Which Expression Is Equivalent To 1.2 Y + 4.5 − 3.4 Y − 6.3 1.2y + 4.5 - 3.4y - 6.3 1.2 Y + 4.5 − 3.4 Y − 6.3 ?A. − 2.2 Y − 1.8 -2.2y - 1.8 − 2.2 Y − 1.8 B. − 2.2 Y + 11.1 -2.2y + 11.1 − 2.2 Y + 11.1 C. 4.6 Y − 1.8 4.6y - 1.8 4.6 Y − 1.8 D. 5.5 Y − 10.2 5.5y - 10.2 5.5 Y − 10.2

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will explore the process of simplifying algebraic expressions, with a focus on combining like terms. We will also apply this concept to a specific problem, where we need to simplify the expression $1.2y + 4.5 - 3.4y - 6.3$.

What are Like Terms?

Like terms are terms that have the same variable raised to the same power. In other words, they are terms that have the same "name" and "exponent". For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. On the other hand, $2x$ and $3y$ are not like terms because they have different variables.

Combining Like Terms

Combining like terms involves adding or subtracting the coefficients of like terms. The coefficient is the number that is multiplied by the variable. For example, in the expression $2x + 5x$, the like terms are $2x$ and $5x$. To combine these terms, we add their coefficients: $2 + 5 = 7$. Therefore, the simplified expression is $7x$.

Simplifying the Expression $1.2y + 4.5 - 3.4y - 6.3$

Now that we have a good understanding of like terms and combining them, let's apply this concept to the expression $1.2y + 4.5 - 3.4y - 6.3$. The first step is to identify the like terms in the expression. In this case, the like terms are $1.2y$ and $-3.4y$, which both have the variable $y$ raised to the power of 1.

Next, we combine the coefficients of the like terms. To do this, we add the coefficients of $1.2y$ and $-3.4y$: $1.2 + (-3.4) = -2.2$. Therefore, the simplified expression is $-2.2y$.

However, we are not done yet. We still need to combine the constant terms in the expression. The constant terms are $4.5$ and $-6.3$. To combine these terms, we add them: $4.5 + (-6.3) = -1.8$. Therefore, the final simplified expression is $-2.2y - 1.8$.

Conclusion

In this article, we explored the process of simplifying algebraic expressions by combining like terms. We applied this concept to the expression $1.2y + 4.5 - 3.4y - 6.3$ and simplified it to $-2.2y - 1.8$. This process is an essential skill in mathematics, and it is used extensively in algebra, calculus, and other branches of mathematics.

Which Expression is Equivalent to $1.2y + 4.5 - 3.4y - 6.3$?

Based on our simplification of the expression $1.2y + 4.5 - 3.4y - 6.3$, we can conclude that the equivalent expression is:

• A. $-2.2y - 1.8$

This is the correct answer because it is the simplified expression that we obtained by combining like terms.

Other Options

The other options are not correct because they do not accurately represent the simplified expression. Option B is incorrect because it has a positive coefficient for the variable $y$, whereas our simplified expression has a negative coefficient. Option C is incorrect because it has a positive coefficient for the variable $y$ and a negative constant term, whereas our simplified expression has a negative coefficient for the variable $y$ and a negative constant term. Option D is incorrect because it has a positive coefficient for the variable $y$ and a negative constant term, whereas our simplified expression has a negative coefficient for the variable $y$ and a negative constant term.

Final Answer

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to identify the like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract the coefficients of the like terms. The coefficient is the number that is multiplied by the variable.

Q: What is the difference between combining like terms and adding or subtracting terms?

A: Combining like terms involves adding or subtracting the coefficients of like terms, whereas adding or subtracting terms involves adding or subtracting the entire terms.

Q: Can I simplify an algebraic expression by combining unlike terms?

A: No, you cannot simplify an algebraic expression by combining unlike terms. Unlike terms are terms that have different variables or different exponents.

Q: How do I know if two terms are like terms?

A: Two terms are like terms if they have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: Can I simplify an algebraic expression by combining constants?

A: Yes, you can simplify an algebraic expression by combining constants. Constants are numbers that are not multiplied by a variable.

Q: How do I combine constants?

A: To combine constants, you add or subtract the constants. For example, $4 + 5 = 9$ and $-3 + 2 = -1$.

Q: What is the final step in simplifying an algebraic expression?

A: The final step in simplifying an algebraic expression is to write the simplified expression in the simplest form possible.

Q: Can I simplify an algebraic expression by using a calculator?

A: Yes, you can simplify an algebraic expression by using a calculator. However, it is always a good idea to simplify an algebraic expression by hand to ensure that you understand the process.

Q: Why is it important to simplify algebraic expressions?

A: Simplifying algebraic expressions is important because it helps to make the expression easier to work with and understand. It also helps to avoid errors and make calculations more efficient.

Q: Can I simplify an algebraic expression with variables in the denominator?

A: Yes, you can simplify an algebraic expression with variables in the denominator. However, you need to be careful when simplifying expressions with variables in the denominator to avoid dividing by zero.

Q: How do I simplify an algebraic expression with variables in the denominator?

A: To simplify an algebraic expression with variables in the denominator, you need to multiply the numerator and denominator by the reciprocal of the variable in the denominator.

Q: Can I simplify an algebraic expression with fractions?

A: Yes, you can simplify an algebraic expression with fractions. However, you need to be careful when simplifying expressions with fractions to avoid errors.

Q: How do I simplify an algebraic expression with fractions?

A: To simplify an algebraic expression with fractions, you need to find the least common multiple (LCM) of the denominators and multiply the numerator and denominator by the LCM.

Q: Why is it important to check your work when simplifying algebraic expressions?

A: It is important to check your work when simplifying algebraic expressions to ensure that you have not made any errors. Checking your work helps to avoid mistakes and ensures that you have the correct simplified expression.