An Expression Is Shown:${ X + 2x + 3x + 24y } U S E T H E D R O P − D O W N M E N U S T O C O M P L E T E A N E Q U I V A L E N T E X P R E S S I O N . Use The Drop-down Menus To Complete An Equivalent Expression. U Se T H E D Ro P − D O W Nm E N U S T Oco M Pl E T E An E Q U I V A L E N T E X P Ress I O N . { 1(x + 0 \, \square \, N) \}

Understanding the Problem

When dealing with algebraic expressions, it's essential to simplify them to make calculations easier and more manageable. The given expression, $x + 2x + 3x + 24y$, is a combination of like terms, which can be simplified using basic algebraic rules. In this article, we'll break down the process of simplifying this expression and provide a step-by-step guide on how to do it.

What are Like Terms?

Like terms are terms in an algebraic expression that have the same variable(s) raised to the same power. In the given expression, $x + 2x + 3x + 24y$, the terms $x$, $2x$, and $3x$ are like terms because they all have the variable $x$ raised to the power of 1. On the other hand, the term $24y$ is not a like term because it has a different variable, $y$.

Simplifying the Expression

To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms. In this case, we can add the coefficients of the $x$ terms:

$x + 2x + 3x = (1 + 2 + 3)x = 6x$

So, the simplified expression is $6x + 24y$.

Using the Drop-Down Menus to Complete an Equivalent Expression

Now, let's use the drop-down menus to complete an equivalent expression. We have the expression $1(x + 0 \, \square \, n)$, and we need to fill in the blank with a value that will make the expression equivalent to the simplified expression we obtained earlier, $6x + 24y$.

Step 1: Identify the Variable

The first step is to identify the variable in the expression. In this case, the variable is $x$. We can see that the expression $1(x + 0 \, \square \, n)$ has a coefficient of 1, which means that the variable $x$ is being multiplied by 1.

Step 2: Determine the Coefficient

The next step is to determine the coefficient of the variable $x$. In the simplified expression $6x + 24y$, the coefficient of $x$ is 6. We need to find a value that will make the coefficient of $x$ in the expression $1(x + 0 \, \square \, n)$ equal to 6.

Step 3: Fill in the Blank

To make the coefficient of $x$ equal to 6, we need to multiply the variable $x$ by 6. However, we also need to consider the value of $n$ in the expression $1(x + 0 \, \square \, n)$. Since the expression is equivalent to $6x + 24y$, we can see that the value of $n$ is not relevant to the coefficient of $x$. Therefore, we can fill in the blank with any value that will make the expression equivalent to $6x + 24y$.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By combining like terms and using basic algebraic rules, we can simplify expressions and make calculations easier. In this article, we used the drop-down menus to complete an equivalent expression, and we found that the value of $n$ is not relevant to the coefficient of $x$. We hope that this article has provided a clear and concise guide on how to simplify algebraic expressions and complete equivalent expressions.

Additional Tips and Resources

• When simplifying algebraic expressions, always look for like terms and combine them using basic algebraic rules.
• Use the distributive property to expand expressions and simplify them.
• Practice simplifying algebraic expressions with different variables and coefficients to become more comfortable with the process.
• 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

Final Answer

The final answer is: $\boxed{6x + 24y}$

Understanding the Basics

Simplifying algebraic expressions is a fundamental concept in mathematics. It involves combining like terms and using basic algebraic rules to make calculations easier. In this article, we'll provide a Q&A guide to help you understand the basics of simplifying algebraic expressions.

Q: What are like terms?

A: Like terms are terms in an algebraic expression that have the same variable(s) raised to the same power. For example, in the expression $x + 2x + 3x + 24y$, the terms $x$, $2x$, and $3x$ are like terms because they all have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. In the example above, we can combine the like terms $x$, $2x$, and $3x$ by adding their coefficients:

$x + 2x + 3x = (1 + 2 + 3)x = 6x$

Q: What is the distributive property?

A: The distributive property is a rule that allows you to expand expressions by multiplying each term inside the parentheses by the coefficient outside the parentheses. For example, in the expression $2(x + 3)$, we can use the distributive property to expand it as follows:

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

Q: How do I simplify expressions with variables and constants?

A: To simplify expressions with variables and constants, you need to combine like terms and use the distributive property. For example, in the expression $x + 2x + 3 + 24y$, we can simplify it as follows:

$x + 2x + 3 + 24y = (1 + 2)x + 3 + 24y = 3x + 3 + 24y$

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 expressions. The order of operations is as follows:

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 expressions with fractions?

A: To simplify expressions with fractions, you need to combine like terms and use the distributive property. For example, in the expression $\frac{x}{2} + \frac{2x}{2} + \frac{3}{2} + 24y$, we can simplify it as follows:

$\frac{x}{2} + \frac{2x}{2} + \frac{3}{2} + 24y = \frac{(1 + 2)x}{2} + \frac{3}{2} + 24y = \frac{3x}{2} + \frac{3}{2} + 24y$

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not combining like terms
• Not using the distributive property
• Not following the order of operations
• Not simplifying fractions

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By combining like terms, using the distributive property, and following the order of operations, you can simplify expressions and make calculations easier. We hope that this Q&A guide has provided a clear and concise overview of the basics of simplifying algebraic expressions.

Additional Tips and Resources

• Practice simplifying algebraic expressions with different variables and coefficients to become more comfortable with the process.
• Use online resources, such as Khan Academy and Mathway, to practice simplifying algebraic expressions.
• 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

Final Answer

The final answer is: $\boxed{3x + 3 + 24y}$