Marlena Solved The Equation $2x + 5 = -10 - X$. Her Steps Are Shown Below.1. $3x + 5 = -10$2. $3x = -15$3. $x = -5$Use The Drop-down Menus To Justify Marlena's Work In Each Step Of The Process.Step 1:

Marlena's Algebraic Journey: A Step-by-Step Analysis of the Equation $2x + 5 = -10 - x$

In algebra, solving equations is a fundamental concept that requires a deep understanding of mathematical operations and properties. Marlena, a diligent student, has attempted to solve the equation $2x + 5 = -10 - x$. In this article, we will analyze each step of her process, providing justification for her work and highlighting any potential errors or areas for improvement.

Step 1: $2x + 5 = -10 - x$

Initial Equation

Marlena starts with the given equation: $2x + 5 = -10 - x$. This is a linear equation with two variables, $x$, and a constant term.

Step 1: Justification

Marlena's first step is to add $x$ to both sides of the equation, resulting in $3x + 5 = -10$. This step is justified by the addition property of equality, which states that when we add the same value to both sides of an equation, the equation remains balanced.

2x + 5 = -10 - x
2x + x + 5 = -10
3x + 5 = -10

Error or Improvement

Marlena's work is correct up to this point. However, it's worth noting that she could have simplified the equation further by combining like terms on the left-hand side.

Step 2: $3x + 5 = -10$

Simplified Equation

Marlena's next step is to subtract 5 from both sides of the equation, resulting in $3x = -15$. This step is justified by the subtraction property of equality, which states that when we subtract the same value from both sides of an equation, the equation remains balanced.

3x + 5 = -10
3x + 5 - 5 = -10 - 5
3x = -15

Error or Improvement

Marlena's work is correct up to this point. However, it's worth noting that she could have simplified the equation further by combining like terms on the left-hand side.

Step 3: $x = -5$

Final Solution

Marlena's final step is to divide both sides of the equation by 3, resulting in $x = -5$. This step is justified by the division property of equality, which states that when we divide both sides of an equation by a non-zero value, the equation remains balanced.

3x = -15
3x / 3 = -15 / 3
x = -5

Error or Improvement

Marlena's work is correct, and she has successfully solved the equation. However, it's worth noting that she could have checked her solution by substituting $x = -5$ back into the original equation to verify that it is true.

In conclusion, Marlena's algebraic journey has been a successful one. She has demonstrated a clear understanding of mathematical operations and properties, and has successfully solved the equation $2x + 5 = -10 - x$. By analyzing each step of her process, we have identified areas for improvement and highlighted the importance of justification and verification in mathematical problem-solving.

Recommendations for Future Improvement

• Marlena should strive to simplify equations further by combining like terms on the left-hand side.
• Marlena should verify her solution by substituting $x = -5$ back into the original equation to ensure that it is true.
• Marlena should continue to practice solving linear equations with two variables to build her confidence and fluency.

By following these recommendations, Marlena will be well on her way to becoming a proficient algebraic problem-solver.
Marlena's Algebraic Journey: A Step-by-Step Analysis of the Equation $2x + 5 = -10 - x$ - Q&A

In our previous article, we analyzed Marlena's steps in solving the equation $2x + 5 = -10 - x$. We identified areas for improvement and highlighted the importance of justification and verification in mathematical problem-solving. In this article, we will address some common questions and concerns related to Marlena's algebraic journey.

Q: Why did Marlena add $x$ to both sides of the equation in Step 1?

A: Marlena added $x$ to both sides of the equation to isolate the variable $x$ on one side of the equation. This is a common technique used in algebra to solve equations.

Q: Is it correct to add $x$ to both sides of the equation in Step 1?

A: Yes, it is correct to add $x$ to both sides of the equation in Step 1. This is justified by the addition property of equality, which states that when we add the same value to both sides of an equation, the equation remains balanced.

Q: Why did Marlena subtract 5 from both sides of the equation in Step 2?

A: Marlena subtracted 5 from both sides of the equation to isolate the variable $x$ on one side of the equation. This is a common technique used in algebra to solve equations.

Q: Is it correct to subtract 5 from both sides of the equation in Step 2?

A: Yes, it is correct to subtract 5 from both sides of the equation in Step 2. This is justified by the subtraction property of equality, which states that when we subtract the same value from both sides of an equation, the equation remains balanced.

Q: Why did Marlena divide both sides of the equation by 3 in Step 3?

A: Marlena divided both sides of the equation by 3 to solve for the variable $x$. This is a common technique used in algebra to solve equations.

Q: Is it correct to divide both sides of the equation by 3 in Step 3?

A: Yes, it is correct to divide both sides of the equation by 3 in Step 3. This is justified by the division property of equality, which states that when we divide both sides of an equation by a non-zero value, the equation remains balanced.

Q: What is the final solution to the equation $2x + 5 = -10 - x$?

A: The final solution to the equation $2x + 5 = -10 - x$ is $x = -5$.

Q: How can I verify that the solution is correct?

A: To verify that the solution is correct, you can substitute $x = -5$ back into the original equation and check if it is true.

Q: What are some common mistakes to avoid when solving linear equations with two variables?

A: Some common mistakes to avoid when solving linear equations with two variables include:

• Not following the order of operations
• Not isolating the variable on one side of the equation
• Not checking the solution by substituting it back into the original equation

By following these tips and avoiding common mistakes, you can become proficient in solving linear equations with two variables.

In conclusion, Marlena's algebraic journey has been a successful one. She has demonstrated a clear understanding of mathematical operations and properties, and has successfully solved the equation $2x + 5 = -10 - x$. By analyzing each step of her process, we have identified areas for improvement and highlighted the importance of justification and verification in mathematical problem-solving.

Recommendations for Future Improvement

• Practice solving linear equations with two variables to build confidence and fluency.
• Verify solutions by substituting them back into the original equation.
• Avoid common mistakes such as not following the order of operations and not isolating the variable on one side of the equation.

By following these recommendations, you will be well on your way to becoming a proficient algebraic problem-solver.