Jill Simplified The Expression Shown:${4x - 2y - X + 5y - 8}$What Is The Coefficient Of The { X$}$-term In The Fully Simplified Expression?A. 3 B. 4 C. 6 D. 8

Understanding Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will explore how to simplify algebraic expressions, with a focus on the given problem: $4x - 2y - x + 5y - 8$. We will break down the steps involved in simplifying this expression and identify the coefficient of the $x$-term in the fully simplified expression.

Step 1: Combine Like Terms

The first step in simplifying an algebraic expression is to combine like terms. Like terms are terms that have the same variable raised to the same power. In the given expression, we have two terms with the variable $x$: $4x$ and $-x$. We can combine these two terms by adding their coefficients.

Combining Coefficients

The coefficient of a term is the numerical value that multiplies the variable. In the case of the $x$-term, the coefficient is 4. When we combine the two $x$-terms, we add their coefficients: $4 + (-1) = 3$. Therefore, the simplified expression for the $x$-term is $3x$.

Step 2: Simplify the Constant Term

In addition to combining like terms, we also need to simplify the constant term. The constant term is the term that does not have a variable. In the given expression, the constant term is $-8$. We can simplify this term by combining it with any other constant terms.

Simplifying the Constant Term

In this case, there are no other constant terms to combine with the $-8$ term. Therefore, the simplified expression for the constant term is still $-8$.

Step 3: Write the Fully Simplified Expression

Now that we have combined like terms and simplified the constant term, we can write the fully simplified expression. The fully simplified expression is obtained by combining all the simplified terms.

Fully Simplified Expression

The fully simplified expression is $3x + 5y - 8$.

Identifying the Coefficient of the $x$-Term

The coefficient of the $x$-term is the numerical value that multiplies the variable $x$. In the fully simplified expression, the coefficient of the $x$-term is 3.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill to master in mathematics. By following the steps outlined in this article, we can simplify complex expressions and identify the coefficients of the variables. In the given problem, we simplified the expression $4x - 2y - x + 5y - 8$ and identified the coefficient of the $x$-term as 3.

Final Answer

The final answer is $\boxed{3}$.

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Algebra.com: Simplifying Algebraic Expressions

Discussion Questions

1. What is the coefficient of the $y$-term in the fully simplified expression?
2. How do you simplify an algebraic expression with multiple variables?
3. What is the difference between combining like terms and simplifying the constant term?

Answer Key

1. The coefficient of the $y$-term is 5.
2. To simplify an algebraic expression with multiple variables, you need to combine like terms and simplify the constant term.
3. Combining like terms involves adding or subtracting the coefficients of terms with the same variable, while simplifying the constant term involves combining constant terms.
   Simplifying Algebraic Expressions: A Q&A Guide =====================================================

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about simplifying algebraic expressions.

Q: What is the difference between combining like terms and simplifying the constant term?

A: Combining like terms involves adding or subtracting the coefficients of terms with the same variable, while simplifying the constant term involves combining constant terms.

Q: How do I simplify an algebraic expression with multiple variables?

A: To simplify an algebraic expression with multiple variables, you need to combine like terms and simplify the constant term. This involves identifying the terms with the same variable and combining their coefficients, as well as combining any constant terms.

Q: What is the coefficient of the $y$-term in the fully simplified expression?

A: The coefficient of the $y$-term in the fully simplified expression is 5.

Q: How do I identify the coefficient of a term?

A: The coefficient of a term is the numerical value that multiplies the variable. For example, in the term $3x$, the coefficient is 3.

Q: Can I simplify an algebraic expression with variables raised to different powers?

A: Yes, you can simplify an algebraic expression with variables raised to different powers. This involves combining like terms and simplifying the constant term, just like with expressions with variables raised to the same power.

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a mathematical statement that contains variables and constants, while an equation is a mathematical statement that states that two expressions are equal.

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

A: To simplify an algebraic expression with fractions, you need to combine like terms and simplify the constant term, just like with expressions without fractions. You may also need to simplify the fractions themselves by finding a common denominator.

Q: Can I simplify an algebraic expression with negative coefficients?

A: Yes, you can simplify an algebraic expression with negative coefficients. This involves combining like terms and simplifying the constant term, just like with expressions with positive coefficients.

Q: What is the final answer to the given problem?

A: The final answer to the given problem is $\boxed{3}$.

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Algebra.com: Simplifying Algebraic Expressions

Discussion Questions

1. What is the coefficient of the $x$-term in the fully simplified expression?
2. How do you simplify an algebraic expression with multiple variables?
3. What is the difference between combining like terms and simplifying the constant term?

Answer Key

1. The coefficient of the $x$-term is 3.
2. To simplify an algebraic expression with multiple variables, you need to combine like terms and simplify the constant term.
3. Combining like terms involves adding or subtracting the coefficients of terms with the same variable, while simplifying the constant term involves combining constant terms.