Simplify The Expression:${ \begin{tabular}{l} 9 X + 7 9x + 7 9 X + 7 \ − ( 3 X + 9 ) -(3x + 9) − ( 3 X + 9 ) \ \hline \end{tabular} }$

Mar 12, 2025 by ADMIN 136 views

**Simplifying Algebraic Expressions: A Step-by-Step Guide**

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying the given expression: $9x + 7$ and $-(3x + 9)$ . We will break down the steps involved in simplifying these expressions and provide a clear understanding of the process.

Understanding the Expression

The given expression consists of two terms: $9x + 7$ and $-(3x + 9)$ . The first term is a simple linear expression, while the second term is a linear expression with a negative sign in front of it. To simplify this expression, we need to combine like terms and apply the rules of algebra.

Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

Parentheses: Evaluate the expressions inside the parentheses.
Exponents: Evaluate any exponential expressions.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

In this case, we need to evaluate the expression inside the parentheses first. The expression inside the parentheses is $-(3x + 9)$ .

Evaluating the Expression Inside the Parentheses

To evaluate the expression inside the parentheses, we need to apply the distributive property:

-(3x + 9) = -3x - 9

Now that we have evaluated the expression inside the parentheses, we can rewrite the original expression as:

9x + 7 - 3x - 9

Combining Like Terms

The next step is to combine like terms. We can combine the terms with the variable $x$ and the constant terms separately:

9x - 3x + 7 - 9

Simplifying the Expression

Now that we have combined like terms, we can simplify the expression further:

6x - 2

Conclusion

In this article, we have simplified the given expression $9x + 7$ and $-(3x + 9)$ by following the order of operations and combining like terms. We have broken down the steps involved in simplifying these expressions and provided a clear understanding of the process. By following these steps, you can simplify any algebraic expression and solve problems with confidence.

Tips and Tricks

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

Follow the order of operations: Always follow the order of operations (PEMDAS) when simplifying algebraic expressions.
Combine like terms: Combine like terms to simplify the expression.
Apply the distributive property: Apply the distributive property to evaluate expressions inside parentheses.
Simplify the expression: Simplify the expression by combining like terms and applying the rules of algebra.

Practice Problems

Here are some practice problems to help you practice simplifying algebraic expressions:

Problem 1: Simplify the expression $2x + 5$ and $-(x + 3)$ .
Problem 2: Simplify the expression $3x - 2$ and $-(2x + 1)$ .
Problem 3: Simplify the expression $x + 2$ and $-(x - 3)$ .

Real-World Applications

Simplifying algebraic expressions has many real-world applications. Here are a few examples:

Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
Finance: Algebraic expressions are used to model financial systems, such as investments and loans.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for students and professionals alike. By following the order of operations and combining like terms, you can simplify any algebraic expression and solve problems with confidence. Remember to practice regularly and apply the rules of algebra to simplify expressions. With practice and patience, you can become proficient in simplifying algebraic expressions and apply them to real-world problems.

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Introduction

In our previous article, we discussed the steps involved in simplifying algebraic expressions. In this article, we will provide a Q&A guide to help you understand the concepts and apply them to real-world problems.

Q&A: Simplifying Algebraic Expressions

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is:

Parentheses: Evaluate the expressions inside the parentheses.
Exponents: Evaluate any exponential expressions.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable and coefficient. Then, you can add or subtract the coefficients to simplify the expression.

Q: What is the distributive property?

A: The distributive property is a rule that allows you to multiply a single term to multiple terms inside parentheses. The distributive property is:

a(b + c) = ab + ac

Q: How do I simplify an expression with a negative sign?

A: To simplify an expression with a negative sign, you need to apply the distributive property and then combine like terms.

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

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

Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying an expression.
Not combining like terms: Make sure to combine like terms to simplify the expression.
Not applying the distributive property: Make sure to apply the distributive property when simplifying expressions with parentheses.

Q&A: Real-World Applications

Q: How are algebraic expressions used in science?

A: Algebraic expressions are used in science to model real-world phenomena, such as the motion of objects and the behavior of populations.

Q: How are algebraic expressions used in engineering?

A: Algebraic expressions are used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.

Q: How are algebraic expressions used in finance?

A: Algebraic expressions are used in finance to model financial systems, such as investments and loans.

Conclusion

Tips and Tricks

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

Practice regularly: Practice simplifying algebraic expressions regularly to build your skills and confidence.
Use the order of operations: Always follow the order of operations (PEMDAS) when simplifying an expression.
Combine like terms: Combine like terms to simplify the expression.
Apply the distributive property: Apply the distributive property when simplifying expressions with parentheses.

Real-World Examples

Here are some real-world examples of algebraic expressions:

Example 1: A company wants to invest in a new project. The company's financial advisor uses algebraic expressions to model the potential returns on investment.
Example 2: A scientist wants to study the motion of a particle. The scientist uses algebraic expressions to model the particle's motion and predict its trajectory.
Example 3: An engineer wants to design a new electrical circuit. The engineer uses algebraic expressions to model the circuit's behavior and optimize its performance.