What Should Be Added To ( 2 X − 3 Y (2x - 3y ( 2 X − 3 Y ] To Obtain ( X − 2 Y (x - 2y ( X − 2 Y ]?A. ( 5 Y − X (5y - X ( 5 Y − X ] B. ( X − 5 Y (x - 5y ( X − 5 Y ] C. ( Y − X (y - X ( Y − X ] D. ( X − Y (x - Y ( X − Y ]

Understanding the Problem

To solve this problem, we need to find the value that, when added to $(2x - 3y)$, will result in $(x - 2y)$. This involves performing algebraic operations to simplify the given expressions and identify the missing term.

Algebraic Manipulation

Let's start by examining the given expressions:

$(2x - 3y)$ and $(x - 2y)$

We can rewrite $(x - 2y)$ as $(-2y + x)$ to make it easier to compare with $(2x - 3y)$.

Identifying the Missing Term

To find the missing term, we need to determine what value, when added to $(2x - 3y)$, will result in $(-2y + x)$. This involves identifying the difference between the two expressions.

Step 1: Subtract $(2x - 3y)$ from $(-2y + x)$

To find the missing term, we can subtract $(2x - 3y)$ from $(-2y + x)$:

$(-2y + x) - (2x - 3y)$

Step 2: Simplify the Expression

Now, let's simplify the expression by combining like terms:

$(-2y + x) - (2x - 3y)$

$= -2y + x - 2x + 3y$

$= -2y - 2x + 3y + x$

$= -2y + 3y - 2x + x$

$= y - x$

Conclusion

Based on the algebraic manipulation, we can see that the missing term is $(y - x)$. Therefore, the correct answer is:

C. $(y - x)$

This result makes sense, as adding $(y - x)$ to $(2x - 3y)$ will indeed result in $(x - 2y)$.

Final Answer

The final answer is C. $(y - x)$.

Understanding the Problem

To solve this problem, we need to find the value that, when added to $(2x - 3y)$, will result in $(x - 2y)$. This involves performing algebraic operations to simplify the given expressions and identify the missing term.

Q&A Guide

Q: What is the given problem?

A: The given problem is to find the value that, when added to $(2x - 3y)$, will result in $(x - 2y)$.

Q: What are the given expressions?

A: The given expressions are $(2x - 3y)$ and $(x - 2y)$.

Q: How can we rewrite $(x - 2y)$ to make it easier to compare with $(2x - 3y)$?

A: We can rewrite $(x - 2y)$ as $(-2y + x)$ to make it easier to compare with $(2x - 3y)$.

Q: What is the missing term that needs to be added to $(2x - 3y)$ to obtain $(x - 2y)$?

A: The missing term is $(y - x)$.

Q: How can we find the missing term?

A: We can find the missing term by subtracting $(2x - 3y)$ from $(-2y + x)$ and simplifying the expression.

Q: What is the result of subtracting $(2x - 3y)$ from $(-2y + x)$?

A: The result of subtracting $(2x - 3y)$ from $(-2y + x)$ is $(y - x)$.

Q: Why is the correct answer $(y - x)$?

A: The correct answer is $(y - x)$ because adding $(y - x)$ to $(2x - 3y)$ will indeed result in $(x - 2y)$.

Common Mistakes

• Many students make the mistake of adding $(2x - 3y)$ and $(x - 2y)$ directly, without considering the algebraic operations involved.
• Others may forget to simplify the expression after subtracting $(2x - 3y)$ from $(-2y + x)$.

Tips and Tricks

• When solving algebraic problems, it's essential to simplify the expressions and identify the missing terms.
• Use algebraic manipulation to rewrite the given expressions and make them easier to compare.
• Pay attention to the signs and coefficients of the variables.

Conclusion

In conclusion, the missing term that needs to be added to $(2x - 3y)$ to obtain $(x - 2y)$ is $(y - x)$. By following the steps outlined in this Q&A guide, you can solve similar problems and become more confident in your algebraic skills.

Final Answer

The final answer is C. $(y - x)$.