For The Following Expression, Write An Equivalent Expression:$\[ 6(0.5x - 3y) - 8(0.25x + Y) \\]

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying the given expression $6(0.5x - 3y) - 8(0.25x + y)$ and provide an equivalent expression.

Understanding the Expression

The given expression is a combination of two terms, each containing a coefficient and a variable. The first term is $6(0.5x - 3y)$, and the second term is $-8(0.25x + y)$. To simplify this expression, we need to apply the distributive property and combine like terms.

Applying the Distributive Property

The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We can apply this property to the given expression by multiplying the coefficient with each term inside the parentheses.

6(0.5x - 3y) = 6(0.5x) - 6(3y)
= 3x - 18y

Similarly, we can apply the distributive property to the second term:

-8(0.25x + y) = -8(0.25x) - 8(y)
= -2x - 8y

Combining Like Terms

Now that we have applied the distributive property, 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 $x$ and two terms with the variable $y$.

(3x - 18y) + (-2x - 8y) = (3x - 2x) + (-18y - 8y)
= x - 26y

Equivalent Expression

The simplified expression is $x - 26y$. This is an equivalent expression to the original expression $6(0.5x - 3y) - 8(0.25x + y)$.

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and find equivalent expressions. In this article, we have simplified the expression $6(0.5x - 3y) - 8(0.25x + y)$ and found an equivalent expression $x - 26y$.

Tips and Tricks

• Always apply the distributive property to simplify expressions.
• Combine like terms to simplify expressions.
• Use parentheses to group terms and make it easier to simplify expressions.

Real-World Applications

Simplifying algebraic expressions 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 economic systems. In computer science, we use algebraic expressions to write algorithms and solve problems.

Common Mistakes

• Failing to apply the distributive property.
• Failing to combine like terms.
• Not using parentheses to group terms.

Practice Problems

1. Simplify the expression $4(2x + 3y) - 2(3x - 2y)$.
2. Simplify the expression $6(0.25x - 0.5y) + 8(0.5x + 0.25y)$.
3. Simplify the expression $3(2x - 4y) + 2(4x + 2y)$.

Answer Key

1. $8x + 2y$
2. $2x - 2y$
3. $14x - 2y$

Conclusion

$$$$

Introduction

In our previous article, we discussed how to simplify algebraic expressions by applying the distributive property and combining like terms. In this article, we will provide a Q&A guide to help you master the art of simplifying algebraic expressions.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means that we can multiply a coefficient with each term inside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the coefficient with each term inside the parentheses. For example, if we have the expression $6(0.5x - 3y)$, we can apply the distributive property by multiplying 6 with each term inside the parentheses: $6(0.5x) - 6(3y)$.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression $3x - 2x$, $3x$ and $-2x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, simply add or subtract the coefficients of the like terms. For example, in the expression $3x - 2x$, we can combine the like terms by adding the coefficients: $3x - 2x = x$.

Q: What is the difference between the distributive property and combining like terms?

A: The distributive property is used to multiply a coefficient with each term inside the parentheses, while combining like terms is used to add or subtract the coefficients of like terms.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables by applying the distributive property and combining like terms. For example, if we have the expression $6(0.5x - 3y) - 8(0.25x + y)$, we can simplify it by applying the distributive property and combining 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:

• Failing to apply the distributive property
• Failing to combine like terms
• Not using parentheses to group terms

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through practice problems, such as the ones provided in our previous article. You can also try simplifying expressions on your own and checking your work with a calculator or a friend.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects.
• Economics: Algebraic expressions are used to model economic systems.
• Computer Science: Algebraic expressions are used to write algorithms and solve problems.

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and find equivalent expressions. In this article, we have provided a Q&A guide to help you master the art of simplifying algebraic expressions. We hope this guide has been helpful in answering your questions and providing you with the skills and confidence you need to simplify algebraic expressions.