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

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Introduction

In mathematics, solving equations is a fundamental concept that forms the basis of various mathematical operations. Equations are statements that express the equality of two mathematical expressions, and solving them involves finding the value of the variable that makes the equation true. 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 x2−7=−7\frac{x}{2}-7=-7. Our goal is to solve for the value of xx that makes this equation true.

Step-by-Step Solution

Step 1: Add 7 to Both Sides of the Equation

The first step in solving the equation is to add 7 to both sides of the equation. This will help us isolate the term containing the variable xx.

x2−7+7=−7+7\frac{x}{2}-7+7=-7+7

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

By adding 7 to both sides of the equation, we get:

x2=0\frac{x}{2}=0

Step 2: Multiply Both Sides of the Equation by 2

The next step is to multiply both sides of the equation by 2. This will help us eliminate the fraction and solve for the value of xx.

2⋅x2=2⋅02 \cdot \frac{x}{2}=2 \cdot 0

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

By multiplying both sides of the equation by 2, we get:

x=0x=0

Discussion

In this article, we have solved a given equation step by step, using a table to illustrate each step of the solution process. The equation was x2−7=−7\frac{x}{2}-7=-7, and we solved for the value of xx that makes this equation true. By adding 7 to both sides of the equation and then multiplying both sides by 2, we were able to isolate the term containing the variable xx and solve for its value.

Conclusion

Solving equations is a fundamental concept in mathematics that forms the basis of various mathematical operations. In this article, we have solved a given equation step by step, using a table to illustrate each step of the solution process. By following these steps, we were able to solve for the value of xx that makes the equation true. We hope that this article has provided a clear and concise explanation of how to solve equations, and we encourage readers to practice solving equations on their own.

Additional Resources

For additional resources on solving equations, we recommend the following:

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

FAQs

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the term containing the variable and then solve for its 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.

Q: How do I graph an equation?

A: To graph an equation, you need to plot the points that satisfy the equation and then connect them to form a graph.

Glossary

  • Equation: A statement that expresses the equality of two mathematical expressions.
  • Variable: A symbol that represents a value that can change.
  • Constant: A value that does not change.
  • Linear equation: An equation in which the highest power of the variable is 1.
  • Quadratic equation: An equation in which the highest power of the variable is 2.
  • Graph: A visual representation of an equation.
    Frequently Asked Questions (FAQs) on Solving Equations ===========================================================

Introduction

Solving equations is a fundamental concept in mathematics that forms the basis of various mathematical operations. In our previous article, we provided a step-by-step solution to a given equation using a table to illustrate each step of the solution process. In this article, we will answer some frequently asked questions (FAQs) on solving equations.

Q&A

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It is a mathematical sentence that states that two expressions are equal.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the term containing the variable and then solve for its value. 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 x+3=5x + 3 = 5 is a linear equation, while the equation x2+4x+4=0x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I graph an equation?

A: To graph an equation, you need to plot the points that satisfy the equation and then connect them to form a graph. This can be done using a coordinate plane and a ruler or a graphing calculator.

Q: What is the order of operations when solving an equation?

A: The order of operations when solving an equation is:

  1. Parentheses: Evaluate any 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 simplify an equation?

A: To simplify an equation, you need to combine like terms and eliminate any unnecessary variables or constants. 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 solution and a solution set?

A: A solution to an equation is a value that makes the equation true. A solution set is a set of all possible solutions to an equation.

Q: How do I find the solution set of an equation?

A: To find the solution set of an equation, you need to solve the equation for all possible values of the variable. This can be done by using algebraic methods, such as factoring or using the quadratic formula.

Common Mistakes to Avoid

When solving equations, there are several common mistakes to avoid:

  • Not following the order of operations: Make sure to follow the order of operations when solving an equation.
  • Not simplifying the equation: Make sure to simplify the equation by combining like terms and eliminating any unnecessary variables or constants.
  • Not checking for extraneous solutions: Make sure to check for extraneous solutions by plugging the solution back into the original equation.
  • Not using the correct method: Make sure to use the correct method for solving the equation, such as factoring or using the quadratic formula.

Conclusion

Solving equations is a fundamental concept in mathematics that forms the basis of various mathematical operations. In this article, we have answered some frequently asked questions (FAQs) on solving equations, including questions on the difference between a linear equation and a quadratic equation, how to graph an equation, and how to simplify an equation. We hope that this article has provided a clear and concise explanation of how to solve equations and has helped to clarify any confusion.

Additional Resources

For additional resources on solving equations, we recommend the following:

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

Glossary

  • Equation: A statement that expresses the equality of two mathematical expressions.
  • Variable: A symbol that represents a value that can change.
  • Constant: A value that does not change.
  • Linear equation: An equation in which the highest power of the variable is 1.
  • Quadratic equation: An equation in which the highest power of the variable is 2.
  • Graph: A visual representation of an equation.
  • Solution: A value that makes an equation true.
  • Solution set: A set of all possible solutions to an equation.