Simplify The Expression: $5 - 2(a - 4$\]

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Introduction

In algebra, 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 simplify the expression $5 - 2(a - 4)$ using the order of operations and algebraic properties.

Understanding the Expression

The given expression is $5 - 2(a - 4)$. To simplify this expression, we need to understand the order of operations and the properties of algebra. The expression consists of two main parts: the constant term $5$ and the term $2(a - 4)$.

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 acronym PEMDAS is commonly used to remember the order of operations:

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

Simplifying the Expression

Now that we understand the order of operations, let's simplify the expression $5 - 2(a - 4)$.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to the terms inside the parentheses. This means multiplying the negative sign by each term inside the parentheses.

-2(a - 4) = -2a + 8

Step 2: Rewrite the Expression

Now that we have distributed the negative sign, we can rewrite the expression as:

5 - 2a + 8

Step 3: Combine Like Terms

The next step is to combine like terms. In this expression, we have two constant terms: $5$ and $8$. We can combine these terms by adding them together.

5 + 8 = 13

So, the expression becomes:

13 - 2a

Step 4: Final Simplification

The final step is to simplify the expression by combining the constant term with the variable term. In this case, we have a constant term $13$ and a variable term $-2a$. We can combine these terms by subtracting $2a$ from $13$.

13 - 2a = -2a + 13

Therefore, the simplified expression is:

-2a + 13

Conclusion

In this article, we simplified the expression $5 - 2(a - 4)$ using the order of operations and algebraic properties. We distributed the negative sign, combined like terms, and finally simplified the expression to get the final answer: $-2a + 13$. This example demonstrates the importance of following the order of operations and using algebraic properties to simplify expressions.

Common Mistakes to Avoid

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

• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
• Not distributing the negative sign: Don't forget to distribute the negative sign to the terms inside the parentheses.
• Not combining like terms: Make sure to combine like terms to simplify the expression.

Practice Problems

To practice simplifying expressions, try the following problems:

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

Answer Key

1. $3 - 2x - 4 = -2x - 1$
2. $4 - 3y + 3 = -3y + 7$
3. $2 - 5z + 15 = -5z + 17$

Final Thoughts

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Introduction

In our previous article, we simplified the expression $5 - 2(a - 4)$ using the order of operations and algebraic properties. Now, let's 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 acronym PEMDAS is commonly used to remember the order of operations:

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

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, follow these steps:

1. Distribute the negative sign to the terms inside the parentheses.
2. Combine like terms.
3. Follow the order of operations.

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

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms with the same variable.

Q: What is the final answer to the expression $5 - 2(a - 4)$?

A: The final answer to the expression $5 - 2(a - 4)$ is $-2a + 13$.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables by following the order of operations and combining like terms.

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

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

• Not following the order of operations
• Not distributing the negative sign
• Not combining like terms

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by trying the following problems:

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

Answer Key

1. $3 - 2x - 4 = -2x - 1$
2. $4 - 3y + 3 = -3y + 7$
3. $2 - 5z + 15 = -5z + 17$

Conclusion

Simplifying expressions is an essential skill in algebra. By following the order of operations and using algebraic properties, we can simplify complex expressions and solve equations and inequalities. Remember to distribute the negative sign, combine like terms, and follow the order of operations to simplify expressions. With practice, you'll become a pro at simplifying expressions in no time!

Additional Resources

• Algebra Handbook: A comprehensive guide to algebra, including simplifying expressions.
• Mathematics Online: A website with interactive math lessons and exercises.
• Khan Academy: A free online resource with video lessons and practice exercises on algebra and other math topics.

Final Thoughts

Simplifying expressions is a crucial skill in algebra. By following the order of operations and using algebraic properties, we can simplify complex expressions and solve equations and inequalities. Remember to practice regularly and seek help when needed. With dedication and persistence, you'll become a master of simplifying expressions in no time!