Simplify The Expression: − A + 5 B − 6 A + 5 ( A + 1 -a + 5b - 6a + 5(a + 1 − A + 5 B − 6 A + 5 ( A + 1 ]

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, which are terms that have the same variable raised to the same power. In this article, we will simplify the expression $-a + 5b - 6a + 5(a + 1)$ using the distributive property and combining like terms.

Understanding the Expression

The given expression is $-a + 5b - 6a + 5(a + 1)$. To simplify this expression, we need to understand the order of operations and the properties of algebraic expressions.

Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Properties of Algebraic Expressions

Algebraic expressions have several properties that help us simplify them. Some of these properties include:

• Commutative Property: The order of the terms in an expression does not change the value of the expression.
• Associative Property: The order in which we perform operations on terms in an expression does not change the value of the expression.
• Distributive Property: We can distribute a coefficient to each term inside a set of parentheses.

Simplifying the Expression

Now that we have a good understanding of the order of operations and the properties of algebraic expressions, let's simplify the given expression.

Step 1: Distribute the Coefficient

The first step in simplifying the expression is to distribute the coefficient 5 to each term inside the parentheses.

$-a + 5b - 6a + 5(a + 1)$

Using the distributive property, we get:

$-a + 5b - 6a + 5a + 5$

Step 2: Combine Like Terms

Now that we have distributed the coefficient, we can combine like terms. Like terms are terms that have the same variable raised to the same power.

$-a + 5b - 6a + 5a + 5$

Combining the like terms, we get:

$-a - 6a + 5a + 5b + 5$

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by combining the constants.

$-a - 6a + 5a + 5b + 5$

Combining the constants, we get:

$-2a + 5b + 5$

Final Answer

The simplified expression is $-2a + 5b + 5$.

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By understanding the order of operations and the properties of algebraic expressions, we can simplify complex expressions like $-a + 5b - 6a + 5(a + 1)$. In this article, we used the distributive property and combining like terms to simplify the expression. The final answer is $-2a + 5b + 5$.

Common Mistakes to Avoid

When simplifying expressions, there are several common mistakes to avoid. Some of these mistakes include:

• Not distributing coefficients: Failing to distribute coefficients to each term inside a set of parentheses can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying constants: Failing to simplify constants can lead to incorrect simplifications.

Practice Problems

To practice simplifying expressions, try the following problems:

1. Simplify the expression $2x + 3y - 4x + 2(3x + 1)$.
2. Simplify the expression $-2a + 5b - 3a + 2(a + 1)$.
3. Simplify the expression $x + 2y - 3x + 4(2x - 1)$.

Answer Key

1. $-2x + 3y + 6x + 2$
2. $-5a + 5b + 2$
3. $-2x + 2y + 8x - 4$

Final Thoughts

$$$$

Introduction

In our previous article, we simplified the expression $-a + 5b - 6a + 5(a + 1)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the distributive property?

A: The distributive property is a property of algebraic expressions that allows us to distribute a coefficient to each term inside a set of parentheses. For example, if we have the expression $2(x + 3)$, we can distribute the coefficient 2 to each term inside the parentheses to get $2x + 6$.

Q: How do I combine like terms?

A: To combine like terms, we need to identify the terms that have the same variable raised to the same power. We can then add or subtract the coefficients of these terms to get the simplified expression. For example, if we have the expression $2x + 3x$, we can combine the like terms to get $5x$.

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

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

• Not distributing coefficients: Failing to distribute coefficients to each term inside a set of parentheses can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying constants: Failing to simplify constants can lead to incorrect simplifications.

Q: How do I simplify expressions with variables in the denominator?

A: To simplify expressions with variables in the denominator, we need to follow the order of operations and simplify the expression inside the parentheses first. We can then simplify the expression by combining like terms and simplifying the constants.

Q: Can I simplify expressions with negative coefficients?

A: Yes, we can simplify expressions with negative coefficients by following the same steps as we would for positive coefficients. We need to distribute the coefficient to each term inside the parentheses, combine like terms, and simplify the constants.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, we need to follow the order of operations and simplify the expression inside the parentheses first. We can then simplify the expression by combining like terms and simplifying the constants.

Practice Problems

To practice simplifying expressions, try the following problems:

1. Simplify the expression $2x + 3y - 4x + 2(3x + 1)$.
2. Simplify the expression $-2a + 5b - 3a + 2(a + 1)$.
3. Simplify the expression $x + 2y - 3x + 4(2x - 1)$.

Answer Key

1. $-2x + 3y + 6x + 2$
2. $-5a + 5b + 2$
3. $-2x + 2y + 8x - 4$

Final Thoughts

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By understanding the order of operations and the properties of algebraic expressions, we can simplify complex expressions like $-a + 5b - 6a + 5(a + 1)$. In this article, we answered some frequently asked questions about simplifying expressions and provided practice problems to help you improve your skills.

Common Mistakes to Avoid

When simplifying expressions, there are several common mistakes to avoid. Some of these mistakes include:

• Not distributing coefficients: Failing to distribute coefficients to each term inside a set of parentheses can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying constants: Failing to simplify constants can lead to incorrect simplifications.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions:

• Read the expression carefully: Before simplifying an expression, read it carefully to make sure you understand what it says.
• Use the distributive property: The distributive property is a powerful tool for simplifying expressions. Use it to distribute coefficients to each term inside a set of parentheses.
• Combine like terms: Combining like terms is an essential step in simplifying expressions. Make sure to combine all like terms in an expression.
• Simplify constants: Simplifying constants is an important step in simplifying expressions. Make sure to simplify all constants in an expression.

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By understanding the order of operations and the properties of algebraic expressions, we can simplify complex expressions like $-a + 5b - 6a + 5(a + 1)$. In this article, we answered some frequently asked questions about simplifying expressions and provided practice problems to help you improve your skills.