equations is a fundamental skill that has numerous real-world applications. In finance, for example, linear equations are used to calculate interest rates, investment returns, and other financial metrics. In science, linear equations are used to model population growth, chemical reactions, and other phenomena.

Tips and Tricks

When solving linear equations, it's essential to remember the following tips and tricks:

• Always multiply both sides of the equation by the same value to maintain equality.
• Use the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation.
• Check your solution by plugging it back into the original equation.

Common Mistakes

When solving linear equations, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not multiplying both sides of the equation by the same value.
• Not using the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation.
• Not checking the solution by plugging it back into the original equation.

Final Thoughts

Solving linear equations is a fundamental skill that requires practice and patience. By following the steps outlined in this article, you can develop the skills necessary to solve linear equations and apply them to real-world problems. Remember to always check your solution and use the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation.

Additional Resources

For more information on solving linear equations, check out the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Conclusion

In conclusion, solving linear equations is a fundamental skill that has numerous real-world applications. By following the steps outlined in this article, you can develop the skills necessary to solve linear equations and apply them to real-world problems. Remember to always check your solution and use the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation.

Introduction

Solving linear equations is a fundamental concept in mathematics that can be a bit tricky to grasp at first. However, with practice and patience, anyone can become proficient in solving linear equations. In this article, we will address 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 is 1. In other words, it is an equation that can be written in the form ax = b, where a and b 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. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation 2x = 5 is a linear equation, while the equation x^2 + 2x + 1 = 0 is a quadratic equation.

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

A: To solve a linear equation with fractions, you need to multiply both sides of the equation by the reciprocal of the fraction. This will cancel out the fraction on the left-hand side of the equation.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 3/4 is 4/3.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug it back into the original equation and see if it is true. If it is true, then your solution is correct.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not multiplying both sides of the equation by the same value
• Not using the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation
• Not checking the solution by plugging it back into the original equation

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

A: To solve a linear equation with decimals, you can multiply both sides of the equation by 10 to eliminate the decimal point.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one variable, while a system of linear equations is a set of two or more equations with two or more variables.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to use methods such as substitution or elimination to find the values of the variables.

Q: What are some real-world applications of linear equations?

A: Linear equations have numerous real-world applications, including:

• Finance: calculating interest rates, investment returns, and other financial metrics
• Science: modeling population growth, chemical reactions, and other phenomena
• Engineering: designing buildings, bridges, and other structures

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By following the steps outlined in this article, you can develop the skills necessary to solve linear equations and apply them to real-world problems. Remember to always check your solution and use the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation.

Additional Resources

For more information on solving linear equations, check out the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Final Thoughts

Solving linear equations is a fundamental skill that requires practice and patience. By following the steps outlined in this article, you can develop the skills necessary to solve linear equations and apply them to real-world problems. Remember to always check your solution and use the reciprocal of the fraction to cancel out the fraction on the left-hand side of the equation.