Solve For The Value Of $x$ That Makes The Equation True. Simplify Your Answer Completely.$\frac{1}{5}(x+8) = 16$

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 linear equation, $\frac{1}{5}(x+8) = 16$, and provide a step-by-step guide on how to simplify the solution completely.

Understanding the Equation

The given equation is $\frac{1}{5}(x+8) = 16$. To solve for the value of $x$, we need to isolate the variable $x$ on one side of the equation. The equation involves a fraction, which can be challenging to work with. However, with the correct steps, we can simplify the equation and find the value of $x$.

Step 1: Multiply Both Sides by 5

To eliminate the fraction, we can multiply both sides of the equation by 5. This will help us get rid of the denominator and make the equation easier to work with.

$\frac{1}{5}(x+8) = 16$

Multiplying both sides by 5:

$1(x+8) = 5(16)$

Simplifying the equation:

$x+8 = 80$

Step 2: Subtract 8 from Both Sides

Now that we have the equation $x+8 = 80$, we can isolate the variable $x$ by subtracting 8 from both sides. This will help us get rid of the constant term and find the value of $x$.

$x+8 = 80$

Subtracting 8 from both sides:

$x = 80 - 8$

Simplifying the equation:

$x = 72$

Conclusion

In this article, we solved the linear equation $\frac{1}{5}(x+8) = 16$ using a step-by-step approach. We multiplied both sides by 5 to eliminate the fraction, and then subtracted 8 from both sides to isolate the variable $x$. The final solution is $x = 72$. This example demonstrates the importance of following the correct steps when solving linear equations.

Tips and Tricks

When solving linear equations, it's essential to follow the correct order of operations. Here are some tips and tricks to help you simplify the solution:

• Multiply both sides of the equation by the same value to eliminate fractions.
• Add or subtract the same value from both sides to isolate the variable.
• Use inverse operations to simplify the equation.
• Check your solution by plugging it back into the original equation.

By following these tips and tricks, you can become more confident in solving linear equations and simplify your solutions completely.

Real-World Applications

Linear equations have numerous real-world applications in various fields, including:

• Physics: Linear equations are used to describe the motion of objects, such as the trajectory of a projectile.
• 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, such as supply and demand curves.

In conclusion, solving linear equations is a crucial skill for students to master. By following the correct steps and using inverse operations, you can simplify the solution and find the value of the variable. The examples and tips provided in this article demonstrate the importance of linear equations in real-world applications.

Common Mistakes to Avoid

When solving linear equations, it's essential to avoid common mistakes that can lead to incorrect solutions. Here are some common mistakes to avoid:

• Not following the correct order of operations.
• Not eliminating fractions by multiplying both sides by the same value.
• Not checking the solution by plugging it back into the original equation.

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

Conclusion

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Introduction

In our previous article, we solved the linear equation $\frac{1}{5}(x+8) = 16$ using a step-by-step approach. We multiplied both sides by 5 to eliminate the fraction, and then subtracted 8 from both sides to isolate the variable $x$. The final solution is $x = 72$. In this article, we will provide a Q&A guide to help you better understand 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. It 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 inverse operations, such as addition, subtraction, multiplication, and division.

Q: What is an inverse operation?

A: An inverse operation is an operation that "reverses" another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to follow these steps:

1. Identify the variable and the constant term on the same side of the equation.
2. Use the inverse operation to eliminate the constant term.
3. Simplify the equation to isolate the variable.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation and see if it is true. If the solution satisfies the equation, then it 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 following the correct order of operations.
• Not eliminating fractions by multiplying both sides by the same value.
• Not checking the solution by plugging it back into the original equation.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to follow these steps:

1. Combine like terms.
2. Eliminate any fractions by multiplying both sides by the same value.
3. Simplify the equation to isolate the variable.

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

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

• Physics: Linear equations are used to describe the motion of objects, such as the trajectory of a projectile.
• 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, such as supply and demand curves.

Conclusion

In this article, we provided a Q&A guide to help you better understand the concept of solving linear equations. We covered topics such as the order of operations, inverse operations, and common mistakes to avoid. By following the correct steps and using inverse operations, you can simplify the solution and find the value of the variable.