The Given Equation Has Been Solved In The Table.$[ \begin{tabular}{|c|c|} \hline \textbf{Step} & \textbf{Statement} \ \hline 1 & 2 3 X − 9 = − 13 \frac{2}{3} X - 9 = -13 3 2 ​ X − 9 = − 13 \ \hline 2 & 2 3 X − 9 + 9 = − 13 + 9 \frac{2}{3} X - 9 + 9 = -13 + 9 3 2 ​ X − 9 + 9 = − 13 + 9 \ \hline 3 & 2 3 X = − 4 \frac{2}{3} X = -4 3 2 ​ X = − 4

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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 the solution process.

The Given Equation

The given equation is:

23x−9=−13\frac{2}{3} x - 9 = -13

This equation involves a fraction and a constant term. Our goal is to isolate the variable xx and find its value.

Step-by-Step Solution

Step 1: Add 9 to Both Sides of the Equation

The first step in solving the equation is to add 9 to both sides of the equation. This will help us eliminate the constant term on the left-hand side of the equation.

23x−9+9=−13+9\frac{2}{3} x - 9 + 9 = -13 + 9

By adding 9 to both sides of the equation, we get:

23x=−4\frac{2}{3} x = -4

Step 2: Multiply Both Sides of the Equation by 3/2

The next step is to multiply both sides of the equation by 3/2. This will help us eliminate the fraction on the left-hand side of the equation.

23x×32=−4×32\frac{2}{3} x \times \frac{3}{2} = -4 \times \frac{3}{2}

By multiplying both sides of the equation by 3/2, we get:

x=−6x = -6

Step 3: Check the Solution

The final step is to check the solution by plugging it back into the original equation.

23x−9=−13\frac{2}{3} x - 9 = -13

Substituting x=−6x = -6 into the equation, we get:

23(−6)−9=−13\frac{2}{3} (-6) - 9 = -13

Simplifying the equation, we get:

−4−9=−13-4 - 9 = -13

Which is true.

Conclusion

In this article, we solved a given equation step by step using a table to illustrate the solution process. We added 9 to both sides of the equation to eliminate the constant term, multiplied both sides of the equation by 3/2 to eliminate the fraction, and checked the solution by plugging it back into the original equation. The final solution is x=−6x = -6.

Discussion

Solving equations is a fundamental concept in mathematics 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 focused on solving a given equation step by step, using a table to illustrate the solution process.

Tips and Tricks

  • When solving equations, it's essential to follow the order of operations (PEMDAS) to ensure that the equation is solved correctly.
  • When adding or subtracting fractions, it's essential to have a common denominator to ensure that the equation is solved correctly.
  • When multiplying or dividing fractions, it's essential to multiply or divide the numerators and denominators separately to ensure that the equation is solved correctly.

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, forces, and energies.
  • Engineering: Solving equations is essential in engineering to design and optimize systems, structures, and processes.
  • Economics: Solving equations is essential in economics to model and analyze economic systems, markets, and behaviors.

Conclusion

Introduction

In our previous article, we solved a given equation step by step using a table to illustrate the solution process. We added 9 to both sides of the equation to eliminate the constant term, multiplied both sides of the equation by 3/2 to eliminate the fraction, and checked the solution by plugging it back into the original equation. The final solution is x=−6x = -6. In this article, we will provide a Q&A section to address any questions or concerns that readers may have.

Q&A

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

A: The first step in solving the equation is to add 9 to both sides of the equation. This will help us eliminate the constant term on the left-hand side of the equation.

Q: Why do we need to add 9 to both sides of the equation?

A: We need to add 9 to both sides of the equation to eliminate the constant term on the left-hand side of the equation. This will help us isolate the variable xx.

Q: What is the next step in solving the equation?

A: The next step in solving the equation is to multiply both sides of the equation by 3/2. This will help us eliminate the fraction on the left-hand side of the equation.

Q: Why do we need to multiply both sides of the equation by 3/2?

A: We need to multiply both sides of the equation by 3/2 to eliminate the fraction on the left-hand side of the equation. This will help us isolate the variable xx.

Q: How do we check the solution?

A: We check the solution by plugging it back into the original equation. If the equation is true, then the solution is correct.

Q: What is the final solution?

A: The final solution is x=−6x = -6.

Q: Can you provide more examples of solving equations?

A: Yes, we can provide more examples of solving equations. Please let us know what type of equation you would like to see solved, and we will do our best to provide a step-by-step solution.

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

A: Solving equations has numerous real-world applications in various fields, including physics, engineering, and economics. We can provide more information on these applications if you are interested.

Tips and Tricks

  • When solving equations, it's essential to follow the order of operations (PEMDAS) to ensure that the equation is solved correctly.
  • When adding or subtracting fractions, it's essential to have a common denominator to ensure that the equation is solved correctly.
  • When multiplying or dividing fractions, it's essential to multiply or divide the numerators and denominators separately to ensure that the equation is solved correctly.

Common Mistakes

  • Not following the order of operations (PEMDAS) when solving equations.
  • Not having a common denominator when adding or subtracting fractions.
  • Not multiplying or dividing the numerators and denominators separately when multiplying or dividing fractions.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics 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 provided a Q&A section to address any questions or concerns that readers may have. We hope that this article has been helpful in understanding the concept of solving equations.

Additional Resources

  • For more information on solving equations, please refer to our previous article on the topic.
  • For more examples of solving equations, please let us know what type of equation you would like to see solved, and we will do our best to provide a step-by-step solution.
  • For more information on real-world applications of solving equations, please let us know what type of application you are interested in, and we will do our best to provide more information.