Solve X 6 = 20 \frac{x}{6} = 20 6 X ​ = 20 .A) X = 14 X = 14 X = 14 B) X = 120 X = 120 X = 120 C) X = 3 X = 3 X = 3 D) X = 26 X = 26 X = 26

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 simple linear equation, $\frac{x}{6} = 20$, and explore the different methods and techniques used to find the solution.

What is a Linear Equation?

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. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation $\frac{x}{6} = 20$

The equation $\frac{x}{6} = 20$ is a simple linear equation that can be solved using basic algebraic manipulation. To solve this equation, we need to isolate the variable $x$ on one side of the equation.

Step 1: Multiply Both Sides by 6

To isolate $x$, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 6, which is the denominator of the fraction.

$\frac{x}{6} = 20$

$6 \times \frac{x}{6} = 6 \times 20$

$x = 120$

Step 2: Check the Solution

Now that we have found the solution, we need to check if it is correct. We can do this by plugging the solution back into the original equation.

$\frac{x}{6} = 20$

$\frac{120}{6} = 20$

$20 = 20$

Since the solution satisfies the original equation, we can conclude that the solution is correct.

Conclusion

Solving linear equations is an essential skill for students to master. In this article, we have focused on solving the equation $\frac{x}{6} = 20$ using basic algebraic manipulation. We have shown that the solution is $x = 120$, and we have checked the solution to ensure that it is correct. With practice and patience, students can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems.

Answer Key

A) $x = 14$ is incorrect B) $x = 120$ is correct C) $x = 3$ is incorrect D) $x = 26$ is incorrect

Tips and Tricks

• When solving linear equations, it is essential to isolate the variable on one side of the equation.
• To get rid of fractions, multiply both sides of the equation by the denominator.
• Check the solution by plugging it back into the original equation.

Real-World Applications

Solving linear equations has numerous real-world applications, including:

• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the area and perimeter of shapes
• Solving problems in physics, engineering, and economics

Common Mistakes

• Failing to isolate the variable on one side of the equation
• Not checking the solution
• Making errors when multiplying or dividing both sides of the equation

Conclusion

Introduction

In our previous article, we explored the concept of linear equations and solved the equation $\frac{x}{6} = 20$. In this article, we will provide a Q&A guide to help students understand and master the concept of 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: 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. You can do this by using basic algebraic manipulation, such as adding, subtracting, multiplying, or dividing both sides of the equation.

Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to simplify the equation by combining like terms. This will help you to isolate the variable and make it easier to solve.

Q: How do I get rid of fractions in a linear equation?

A: To get rid of fractions in a linear equation, you need to multiply both sides of the equation by the denominator. This will help you to eliminate the fraction and make it easier to solve.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. In other words, a linear equation can be written in the form $ax + b = c$, while a quadratic equation can be written in the form $ax^2 + bx + c = 0$.

Q: Can I use a calculator to solve a linear equation?

A: Yes, you can use a calculator to solve a linear equation. However, it is essential to understand the concept of solving linear equations and to be able to solve them by hand. This will help you to develop your problem-solving skills and to understand the underlying mathematics.

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

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

• Failing to isolate the variable on one side of the equation
• Not checking the solution
• Making errors when multiplying or dividing both sides of the equation
• Not simplifying the equation by combining like terms

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through a series of problems, such as:

• Solving simple linear equations, such as $\frac{x}{6} = 20$
• Solving more complex linear equations, such as $2x + 5 = 11$
• Solving linear equations with fractions, such as $\frac{x}{3} + 2 = 5$

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

A: Solving linear equations has numerous real-world applications, including:

• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the area and perimeter of shapes
• Solving problems in physics, engineering, and economics

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By following the steps outlined in this article, students can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems. With practice and patience, students can master the art of solving linear equations and become confident problem-solvers.

Answer Key

Q1: A linear equation is an equation in which the highest power of the variable(s) is 1. Q2: To solve a linear equation, you need to isolate the variable on one side of the equation. Q3: The first step in solving a linear equation is to simplify the equation by combining like terms. Q4: To get rid of fractions in a linear equation, you need to multiply both sides of the equation by the denominator. Q5: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. Q6: Yes, you can use a calculator to solve a linear equation. Q7: Some common mistakes to avoid when solving linear equations include failing to isolate the variable on one side of the equation, not checking the solution, making errors when multiplying or dividing both sides of the equation, and not simplifying the equation by combining like terms. Q8: You can practice solving linear equations by working through a series of problems. Q9: Solving linear equations has numerous real-world applications, including calculating the cost of goods and services, determining the amount of time it takes to complete a task, finding the area and perimeter of shapes, and solving problems in physics, engineering, and economics.