Marlena Solved The Equation $2x + 5 = -10 - X$. Her Steps Are Shown Below.1. $2x + 5 = -10 - X$2. $3x + 5 = -10$3. $3x = -15$4. $x = -5$Use The Drop-down Menus To Justify Marlena's Work In Each Step Of The

Introduction

In mathematics, solving equations is a fundamental concept that requires a deep understanding of algebraic operations and properties. Marlena, a math enthusiast, has attempted to solve the equation $2x + 5 = -10 - x$. In this article, we will analyze each step of her solution and provide a justification for her work.

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

Marlena starts by writing the given equation: $2x + 5 = -10 - x$. This is a correct representation of the equation.

Justification

The equation $2x + 5 = -10 - x$ is a linear equation in one variable, $x$. The left-hand side of the equation consists of two terms: $2x$ and $5$. The right-hand side of the equation consists of two terms: $-10$ and $-x$. The equation is in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants.

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

Marlena then combines like terms on the left-hand side of the equation: $2x + x + 5 = -10 - x$. This simplifies to $3x + 5 = -10$.

Justification

The combination of like terms on the left-hand side of the equation is a valid algebraic operation. The terms $2x$ and $x$ are like terms, as they both contain the variable $x$. By combining these terms, Marlena has simplified the equation.

However, it's worth noting that Marlena has not provided a clear justification for the cancellation of the $-x$ term on the right-hand side of the equation. In a typical solution, one would expect to see a clear explanation for this step.

Step 3: $3x = -15$

Marlena then subtracts $5$ from both sides of the equation: $3x + 5 - 5 = -10 - 5$. This simplifies to $3x = -15$.

Justification

The subtraction of $5$ from both sides of the equation is a valid algebraic operation. By subtracting $5$ from both sides, Marlena has isolated the term $3x$ on the left-hand side of the equation.

However, it's worth noting that Marlena has not provided a clear justification for the cancellation of the $-5$ term on the right-hand side of the equation. In a typical solution, one would expect to see a clear explanation for this step.

Step 4: $x = -5$

Marlena then divides both sides of the equation by $3$: $\frac{3x}{3} = \frac{-15}{3}$. This simplifies to $x = -5$.

Justification

The division of both sides of the equation by $3$ is a valid algebraic operation. By dividing both sides by $3$, Marlena has solved for the variable $x$.

However, it's worth noting that Marlena has not provided a clear justification for the cancellation of the $3$ term on the left-hand side of the equation. In a typical solution, one would expect to see a clear explanation for this step.

Conclusion

In conclusion, Marlena's solution to the equation $2x + 5 = -10 - x$ is a valid one. However, there are a few areas where her justification could be improved. Specifically, she could provide clearer explanations for the cancellation of terms on both sides of the equation.

Recommendations for Improvement

To improve her solution, Marlena could consider the following:

• Provide clear explanations for each step of the solution
• Justify each algebraic operation with a clear explanation
• Avoid cancelling terms without providing a clear explanation for the cancellation

By following these recommendations, Marlena can improve the clarity and validity of her solution.

Final Answer

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Introduction

In our previous article, we analyzed Marlena's solution to the equation $2x + 5 = -10 - x$. We identified areas where her justification could be improved and provided recommendations for improvement. In this article, we will continue to explore Marlena's solution and answer some common questions related to the equation.

Q&A

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

A: The equation $2x + 5 = -10 - x$ is a linear equation in one variable, $x$. It is a simple equation that can be solved using basic algebraic operations.

Q: How do I solve the equation $2x + 5 = -10 - x$?

A: To solve the equation $2x + 5 = -10 - x$, you can follow these steps:

1. Combine like terms on the left-hand side of the equation.
2. Subtract $5$ from both sides of the equation.
3. Divide both sides of the equation by $3$.

Q: Why do I need to combine like terms on the left-hand side of the equation?

A: Combining like terms on the left-hand side of the equation simplifies the equation and makes it easier to solve. In this case, the terms $2x$ and $x$ are like terms, as they both contain the variable $x$. By combining these terms, you can simplify the equation.

Q: Why do I need to subtract $5$ from both sides of the equation?

A: Subtracting $5$ from both sides of the equation isolates the term $3x$ on the left-hand side of the equation. This makes it easier to solve for the variable $x$.

Q: Why do I need to divide both sides of the equation by $3$?

A: Dividing both sides of the equation by $3$ solves for the variable $x$. By dividing both sides by $3$, you can isolate the variable $x$ and find its value.

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

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

Q: How do I check my answer?

A: To check your answer, you can plug the value of $x$ back into the original equation and see if it is true. In this case, you can plug $x = -5$ back into the equation $2x + 5 = -10 - x$ and see if it is true.

Q: What if I get a different answer?

A: If you get a different answer, it may be because you made a mistake in your solution. Double-check your work and make sure that you followed the correct steps. If you are still having trouble, you can ask for help from a teacher or tutor.

Conclusion

In conclusion, solving the equation $2x + 5 = -10 - x$ requires a clear understanding of algebraic operations and properties. By following the steps outlined in this article, you can solve the equation and find the value of the variable $x$. Remember to check your answer and ask for help if you need it.

Recommendations for Further Study

To further improve your understanding of algebraic operations and properties, we recommend the following:

• Practice solving linear equations in one variable.
• Review the properties of algebraic operations, such as addition, subtraction, multiplication, and division.
• Practice solving quadratic equations and other types of equations.

By following these recommendations, you can improve your understanding of algebraic operations and properties and become a more confident and proficient math student.