Which Expression Is The Simplest Form Of 5 ( X − 3 ) − 3 ( 2 X + 4 ) 9 \frac{5(x-3)-3(2x+4)}{9} 9 5 ( X − 3 ) − 3 ( 2 X + 4 ) ?A. 11 X − 27 9 \frac{11x-27}{9} 9 11 X − 27 B. − X − 27 9 \frac{-x-27}{9} 9 − X − 27 C. { -x-3$}$ D. − X − 3 9 \frac{-x-3}{9} 9 − X − 3
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Introduction
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the process to solve various mathematical problems. In this article, we will focus on simplifying the given expression and determine the simplest form of the expression.
Understanding the Expression
The given expression is a rational expression, which is a fraction that contains variables and constants in the numerator and denominator. To simplify the expression, we need to apply the distributive property, combine like terms, and cancel out any common factors.
Step 1: Apply the Distributive Property
The first step in simplifying the expression is to apply the distributive property to the numerator. The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac.
\frac{5(x-3)-3(2x+4)}{9} = \frac{5x-15-6x-12}{9}
Step 2: Combine Like Terms
Now that we have applied the distributive property, we can combine like terms in the numerator. Like terms are terms that have the same variable raised to the same power.
\frac{5x-15-6x-12}{9} = \frac{-x-27}{9}
Step 3: Cancel Out Common Factors
The final step in simplifying the expression is to cancel out any common factors between the numerator and denominator. In this case, there are no common factors, so the expression is already in its simplest form.
Conclusion
In conclusion, the simplest form of the expression is . This expression cannot be simplified further, and it is the simplest form of the given expression.
Comparison with Answer Choices
Now that we have simplified the expression, let's compare it with the answer choices.
- A. : This expression is not equivalent to the simplified expression.
- B. : This expression is equivalent to the simplified expression.
- C. : This expression is not equivalent to the simplified expression.
- D. : This expression is not equivalent to the simplified expression.
Final Answer
Based on the simplification process, the final answer is:
- B.
This is the simplest form of the given expression, and it is the correct answer.
Frequently Asked Questions
Q: What is the simplest form of the expression ?
A: The simplest form of the expression is .
Q: How do I simplify a rational expression?
A: To simplify a rational expression, you need to apply the distributive property, combine like terms, and cancel out any common factors.
Q: What is the distributive property?
A: The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power.
Q: How do I cancel out common factors?
A: To cancel out common factors, you need to find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF.
Conclusion
In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the process to solve various mathematical problems. By applying the distributive property, combining like terms, and canceling out common factors, we can simplify rational expressions and determine the simplest form of the expression. In this article, we simplified the expression and determined the simplest form of the expression to be .
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Introduction
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the process to solve various mathematical problems. In this article, we will provide a Q&A guide to help you understand the concept of simplifying algebraic expressions.
Q&A Guide
Q: What is the simplest form of the expression ?
A: The simplest form of the expression is .
Q: How do I simplify a rational expression?
A: To simplify a rational expression, you need to apply the distributive property, combine like terms, and cancel out any common factors.
Q: What is the distributive property?
A: The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power.
Q: How do I cancel out common factors?
A: To cancel out common factors, you need to find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF.
Q: What is the greatest common factor (GCF)?
A: The greatest common factor (GCF) is the largest factor that divides both the numerator and denominator without leaving a remainder.
Q: How do I find the GCF?
A: To find the GCF, you can list the factors of the numerator and denominator and find the largest factor that is common to both.
Q: What is the difference between a rational expression and a polynomial expression?
A: A rational expression is a fraction that contains variables and constants in the numerator and denominator, while a polynomial expression is an expression that contains variables and constants raised to various powers.
Q: How do I simplify a polynomial expression?
A: To simplify a polynomial expression, you need to combine like terms and cancel out any common factors.
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
- Exponents
- Multiplication and Division
- Addition and Subtraction
Q: How do I apply the order of operations?
A: To apply the order of operations, you need to follow the order of operations and perform the operations in the correct order.
Example Problems
Problem 1: Simplify the expression
A: To simplify the expression, we need to apply the distributive property, combine like terms, and cancel out any common factors.
\frac{2(x+3)-4(x-2)}{5} = \frac{2x+6-4x+8}{5} = \frac{-2x+14}{5}
Problem 2: Simplify the expression
A: To simplify the expression, we need to apply the distributive property, combine like terms, and cancel out any common factors.
\frac{3(x-2)+2(x+3)}{4} = \frac{3x-6+2x+6}{4} = \frac{5x}{4}
Conclusion
In conclusion, simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the process to solve various mathematical problems. By applying the distributive property, combining like terms, and canceling out common factors, we can simplify rational expressions and determine the simplest form of the expression. We also provided a Q&A guide to help you understand the concept of simplifying algebraic expressions.
Frequently Asked Questions
Q: What is the simplest form of the expression ?
A: The simplest form of the expression is .
Q: How do I simplify a rational expression?
A: To simplify a rational expression, you need to apply the distributive property, combine like terms, and cancel out any common factors.
Q: What is the distributive property?
A: The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power.
Q: How do I cancel out common factors?
A: To cancel out common factors, you need to find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF.
Final Answer
Based on the Q&A guide, the final answer is:
- The simplest form of the expression is .
This is the simplest form of the given expression, and it is the correct answer.