Which Expression Is Equivalent To \[$(18x + 9k) + (2x + 6k)\$\]?A. \[$16x + 3k\$\] B. \[$20x + 15k\$\] C. \[$20x + 16k\$\] D. \[$36x + 54k\$\]
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will explore the process of simplifying algebraic expressions, with a focus on combining like terms. We will also examine a specific problem, which involves simplifying the expression {(18x + 9k) + (2x + 6k)$}$, and determine which of the given options is equivalent to it.
What are Algebraic Expressions?
An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Variables are letters or symbols that represent unknown values, while constants are numbers that do not change value. Algebraic expressions can be simple, such as 2x, or complex, involving multiple variables and operations.
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves combining like terms, which are terms that have the same variable raised to the same power. To simplify an expression, we need to combine the coefficients of like terms. The coefficient of a term is the number that multiplies the variable.
Step 1: Identify Like Terms
The first step in simplifying an algebraic expression is to identify like terms. In the expression {(18x + 9k) + (2x + 6k)$}$, we can see that there are two like terms: 18x and 2x, and 9k and 6k.
Step 2: Combine Coefficients
Once we have identified like terms, we can combine their coefficients. To combine the coefficients of 18x and 2x, we add them together: 18 + 2 = 20. Similarly, to combine the coefficients of 9k and 6k, we add them together: 9 + 6 = 15.
Step 3: Simplify the Expression
Now that we have combined the coefficients of like terms, we can simplify the expression. The simplified expression is ${20x + 15k\$}.
Which Expression is Equivalent?
Now that we have simplified the expression {(18x + 9k) + (2x + 6k)$}$, we can compare it to the given options to determine which one is equivalent.
Option A: ${16x + 3k\$}
This option is not equivalent to the simplified expression, as the coefficients of x and k are different.
Option B: ${20x + 15k\$}
This option is equivalent to the simplified expression, as the coefficients of x and k are the same.
Option C: ${20x + 16k\$}
This option is not equivalent to the simplified expression, as the coefficient of k is different.
Option D: ${36x + 54k\$}
This option is not equivalent to the simplified expression, as the coefficients of x and k are different.
Conclusion
In conclusion, the expression {(18x + 9k) + (2x + 6k)$}$ simplifies to $20x + 15k\$}. Therefore, the correct answer is Option B$.
Final Answer
The final answer is Option B: ${20x + 15k\$}.
Additional Resources
For more information on simplifying algebraic expressions, check out the following resources:
- Khan Academy: Simplifying Algebraic Expressions
- Mathway: Simplifying Algebraic Expressions
- Wolfram Alpha: Simplifying Algebraic Expressions
FAQs
Q: What is an algebraic expression? A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms, which are terms that have the same variable raised to the same power.
Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.
Q: How do I combine coefficients? A: To combine coefficients, you add them together.
Introduction
Algebraic expressions are a fundamental concept in mathematics, and understanding them is essential for success in math and science. In this article, we will answer some of the most frequently asked questions about algebraic expressions, covering topics such as simplifying expressions, combining like terms, and more.
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Variables are letters or symbols that represent unknown values, while constants are numbers that do not change value.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, you need to combine like terms, which are terms that have the same variable raised to the same power. To combine like terms, you add their coefficients together.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms, as they both have the variable x raised to the power of 1.
Q: How do I combine coefficients?
A: To combine coefficients, you add them together. For example, to combine the coefficients of 2x and 4x, you add 2 and 4 together, resulting in 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 expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, you need to follow the order of operations. First, evaluate any expressions inside the parentheses. Then, evaluate any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents an unknown value, while a constant is a number that does not change value.
Q: How do I simplify an expression with multiple variables?
A: To simplify an expression with multiple variables, you need to combine like terms, just like you would with a single variable. However, you need to be careful to combine terms with the same variable raised to the same power.
Q: What is the final answer to the expression {(18x + 9k) + (2x + 6k)$}$?
A: The final answer to the expression {(18x + 9k) + (2x + 6k)$}$ is ${20x + 15k\$}.
Q: How do I use algebraic expressions in real-life situations?
A: Algebraic expressions are used in a wide range of real-life situations, including science, engineering, economics, and finance. They are used to model and solve problems, and to make predictions and decisions.
Conclusion
In conclusion, algebraic expressions are a fundamental concept in mathematics, and understanding them is essential for success in math and science. By following the order of operations, combining like terms, and using algebraic expressions in real-life situations, you can become proficient in simplifying and solving algebraic expressions.
Additional Resources
For more information on algebraic expressions, check out the following resources:
- Khan Academy: Algebraic Expressions
- Mathway: Algebraic Expressions
- Wolfram Alpha: Algebraic Expressions
FAQs
Q: What is an algebraic expression? A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms, which are terms that have the same variable raised to the same power.
Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.
Q: How do I combine coefficients? A: To combine coefficients, you add them together.
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 expression.
Q: How do I evaluate an expression with parentheses? A: To evaluate an expression with parentheses, you need to follow the order of operations.
Q: What is the difference between a variable and a constant? A: A variable is a letter or symbol that represents an unknown value, while a constant is a number that does not change value.
Q: How do I simplify an expression with multiple variables? A: To simplify an expression with multiple variables, you need to combine like terms, just like you would with a single variable.
Q: What is the final answer to the expression {(18x + 9k) + (2x + 6k)$}$? A: The final answer to the expression {(18x + 9k) + (2x + 6k)$}$ is ${20x + 15k\$}.