Which Expression Is Equivalent To $5(x+1)-2(x-3)$?A. $3x-1$ B. $ 3 X − 2 3x-2 3 X − 2 [/tex] C. $3x+1$ D. $3x+11$
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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, focusing on the given expression $5(x+1)-2(x-3)$. We will break down the expression step by step, using various techniques to simplify it and arrive at the final equivalent expression.
Understanding the Given Expression
The given expression is $5(x+1)-2(x-3)$. To simplify this expression, we need to apply the distributive property, which states that for any real numbers a, b, and c, a(b+c) = ab + ac.
Step 1: Apply the Distributive Property
We will start by applying the distributive property to the first term, 5(x+1). This means we will multiply 5 by each term inside the parentheses, x and 1.
Using the distributive property, we can simplify the expression as follows:
Step 2: Apply the Distributive Property to the Second Term
Next, we will apply the distributive property to the second term, -2(x-3). This means we will multiply -2 by each term inside the parentheses, x and -3.
Using the distributive property, we can simplify the expression as follows:
Step 3: Combine Like Terms
Now that we have applied the distributive property to both terms, we can combine like terms. Like terms are terms that have the same variable raised to the same power.
We can combine the x terms by adding their coefficients:
We can also combine the constant terms by adding them:
Step 4: Simplify the Expression
Now that we have combined like terms, we can simplify the expression by writing it in the form of a single expression.
Conclusion
In conclusion, the given expression $5(x+1)-2(x-3)$ is equivalent to $3x + 11$. We arrived at this expression by applying the distributive property, combining like terms, and simplifying the expression.
Answer
The correct answer is:
- D. $3x+11$
Discussion
This problem requires the application of the distributive property and combining like terms to simplify the given expression. The distributive property is a fundamental concept in algebra, and combining like terms is a crucial skill to master. By following the steps outlined in this article, you can simplify any algebraic expression and arrive at the final equivalent expression.
Tips and Tricks
- When applying the distributive property, make sure to multiply each term inside the parentheses by the coefficient outside the parentheses.
- When combining like terms, make sure to add the coefficients of the x terms and the constant terms separately.
- When simplifying the expression, make sure to write it in the form of a single expression.
Related Problems
- Simplify the expression $2(x-1) + 3(x+2)$.
- Simplify the expression $4(x+2) - 2(x-1)$.
- Simplify the expression $3(x-2) + 2(x+1)$.
Final Thoughts
Simplifying algebraic expressions is a crucial skill to master in mathematics. By applying the distributive property and combining like terms, you can simplify any expression and arrive at the final equivalent expression. Remember to follow the steps outlined in this article, and you will be able to simplify any algebraic expression with ease.
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Q&A: Simplifying Algebraic Expressions
Q: What is the distributive property, and how is it used in simplifying algebraic expressions?
A: The distributive property is a fundamental concept in algebra that states that for any real numbers a, b, and c, a(b+c) = ab + ac. It is used to simplify algebraic expressions by multiplying each term inside the parentheses by the coefficient outside the parentheses.
Q: How do I apply the distributive property to simplify an algebraic expression?
A: To apply the distributive property, simply multiply each term inside the parentheses by the coefficient outside the parentheses. For example, if you have the expression 5(x+1), you would multiply 5 by each term inside the parentheses, x and 1, to get 5x + 5.
Q: What is the difference between like terms and unlike terms?
A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable. For example, 2x and 3x are like terms, while 2x and 4y are unlike terms.
Q: How do I combine like terms to simplify an algebraic expression?
A: To combine like terms, simply add the coefficients of the like terms. For example, if you have the expression 2x + 3x, you would add the coefficients of the x terms to get 5x.
Q: What is the final step in simplifying an algebraic expression?
A: The final step in simplifying an algebraic expression is to write it in the form of a single expression. This means combining like terms and simplifying the expression to its simplest form.
Q: Can you provide an example of how to simplify an algebraic expression using the distributive property and combining like terms?
A: Let's consider the expression 5(x+1) - 2(x-3). To simplify this expression, we would first apply the distributive property to get 5x + 5 - 2x + 6. Then, we would combine like terms to get 3x + 11.
Q: What are some common mistakes to avoid when simplifying algebraic expressions?
A: Some common mistakes to avoid when simplifying algebraic expressions include:
- Forgetting to apply the distributive property
- Not combining like terms
- Simplifying the expression incorrectly
- Not writing the final expression in the simplest form
Q: How can I practice simplifying algebraic expressions?
A: You can practice simplifying algebraic expressions by working through examples and exercises in your textbook or online resources. You can also try simplifying expressions on your own and checking your work with a calculator or online tool.
Tips and Tricks
- Make sure to apply the distributive property to each term inside the parentheses.
- Combine like terms carefully to avoid making mistakes.
- Simplify the expression to its simplest form by combining like terms and eliminating any unnecessary terms.
- Check your work with a calculator or online tool to ensure that your answer is correct.
Related Problems
- Simplify the expression 2(x-1) + 3(x+2).
- Simplify the expression 4(x+2) - 2(x-1).
- Simplify the expression 3(x-2) + 2(x+1).
Final Thoughts
Simplifying algebraic expressions is a crucial skill to master in mathematics. By applying the distributive property and combining like terms, you can simplify any expression and arrive at the final equivalent expression. Remember to follow the steps outlined in this article, and you will be able to simplify any algebraic expression with ease.