Perform The Following Subtraction Operation:${ \begin{tabular}{l} 2 X − 2 2x - 2 2 X − 2 \ − ( X − 1 ) -(x - 1) − ( X − 1 ) \ \hline \end{tabular} }$

Introduction

In algebra, subtraction operations are performed using the rules of arithmetic and algebraic expressions. When subtracting one expression from another, we need to apply the rules of subtraction, which include changing the sign of the second expression and combining like terms. In this article, we will perform the subtraction operation $2x - 2$ and $-(x - 1)$ using the rules of algebra.

Step 1: Apply the Rule of Subtraction

The first step in performing the subtraction operation is to apply the rule of subtraction, which states that when subtracting one expression from another, we need to change the sign of the second expression. In this case, we have $-(x - 1)$, which means we need to change the sign of the expression $(x - 1)$.

Changing the Sign of the Second Expression

To change the sign of the second expression, we need to multiply it by $-1$. This means that $-(x - 1)$ is equivalent to $-1(x - 1)$.

Distributing the Negative Sign

When we distribute the negative sign to the expression $(x - 1)$, we get $-x + 1$.

Step 2: Combine Like Terms

Now that we have applied the rule of subtraction and changed the sign of the second expression, we can combine like terms. In this case, we have $2x - 2$ and $-x + 1$. We can combine the like terms $2x$ and $-x$ to get $x$.

Combining Like Terms

To combine the like terms $2x$ and $-x$, we need to add their coefficients. In this case, the coefficient of $2x$ is $2$ and the coefficient of $-x$ is $-1$. When we add these coefficients, we get $2 - 1 = 1$. Therefore, the combined term is $x$.

Combining the Constant Terms

We also need to combine the constant terms $-2$ and $1$. When we add these constant terms, we get $-2 + 1 = -1$.

Step 3: Write the Final Answer

Now that we have combined the like terms and constant terms, we can write the final answer. The final answer is $x - 1$.

Conclusion

In conclusion, performing the subtraction operation $2x - 2$ and $-(x - 1)$ using the rules of algebra involves applying the rule of subtraction, changing the sign of the second expression, distributing the negative sign, combining like terms, and combining constant terms. By following these steps, we can perform the subtraction operation and write the final answer.

Example Problems

Here are some example problems that demonstrate the steps involved in performing the subtraction operation:

• $3x - 2$ and $-(2x - 1)$
• $4x + 2$ and $-(3x - 3)$
• $2x - 1$ and $-(x + 2)$

Tips and Tricks

Here are some tips and tricks that can help you perform the subtraction operation:

• Always apply the rule of subtraction first.
• Change the sign of the second expression by multiplying it by $-1$.
• Distribute the negative sign to the expression.
• Combine like terms by adding their coefficients.
• Combine constant terms by adding them.

Common Mistakes

Here are some common mistakes that you should avoid when performing the subtraction operation:

• Failing to apply the rule of subtraction.
• Failing to change the sign of the second expression.
• Failing to distribute the negative sign.
• Failing to combine like terms.
• Failing to combine constant terms.

Real-World Applications

The subtraction operation has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the subtraction operation is used to calculate the net force acting on an object. In engineering, the subtraction operation is used to calculate the difference between two quantities. In economics, the subtraction operation is used to calculate the difference between two prices.

Conclusion

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Q: What is the rule of subtraction in algebra?

A: The rule of subtraction in algebra states that when subtracting one expression from another, we need to change the sign of the second expression and combine like terms.

Q: How do I change the sign of the second expression?

A: To change the sign of the second expression, we need to multiply it by $-1$. This means that $-(x - 1)$ is equivalent to $-1(x - 1)$.

Q: What is the difference between a positive and negative coefficient?

A: A positive coefficient is a number that is multiplied by a variable, while a negative coefficient is a number that is multiplied by a variable and has a negative sign.

Q: How do I combine like terms?

A: To combine like terms, we need to add their coefficients. For example, if we have $2x$ and $-x$, we can combine them by adding their coefficients: $2 - 1 = 1$. Therefore, the combined term is $x$.

Q: What is the difference between a constant term and a variable term?

A: A constant term is a number that is not multiplied by a variable, while a variable term is a number that is multiplied by a variable.

Q: How do I combine constant terms?

A: To combine constant terms, we need to add them. For example, if we have $-2$ and $1$, we can combine them by adding them: $-2 + 1 = -1$.

Q: What is the final answer to the subtraction operation $2x - 2$ and $-(x - 1)$?

A: The final answer to the subtraction operation $2x - 2$ and $-(x - 1)$ is $x - 1$.

Q: Can I use the subtraction operation to solve real-world problems?

A: Yes, the subtraction operation can be used to solve real-world problems in fields such as physics, engineering, and economics.

Q: What are some common mistakes to avoid when performing the subtraction operation?

A: Some common mistakes to avoid when performing the subtraction operation include failing to apply the rule of subtraction, failing to change the sign of the second expression, failing to distribute the negative sign, failing to combine like terms, and failing to combine constant terms.

Q: How can I practice the subtraction operation?

A: You can practice the subtraction operation by working through example problems and exercises. You can also use online resources and practice tests to help you prepare.

Q: What are some tips and tricks for performing the subtraction operation?

A: Some tips and tricks for performing the subtraction operation include always applying the rule of subtraction first, changing the sign of the second expression by multiplying it by $-1$, distributing the negative sign to the expression, combining like terms by adding their coefficients, and combining constant terms by adding them.

Q: Can I use the subtraction operation to solve equations?

A: Yes, the subtraction operation can be used to solve equations. For example, if we have the equation $2x - 2 = -(x - 1)$, we can use the subtraction operation to solve for $x$.

Q: What are some real-world applications of the subtraction operation?

A: Some real-world applications of the subtraction operation include calculating the net force acting on an object in physics, calculating the difference between two quantities in engineering, and calculating the difference between two prices in economics.