Which Expression Is Equivalent To The Expression Below? ( − X + 5 ) + 4.5 X (-x + 5) + 4.5x ( − X + 5 ) + 4.5 X A) − 3 X + 15 -3x + 15 − 3 X + 15 B) 1.5 X + 15 1.5x + 15 1.5 X + 15 C) − 3 X + 4.5 X -3x + 4.5x − 3 X + 4.5 X D) 1.5 X + 5 1.5x + 5 1.5 X + 5

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 the given expression: $(-x + 5) + 4.5x$. We will examine each option and determine which one is equivalent to the given expression.

Understanding the Given Expression

The given expression is $(-x + 5) + 4.5x$. To simplify this expression, we need to 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 $x$: $-x$ and $4.5x$.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to the term $-x$. This will change the sign of the term to positive.

-x + 5 = -x + 5

Step 2: Combine Like Terms

Now that we have distributed the negative sign, we can combine the like terms. We have two terms with the variable $x$: $-x$ and $4.5x$. To combine these terms, we need to add their coefficients.

-x + 4.5x = (4.5 - 1)x

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression. We have $(4.5 - 1)x$, which simplifies to $3.5x$.

(4.5 - 1)x = 3.5x

Step 4: Add the Constant Term

Finally, we need to add the constant term to the expression. We have $3.5x + 5$.

3.5x + 5

Evaluating the Options

Now that we have simplified the expression, we can evaluate the options. We have four options: $-3x + 15$, $1.5x + 15$, $-3x + 4.5x$, and $1.5x + 5$. Let's examine each option and determine which one is equivalent to the simplified expression.

Option A: $-3x + 15$

This option is not equivalent to the simplified expression. The coefficient of the variable $x$ is $-3$, which is different from the coefficient of $3.5x$ in the simplified expression.

Option B: $1.5x + 15$

This option is not equivalent to the simplified expression. The coefficient of the variable $x$ is $1.5$, which is different from the coefficient of $3.5x$ in the simplified expression.

Option C: $-3x + 4.5x$

This option is not equivalent to the simplified expression. The coefficient of the variable $x$ is $1.5$, which is different from the coefficient of $3.5x$ in the simplified expression.

Option D: $1.5x + 5$

This option is equivalent to the simplified expression. The coefficient of the variable $x$ is $1.5$, which is the same as the coefficient of $3.5x$ in the simplified expression. The constant term is also the same.

Conclusion

In conclusion, the expression equivalent to the given expression $(-x + 5) + 4.5x$ is $1.5x + 5$. This option is the only one that matches the simplified expression. Simplifying algebraic expressions is an essential skill in mathematics, and this article has provided a step-by-step guide on how to simplify the given expression.

Final Answer

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it can be a challenging task for many students. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

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

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. You can combine like terms by adding or subtracting their coefficients.

Q: What is a coefficient?

A: A coefficient is a number that is multiplied by a variable. For example, in the expression $3x$, the coefficient is 3.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, in the expression $2x + 4x$, you can combine the like terms by adding their coefficients: $2x + 4x = 6x$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an algebraic 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 simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to evaluate the expression inside the parentheses first. Then, you can simplify the expression outside the parentheses.

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression that has a variable raised to the power of 1. A quadratic expression is an expression that has a variable raised to the power of 2.

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, you need to combine like terms. You can also use the quadratic formula to simplify a quadratic expression.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that can be used to solve quadratic equations. The quadratic formula is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it can be a challenging task for many students. By following the steps outlined in this article, you can simplify algebraic expressions with ease.

Final Tips

• Always combine like terms when simplifying an algebraic expression.
• Use the order of operations to simplify expressions with multiple operations.
• Use the quadratic formula to simplify quadratic expressions.
• Practice, practice, practice! The more you practice simplifying algebraic expressions, the more comfortable you will become with the process.

Common Mistakes

• Failing to combine like terms.
• Not following the order of operations.
• Not using the quadratic formula when simplifying quadratic expressions.
• Not practicing enough to become comfortable with simplifying algebraic expressions.

Additional Resources

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it can be a challenging task for many students. By following the steps outlined in this article, you can simplify algebraic expressions with ease. Remember to always combine like terms, use the order of operations, and practice, practice, practice!