The Given Equation Has Been Solved In The Table.$[ \begin{tabular}{|c|c|} \hline Step & Statement \ \hline 1 & X 2 − 7 = − 7 \frac{x}{2}-7=-7 2 X ​ − 7 = − 7 \ \hline 2 & X 2 − 7 + 7 = − 7 + 7 \frac{x}{2}-7+7=-7+7 2 X ​ − 7 + 7 = − 7 + 7 \ \hline 3 & X 2 = 0 \frac{x}{2}=0 2 X ​ = 0 \ \hline 4 & 2 ⋅ X 2 = 2 ⋅ 0 2 \cdot \frac{x}{2}=2 \cdot 0 2 ⋅ 2 X ​ = 2 ⋅ 0

Introduction

In mathematics, solving equations is a fundamental concept that forms the basis of various mathematical operations. Equations are used to represent relationships between variables, and solving them is essential to understand the underlying relationships. In this article, we will focus on solving a given equation step by step, using a table to illustrate each step of the solution process.

The Given Equation

The given equation is:

$\frac{x}{2}-7=-7$

This equation involves a variable $x$ and a constant $-7$. Our goal is to isolate the variable $x$ and find its value.

Step-by-Step Solution

The solution to the given equation is presented in the following table:

Step 1: Add 7 to Both Sides of the Equation

Step	Statement
1	$\frac{x}{2}-7=-7$
2	$\frac{x}{2}-7+7=-7+7$

In this step, we add 7 to both sides of the equation to eliminate the constant term. This results in:

$\frac{x}{2}=0$

Step 2: Multiply Both Sides of the Equation by 2

Step	Statement
3	$\frac{x}{2}=0$
4	$2 \cdot \frac{x}{2}=2 \cdot 0$

In this step, we multiply both sides of the equation by 2 to eliminate the fraction. This results in:

$x=0$

Discussion

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The solution to the given equation is $x=0$. This means that the value of the variable $x$ is 0. The solution process involved adding 7 to both sides of the equation to eliminate the constant term, and then multiplying both sides of the equation by 2 to eliminate the fraction.

Conclusion

In this article, we solved a given equation step by step, using a table to illustrate each step of the solution process. The solution to the given equation is $x=0$. This demonstrates the importance of following the order of operations and using algebraic manipulations to solve equations.

Key Takeaways

• Solving equations involves using algebraic manipulations to isolate the variable.
• Adding or subtracting the same value to both sides of an equation does not change the equation.
• Multiplying or dividing both sides of an equation by the same non-zero value does not change the equation.

Real-World Applications

Solving equations has numerous real-world applications in various fields, including:

• Physics: Solving equations is essential in physics to describe the motion of objects and predict their behavior.
• Engineering: Solving equations is used in engineering to design and optimize systems, such as bridges and buildings.
• Economics: Solving equations is used in economics to model economic systems and make predictions about economic trends.

Common Mistakes to Avoid

When solving equations, it's essential to avoid common mistakes, such as:

• Forgetting to add or subtract the same value to both sides of the equation.
• Forgetting to multiply or divide both sides of the equation by the same non-zero value.
• Not following the order of operations.

Tips and Tricks

When solving equations, here are some tips and tricks to keep in mind:

• Use algebraic manipulations to isolate the variable.
• Check your work by plugging the solution back into the original equation.
• Use a table or diagram to visualize the solution process.

Conclusion

Introduction

In our previous article, we solved a given equation step by step, using a table to illustrate each step of the solution process. In this article, we will continue to explore the given equation and answer some frequently asked questions (FAQs) related to the solution process.

Q&A

Q: What is the given equation?

A: The given equation is $\frac{x}{2}-7=-7$.

Q: What is the solution to the given equation?

A: The solution to the given equation is $x=0$.

Q: How do I solve the given equation?

A: To solve the given equation, you can follow the step-by-step solution process outlined in our previous article. This involves adding 7 to both sides of the equation to eliminate the constant term, and then multiplying both sides of the equation by 2 to eliminate the fraction.

Q: What is the order of operations when solving equations?

A: When solving equations, it's essential to follow the order of operations, which includes:

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

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

• Forgetting to add or subtract the same value to both sides of the equation.
• Forgetting to multiply or divide both sides of the equation by the same non-zero value.
• Not following the order of operations.

Q: How do I check my work when solving equations?

A: To check your work when solving equations, you can plug the solution back into the original equation and verify that it is true. This ensures that your solution is correct and helps you avoid making mistakes.

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

A: Solving equations has numerous real-world applications in various fields, including:

• Physics: Solving equations is essential in physics to describe the motion of objects and predict their behavior.
• Engineering: Solving equations is used in engineering to design and optimize systems, such as bridges and buildings.
• Economics: Solving equations is used in economics to model economic systems and make predictions about economic trends.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that has numerous real-world applications. By following the order of operations and using algebraic manipulations, we can solve equations and understand the underlying relationships between variables. We hope that this Q&A article has helped to clarify any questions you may have had about the solution process.

Additional Resources

For further learning and practice, we recommend the following resources:

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

Tips and Tricks

When solving equations, here are some additional tips and tricks to keep in mind:

• Use algebraic manipulations to isolate the variable.
• Check your work by plugging the solution back into the original equation.
• Use a table or diagram to visualize the solution process.
• Practice, practice, practice! The more you practice solving equations, the more comfortable you will become with the solution process.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that has numerous real-world applications. By following the order of operations and using algebraic manipulations, we can solve equations and understand the underlying relationships between variables. We hope that this Q&A article has helped to clarify any questions you may have had about the solution process.