Simplify The Following Expression:$ 2x - 7 + 8 - 4 + 9 \div 3 + 6 - 8 + 7 + 12 \div 2 $

Introduction

In this article, we will simplify the given mathematical expression step by step. The expression is: $2x - 7 + 8 - 4 + 9 \div 3 + 6 - 8 + 7 + 12 \div 2$. We will follow the order of operations (PEMDAS) to simplify the expression.

Understanding the 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 stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
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.

Step 1: Simplify the Expression Inside the Parentheses

There are no expressions inside parentheses in the given expression, so we can move on to the next step.

Step 2: Evaluate Exponential Expressions

There are no exponential expressions in the given expression, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division Operations

In the given expression, we have two division operations: $9 \div 3$ and $12 \div 2$. We will evaluate these operations first.

$9 \div 3 = 3$

$12 \div 2 = 6$

So, the expression becomes: $2x - 7 + 8 - 4 + 3 + 6 - 8 + 7 + 6$

Step 4: Evaluate Addition and Subtraction Operations

Now, we will evaluate the addition and subtraction operations from left to right.

$2x - 7 + 8 - 4 + 3 + 6 - 8 + 7 + 6$

First, we will add and subtract the numbers from left to right:

$2x - 7 + 8 = 2x + 1$

$2x + 1 - 4 = 2x - 3$

$2x - 3 + 3 = 2x$

$2x + 6 - 8 = 2x - 2$

$2x - 2 + 7 = 2x + 5$

$2x + 5 + 6 = 2x + 11$

Step 5: Simplify the Expression

The simplified expression is: $2x + 11$

Conclusion

In this article, we simplified the given mathematical expression step by step using the order of operations (PEMDAS). We evaluated the multiplication and division operations first, and then the addition and subtraction operations. The simplified expression is: $2x + 11$.

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 (PEMDAS)
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

Practice Problems

Try simplifying the following expressions using the order of operations (PEMDAS):

1. $3x + 2 - 5 + 8 \div 2$
2. $2x - 3 + 4 - 9 \div 3$
3. $x + 2 - 7 + 11 \div 2$

Answer Key

1. $3x + 5$
2. $2x - 1$
3. $x + 5$

Final Thoughts

Introduction

In our previous article, we simplified the given mathematical expression step by step using the order of operations (PEMDAS). In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

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 stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
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: Why is it important to follow the order of operations?

A: Following the order of operations is crucial to simplify expressions correctly. If we don't follow the order of operations, we may get incorrect results.

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 (PEMDAS)
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, follow these steps:

1. Evaluate expressions inside parentheses first.
2. Evaluate any exponential expressions next.
3. Evaluate multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are two basic arithmetic operations. Addition involves combining two or more numbers to get a total, while subtraction involves finding the difference between two numbers.

Q: How do I simplify expressions with variables?

A: To simplify expressions with variables, follow these steps:

1. Evaluate any numerical expressions first.
2. Evaluate any exponential expressions next.
3. Evaluate multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the importance of simplifying expressions?

A: Simplifying expressions is essential in mathematics because it helps us to:

• Solve equations and inequalities
• Graph functions
• Analyze data
• Make predictions

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by:

• Solving problems in your textbook or online resources
• Working on practice exercises
• Creating your own problems and solving them
• Joining a study group or online community to practice with others

Conclusion

Simplifying expressions is a crucial skill in mathematics. By following the order of operations (PEMDAS) and evaluating expressions step by step, we can simplify even the most complex expressions. Remember to avoid common mistakes and practice simplifying expressions regularly to become proficient in this skill.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• IXL: Simplifying Expressions

Final Thoughts

Simplifying expressions is an essential skill in mathematics. By practicing regularly and following the order of operations (PEMDAS), you can become proficient in simplifying expressions and solve complex problems with ease.