Simplify The Expression: 2 ( 6 − 5 X ) − 3 ( 2 + 2 X 2(6 - 5x) - 3(2 + 2x 2 ( 6 − 5 X ) − 3 ( 2 + 2 X ]

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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 $2(6 - 5x) - 3(2 + 2x)$ using the order of operations and algebraic properties.

Understanding the Expression

The given expression is a combination of two terms, each enclosed in parentheses. The first term is $2(6 - 5x)$, and the second term is $-3(2 + 2x)$. To simplify this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Distributing the Coefficients

To simplify the expression, we need to distribute the coefficients to the terms inside the parentheses. This means multiplying each term inside the parentheses by the coefficient outside the parentheses.

Distributing the Coefficient 2

The first term is $2(6 - 5x)$. To distribute the coefficient 2, we multiply 2 by each term inside the parentheses:

$$2(6 - 5x) = 2(6) - 2(5x)$$

Using the distributive property, we can rewrite this as:

$$2(6 - 5x) = 12 - 10x$$

Distributing the Coefficient -3

The second term is $-3(2 + 2x)$. To distribute the coefficient -3, we multiply -3 by each term inside the parentheses:

$$-3(2 + 2x) = -3(2) - 3(2x)$$

Using the distributive property, we can rewrite this as:

$$-3(2 + 2x) = -6 - 6x$$

Combining Like Terms

Now that we have distributed the coefficients, 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 terms with the variable x: -10x and -6x.

Combining the Constant Terms

We also have two constant terms: 12 and -6. We can combine these terms by adding them together:

$$12 + (-6) = 6$$

Combining the Variable Terms

Now we can combine the variable terms by adding them together:

$$-10x + (-6x) = -16x$$

Simplifying the Expression

Now that we have combined like terms, we can simplify the expression by combining the constant term and the variable term:

$$12 - 10x - 6 - 6x = 6 - 16x$$

Conclusion

In this article, we simplified the expression $2(6 - 5x) - 3(2 + 2x)$ using the order of operations and algebraic properties. We distributed the coefficients to the terms inside the parentheses, combined like terms, and simplified the expression. The final simplified expression is $6 - 16x$.

Tips and Tricks

• When simplifying expressions, always follow the order of operations.
• Use the distributive property to distribute coefficients to terms inside parentheses.
• Combine like terms by adding or subtracting the coefficients of the terms.
• Simplify the expression by combining the constant term and the variable term.

Common Mistakes

• Failing to distribute coefficients to terms inside parentheses.
• Failing to combine like terms.
• Simplifying the expression incorrectly by not following the order of operations.

Real-World Applications

Simplifying expressions is a crucial skill in algebra that has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. In economics, we use algebraic expressions to model the behavior of markets. In computer science, we use algebraic expressions to write algorithms and programs.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that requires practice and patience. By following the order of operations and using algebraic properties, we can simplify complex expressions and solve equations and inequalities. Remember to always distribute coefficients to terms inside parentheses, combine like terms, and simplify the expression by combining the constant term and the variable term. With practice and persistence, you will become proficient in simplifying expressions and solving algebraic problems.

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Introduction

In our previous article, we simplified the expression $2(6 - 5x) - 3(2 + 2x)$ using the order of operations and algebraic properties. In this article, we will answer some frequently asked questions about simplifying expressions and provide additional tips and tricks to help you master this skill.

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 simplifying 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: How do I distribute coefficients to terms inside parentheses?

A: To distribute a coefficient to terms inside parentheses, multiply the coefficient by each term inside the parentheses. For example, if we have the expression $2(6 - 5x)$, we would multiply 2 by each term inside the parentheses:

$$2(6 - 5x) = 2(6) - 2(5x)$$

Using the distributive property, we can rewrite this as:

$$2(6 - 5x) = 12 - 10x$$

Q: What is the distributive property?

A: The distributive property is a rule that allows us to distribute a coefficient to terms inside parentheses. It states that for any numbers a, b, and c:

$$a(b + c) = ab + ac$$

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms. For example, if we have the expression $-10x + (-6x)$, we can combine the like terms by adding the coefficients:

$$-10x + (-6x) = -16x$$

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $-10x$ and $-6x$ are like terms because they both have the variable x raised to the power of 1.

Q: How do I simplify an expression?

A: To simplify an expression, follow the order of operations and use algebraic properties such as the distributive property and combining like terms. For example, if we have the expression $2(6 - 5x) - 3(2 + 2x)$, we can simplify it by following the order of operations and using algebraic properties:

$$2(6 - 5x) - 3(2 + 2x) = 12 - 10x - 6 - 6x$$

Combining like terms, we get:

$$12 - 10x - 6 - 6x = 6 - 16x$$

Tips and Tricks

• Always follow the order of operations when simplifying an expression.
• Use the distributive property to distribute coefficients to terms inside parentheses.
• Combine like terms by adding or subtracting the coefficients of the terms.
• Simplify the expression by combining the constant term and the variable term.

Common Mistakes

• Failing to distribute coefficients to terms inside parentheses.
• Failing to combine like terms.
• Simplifying the expression incorrectly by not following the order of operations.

Real-World Applications

Simplifying expressions is a crucial skill in algebra that has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. In economics, we use algebraic expressions to model the behavior of markets. In computer science, we use algebraic expressions to write algorithms and programs.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that requires practice and patience. By following the order of operations and using algebraic properties, we can simplify complex expressions and solve equations and inequalities. Remember to always distribute coefficients to terms inside parentheses, combine like terms, and simplify the expression by combining the constant term and the variable term. With practice and persistence, you will become proficient in simplifying expressions and solving algebraic problems.