What Is The Solution To This Equation? 2 X + 6 = 20 2x + 6 = 20 2 X + 6 = 20 A. X = 13 X = 13 X = 13 B. X = 52 X = 52 X = 52 C. X = 7 X = 7 X = 7 D. X = 28 X = 28 X = 28

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, $2x + 6 = 20$, and explore the different solution options.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

The Equation $2x + 6 = 20$

The equation $2x + 6 = 20$ is a linear equation in which the highest power of the variable $x$ is 1. To solve this equation, we need to isolate the variable $x$.

Step 1: Subtract 6 from Both Sides

The first step in solving the equation is to subtract 6 from both sides of the equation. This will help us get rid of the constant term on the left-hand side of the equation.

$2x + 6 - 6 = 20 - 6$

This simplifies to:

$2x = 14$

Step 2: Divide Both Sides by 2

Now that we have $2x = 14$, we can divide both sides of the equation by 2 to solve for $x$.

$\frac{2x}{2} = \frac{14}{2}$

This simplifies to:

$x = 7$

Solution Options

Now that we have solved the equation, let's take a look at the solution options provided.

A. $x = 13$ B. $x = 52$ C. $x = 7$ D. $x = 28$

As we can see, the correct solution is option C, $x = 7$.

Why is $x = 7$ the Correct Solution?

The correct solution, $x = 7$, is the only option that satisfies the original equation $2x + 6 = 20$. If we substitute $x = 7$ into the original equation, we get:

$2(7) + 6 = 14 + 6 = 20$

This shows that $x = 7$ is indeed the correct solution to the equation.

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a step-by-step approach. In this article, we solved the equation $2x + 6 = 20$ and explored the different solution options. We found that the correct solution is $x = 7$, and we explained why this is the case.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Always start by simplifying the equation by combining like terms.
• Use inverse operations to isolate the variable.
• Check your solution by substituting it back into the original equation.

By following these tips and tricks, you can become proficient in solving linear equations and tackle more complex equations with confidence.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

• Not simplifying the equation before solving it.
• Not using inverse operations to isolate the variable.
• Not checking the solution by substituting it back into the original equation.

By avoiding these common mistakes, you can ensure that your solutions are accurate and reliable.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

By understanding how to solve linear equations, you can apply this knowledge to real-world problems and make informed decisions.

Conclusion

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Introduction

In our previous article, we explored the concept of linear equations and solved the equation $2x + 6 = 20$. In this article, we will answer some 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 (in this case, $x$) is 1. Linear equations 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. This can be done by using inverse operations, such as addition, subtraction, multiplication, and division. For example, to solve the equation $2x + 6 = 20$, you would subtract 6 from both sides and then divide both sides by 2.

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 $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 6 = 20$ is a linear equation.

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

A: To check your solution to a linear equation, you need to substitute the solution back into the original equation and see if it is true. For example, if you solve the equation $2x + 6 = 20$ and get $x = 7$, you would substitute $x = 7$ back into the original equation to get $2(7) + 6 = 14 + 6 = 20$, which is true.

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

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

• Not simplifying the equation before solving it.
• Not using inverse operations to isolate the variable.
• Not checking the solution by substituting it back into the original equation.

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

A: To solve a linear equation with fractions, you need to get rid of the fractions by multiplying both sides of the equation by the denominator. For example, to solve the equation $\frac{2x}{3} + 2 = 4$, you would multiply both sides by 3 to get $2x + 6 = 12$.

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

A: To solve a linear equation with decimals, you need to get rid of the decimals by multiplying both sides of the equation by 10. For example, to solve the equation $2x + 0.6 = 2.2$, you would multiply both sides by 10 to get $20x + 6 = 22$.

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

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your solution by substituting it back into the original equation to make sure it's true.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it requires a step-by-step approach. In this article, we answered some frequently asked questions about solving linear equations and provided tips and tricks to help you become proficient in solving linear equations. By following the advice outlined in this article, you can tackle more complex equations with confidence.

Tips and Tricks

Here are some additional tips and tricks to help you solve linear equations:

• Always start by simplifying the equation by combining like terms.
• Use inverse operations to isolate the variable.
• Check your solution by substituting it back into the original equation.
• Use a calculator to check your solution, but always double-check it by hand.

By following these tips and tricks, you can become proficient in solving linear equations and tackle more complex equations with confidence.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

By understanding how to solve linear equations, you can apply this knowledge to real-world problems and make informed decisions.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it requires a step-by-step approach. In this article, we answered some frequently asked questions about solving linear equations and provided tips and tricks to help you become proficient in solving linear equations. By following the advice outlined in this article, you can tackle more complex equations with confidence.