Simplify The Expression: ( − X + 3 ) − ( X − 5 ) = (-x+3)-(x-5)= ( − X + 3 ) − ( X − 5 ) =

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, removing parentheses, and performing other operations to make the expression more manageable. In this article, we will focus on simplifying the expression $(-x+3)-(x-5)=$ using various mathematical techniques.

Understanding the Expression

The given expression is a combination of two terms: $(-x+3)$ and $(x-5)$. To simplify this expression, we need to apply the rules of arithmetic operations, such as addition, subtraction, multiplication, and division. We will also use the concept of like terms, which are terms that have the same variable raised to the same power.

Distributive Property

To simplify the expression, we can use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We can apply this property to the given expression by distributing the negative sign to the terms inside the parentheses.

Step 1: Distribute the Negative Sign

Using the distributive property, we can rewrite the expression as:

$$(-x+3)-(x-5) = -x + 3 - x + 5$$

Step 2: Combine Like Terms

Now that we have distributed the negative sign, we can combine like terms. The like terms in this expression are $-x$ and $-x$, and $3$ and $5$. We can combine these terms by adding or subtracting their coefficients.

Step 3: Simplify the Expression

Combining the like terms, we get:

$$-x + 3 - x + 5 = -2x + 8$$

Conclusion

In this article, we simplified the expression $(-x+3)-(x-5)=$ using the distributive property and combining like terms. We started by distributing the negative sign to the terms inside the parentheses and then combined the like terms to get the final simplified expression. This process helps us solve equations and inequalities by making the expression more manageable.

Tips and Tricks

• When simplifying expressions, always look for like terms and combine them.
• Use the distributive property to distribute negative signs and other coefficients.
• Check your work by plugging in values or using a calculator to verify the simplified expression.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. For example, in physics, we use simplified expressions to describe the motion of objects. In economics, we use simplified expressions to model the behavior of markets. In computer science, we use simplified expressions to write efficient algorithms.

Common Mistakes

When simplifying expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not distributing negative signs correctly
• Not combining like terms
• Not checking work

Final Answer

The final answer to the expression $(-x+3)-(x-5)=$ is:

$$-2x + 8$$

This simplified expression can be used to solve equations and inequalities, and it has many real-world applications in physics, economics, and computer science.

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Introduction

In our previous article, we simplified the expression $(-x+3)-(x-5)=$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical rule that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property allows us to distribute a coefficient to the terms inside the parentheses.

Q: How do I distribute a negative sign?

A: To distribute a negative sign, we can use the distributive property. For example, if we have the expression $-x + 3$, we can distribute the negative sign to the terms inside the parentheses by rewriting it as $-x - 3$.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $-x$ and $-x$ are like terms, as are $3$ and $5$.

Q: How do I combine like terms?

A: To combine like terms, we can add or subtract their coefficients. For example, if we have the expression $-x + 3 - x + 5$, we can combine the like terms by adding their coefficients: $-x - x = -2x$ and $3 + 5 = 8$.

Q: What is the final answer to the expression $(-x+3)-(x-5)=$?

A: The final answer to the expression $(-x+3)-(x-5)=$ is $-2x + 8$.

Q: Can I use a calculator to simplify expressions?

A: Yes, you can use a calculator to simplify expressions. However, it's always a good idea to check your work by plugging in values or using a calculator to verify the simplified expression.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not distributing negative signs correctly
• Not combining like terms
• Not checking work

Q: How do I apply the distributive property to expressions with multiple variables?

A: To apply the distributive property to expressions with multiple variables, we can use the same rule as before: $a(b+c) = ab + ac$. For example, if we have the expression $2x + 3y - 4z$, we can distribute the negative sign to the terms inside the parentheses by rewriting it as $2x - 4z + 3y$.

Q: Can I use the distributive property to simplify expressions with fractions?

A: Yes, you can use the distributive property to simplify expressions with fractions. For example, if we have the expression $\frac{1}{2}x + \frac{3}{4}y - \frac{1}{3}z$, we can distribute the fractions to the terms inside the parentheses by rewriting it as $\frac{1}{2}x - \frac{1}{3}z + \frac{3}{4}y$.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to simplifying expressions. We covered topics such as the distributive property, like terms, and common mistakes to avoid. We also provided examples of how to apply the distributive property to expressions with multiple variables and fractions.

Tips and Tricks

• Always check your work by plugging in values or using a calculator to verify the simplified expression.
• Use the distributive property to distribute negative signs and other coefficients.
• Combine like terms to simplify expressions.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. For example, in physics, we use simplified expressions to describe the motion of objects. In economics, we use simplified expressions to model the behavior of markets. In computer science, we use simplified expressions to write efficient algorithms.

Final Answer

The final answer to the expression $(-x+3)-(x-5)=$ is:

$$-2x + 8$$