Simplify The Expression:${ -(2y - 6) + 9 }$

Mar 9, 2025 by ADMIN 45 views

**Simplify the Expression: A Step-by-Step Guide**

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, removing unnecessary brackets, and rearranging the expression to make it easier to understand. In this article, we will simplify the given expression: $-(2y - 6) + 9$ . We will break down the steps involved in simplifying the expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is $-(2y - 6) + 9$ . To simplify this expression, we need to understand the order of operations (PEMDAS) and the properties of negative numbers.

Order of Operations (PEMDAS)

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:

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

Properties of Negative Numbers

Negative numbers have some special properties that we need to understand when simplifying expressions. When we multiply a negative number by a positive number, the result is always negative. When we add a negative number to a positive number, the result is always less than the original positive number.

Simplifying the Expression

Now that we have a good understanding of the order of operations and the properties of negative numbers, let's simplify the expression $-(2y - 6) + 9$ .

Step 1: Remove the Negative Sign

The first step in simplifying the expression is to remove the negative sign in front of the parentheses. When we remove the negative sign, we change the sign of the terms inside the parentheses.

$-(2y - 6) + 9 = (2y - 6) + 9$

Step 2: Distribute the Positive Sign

The next step is to distribute the positive sign to the terms inside the parentheses. When we distribute the positive sign, we multiply each term inside the parentheses by 1.

$(2y - 6) + 9 = 2y - 6 + 9$

Step 3: Combine Like Terms

Now that we have distributed the positive sign, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: $-6$ and $9$ .

$2y - 6 + 9 = 2y + 3$

Step 4: Simplify the Expression

The final step is to simplify the expression by removing any unnecessary brackets or parentheses.

$2y + 3$

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. In this article, we simplified the expression $-(2y - 6) + 9$ by removing the negative sign, distributing the positive sign, combining like terms, and simplifying the expression. We hope that this article has provided a clear explanation of each step involved in simplifying the expression.

Example Problems

Here are some example problems that you can try to practice simplifying expressions:

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

Tips and Tricks

Here are some tips and tricks that you can use to simplify expressions:

Always follow the order of operations (PEMDAS).
Remove any unnecessary brackets or parentheses.
Combine like terms.
Simplify the expression by removing any negative signs.

Common Mistakes

Here are some common mistakes that you can avoid when simplifying expressions:

Not following the order of operations (PEMDAS).
Not removing unnecessary brackets or parentheses.
Not combining like terms.
Not simplifying the expression by removing any negative signs.

Final Thoughts

Introduction

In our previous article, we simplified the expression $-(2y - 6) + 9$ by removing the negative sign, distributing the positive sign, combining like terms, and simplifying the expression. In this article, we will answer some frequently asked questions about 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:

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

Q: How do I simplify an expression with multiple negative signs?

A: When simplifying an expression with multiple negative signs, we need to follow the order of operations (PEMDAS). We start by removing the negative signs from the parentheses, then distribute the positive sign to the terms inside the parentheses, combine like terms, and finally simplify the expression.

Q: What is the difference between a negative sign and a positive sign?

A: A negative sign is a symbol that indicates that a number is negative, while a positive sign is a symbol that indicates that a number is positive. When we multiply a negative number by a positive number, the result is always negative. When we add a negative number to a positive number, the result is always less than the original positive number.

Q: How do I simplify an expression with variables?

A: When simplifying an expression with variables, we need to follow the order of operations (PEMDAS). We start by removing any unnecessary brackets or parentheses, then combine like terms, and finally simplify the expression.

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

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change. In an expression, variables are represented by letters such as x, y, or z, while constants are represented by numbers such as 2, 3, or 4.

Q: How do I simplify an expression with fractions?

A: When simplifying an expression with fractions, we need to follow the order of operations (PEMDAS). We start by removing any unnecessary brackets or parentheses, then combine like terms, and finally simplify the expression.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of representing a part of a whole, while a decimal is a way of representing a part of a whole using a decimal point. For example, the fraction 1/2 is equal to the decimal 0.5.

Q: How do I simplify an expression with exponents?

A: When simplifying an expression with exponents, we need to follow the order of operations (PEMDAS). We start by evaluating any exponential expressions, then combine like terms, and finally simplify the expression.

Q: What is the difference between an exponent and a power?

A: An exponent is a small number that is raised to a power, while a power is the result of raising a number to a certain exponent. For example, the expression 2^3 is equal to the expression 2 × 2 × 2.