Mikayla And Jesse Both Solved The Equation $x - 15 = 12 - 8$ Using Substitution.Mikayla Says The Answer Is $x = 19$, And Jesse Says The Answer Is $x = 27$.Which Student Is Correct, And How Do You Know? Show Your Work And

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Introduction

In mathematics, equations are a fundamental concept that help us solve problems and understand relationships between variables. When solving equations, it's essential to follow the correct steps to ensure accuracy. In this article, we'll delve into the equation x−15=12−8x - 15 = 12 - 8 and analyze the solutions provided by Mikayla and Jesse. We'll examine their work, identify any errors, and determine which student is correct.

The Equation

The given equation is:

x−15=12−8x - 15 = 12 - 8

Mikayla's Solution

Mikayla's solution is as follows:

  1. Subtract 15 from both sides: x−15−15=12−8−15x - 15 - 15 = 12 - 8 - 15
  2. Simplify: x−30=−3x - 30 = -3
  3. Add 30 to both sides: x−30+30=−3+30x - 30 + 30 = -3 + 30
  4. Simplify: x=27x = 27

Jesse's Solution

Jesse's solution is as follows:

  1. Subtract 8 from both sides: x−15−8=12−8−8x - 15 - 8 = 12 - 8 - 8
  2. Simplify: x−23=4x - 23 = 4
  3. Add 23 to both sides: x−23+23=4+23x - 23 + 23 = 4 + 23
  4. Simplify: x=27x = 27

Analysis

At first glance, both Mikayla and Jesse's solutions seem to be correct, as they both arrive at the same answer, x=27x = 27. However, let's take a closer look at their work.

Mikayla's solution is incorrect because she subtracted 15 from both sides, but then added 30 to both sides. This is a mistake, as she should have added 15 to both sides to maintain the equality.

Jesse's solution is also incorrect because he subtracted 8 from both sides, but then added 23 to both sides. Again, this is a mistake, as he should have added 8 to both sides to maintain the equality.

Correct Solution

To solve the equation correctly, we need to follow the correct order of operations. Here's the correct solution:

  1. Subtract 15 from both sides: x−15−15=12−8−15x - 15 - 15 = 12 - 8 - 15
  2. Simplify: x−30=−3x - 30 = -3
  3. Add 30 to both sides: x−30+30=−3+30x - 30 + 30 = -3 + 30
  4. Simplify: x=27x = 27

However, we can simplify the equation further by combining the constants on the right-hand side:

x−15=4x - 15 = 4

Now, we can add 15 to both sides to solve for x:

x−15+15=4+15x - 15 + 15 = 4 + 15

x=19x = 19

Conclusion

In conclusion, Mikayla's solution is incorrect, and Jesse's solution is also incorrect. The correct solution to the equation x−15=12−8x - 15 = 12 - 8 is x=19x = 19. We hope this analysis has helped you understand the importance of following the correct order of operations when solving equations.

Discussion

What do you think? Do you agree with our analysis? Have you ever encountered a similar situation where two students arrived at different answers? Share your thoughts and experiences in the comments below!

Additional Resources

If you're struggling with equations or need additional practice, here are some resources to help you:

  • Khan Academy: Equations and Inequalities
  • Mathway: Equation Solver
  • IXL: Equations and Inequalities

Introduction

In our previous article, we analyzed the equation x−15=12−8x - 15 = 12 - 8 and determined that Mikayla's solution was incorrect, while Jesse's solution was also incorrect. The correct solution to the equation is x=19x = 19. In this article, we'll answer some frequently asked questions related to the equation and provide additional insights to help you better understand the concept.

Q&A Session

Q: Why did Mikayla and Jesse arrive at different answers?

A: Mikayla and Jesse both used the substitution method to solve the equation, but they made different mistakes along the way. Mikayla subtracted 15 from both sides, but then added 30 to both sides, while Jesse subtracted 8 from both sides, but then added 23 to both sides. These mistakes led to incorrect solutions.

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

A: When solving equations, it's essential to follow the correct order of operations. This 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: How can I avoid making mistakes when solving equations?

A: To avoid making mistakes when solving equations, make sure to:

  1. Read the equation carefully and understand what's being asked.
  2. Follow the correct order of operations.
  3. Check your work by plugging the solution back into the original equation.
  4. Use a calculator or online tools to verify your solution.

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

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

  1. Not following the correct order of operations.
  2. Not checking your work.
  3. Not using a calculator or online tools to verify your solution.
  4. Not considering the possibility of multiple solutions.

Q: How can I practice solving equations?

A: To practice solving equations, try the following:

  1. Use online resources, such as Khan Academy or Mathway, to practice solving equations.
  2. Work on worksheets or practice problems from your textbook.
  3. Ask a teacher or tutor for help.
  4. Join a study group or online community to practice solving equations with others.

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

A: Solving equations has many real-world applications, including:

  1. Science: Solving equations is essential in scientific fields, such as physics and chemistry.
  2. Engineering: Solving equations is used in engineering to design and optimize systems.
  3. Finance: Solving equations is used in finance to calculate interest rates and investment returns.
  4. Computer Science: Solving equations is used in computer science to develop algorithms and solve problems.

Conclusion

In conclusion, solving equations is an essential skill that has many real-world applications. By following the correct order of operations and avoiding common mistakes, you can become proficient in solving equations. Remember to practice regularly and seek help when needed. With dedication and persistence, you'll become a math whiz in no time!

Additional Resources

If you're struggling with equations or need additional practice, here are some resources to help you:

  • Khan Academy: Equations and Inequalities
  • Mathway: Equation Solver
  • IXL: Equations and Inequalities
  • Wolfram Alpha: Equation Solver

Remember, practice makes perfect! Keep practicing, and you'll become a math whiz in no time!