Simplify $5(x-2)-3x+7$.A. $-10x+25$ B. $2x-3$ C. $2x-5$ D. $8x-3$
Understanding the Problem
Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of the rules of arithmetic operations. In this problem, we are given the expression $5(x-2)-3x+7$ and we need to simplify it. The correct simplification of this expression will be our final answer.
Distributive Property
To simplify the given expression, we need to apply the distributive property, which states that for any real numbers a, b, and c, $a(b+c) = ab + ac$. We can use this property to expand the expression $5(x-2)$.
Expanding the Expression
Using the distributive property, we can expand the expression $5(x-2)$ as follows:
Now, we can rewrite the original expression as:
Combining Like Terms
The next step in simplifying the expression is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: $5x$ and $-3x$. We can combine these terms by adding their coefficients.
Combining Like Terms
Combining the like terms $5x$ and $-3x$, we get:
Now, we can rewrite the expression as:
Simplifying the Expression
Finally, we can simplify the expression by combining the constant terms.
Simplifying the Expression
Combining the constant terms $-10$ and $7$, we get:
Now, we can rewrite the expression as:
Conclusion
In conclusion, the correct simplification of the expression $5(x-2)-3x+7$ is $2x - 3$. This is the final answer to the problem.
Answer Choice
The correct answer choice is B. $2x - 3$.
Step-by-Step Solution
Here is the step-by-step solution to the problem:
- Expand the expression $5(x-2)$ using the distributive property.
- Rewrite the original expression using the expanded expression.
- Combine like terms by adding the coefficients of the like terms.
- Simplify the expression by combining the constant terms.
Final Answer
The final answer is $2x - 3$.
Understanding the Problem
Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a clear understanding of the rules of arithmetic operations. In this problem, we are given the expression $5(x-2)-3x+7$ and we need to simplify it. The correct simplification of this expression will be our final answer.
Q&A
Q: What is the distributive property?
A: The distributive property is a rule in arithmetic that states that for any real numbers a, b, and c, $a(b+c) = ab + ac$. This property allows us to expand expressions by multiplying each term inside the parentheses by the factor outside the parentheses.
Q: How do I expand the expression $5(x-2)$?
A: To expand the expression $5(x-2)$, we need to apply the distributive property. This means that we multiply each term inside the parentheses by the factor outside the parentheses. In this case, we get:
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. In the expression $5(x-2)-3x+7$, the like terms are $5x$ and $-3x$.
Q: How do I combine like terms?
A: To combine like terms, we add their coefficients. In the expression $5(x-2)-3x+7$, we have two like terms: $5x$ and $-3x$. Combining these terms, we get:
Q: What is the final answer to the problem?
A: The final answer to the problem is $2x - 3$.
Q: What is the correct answer choice?
A: The correct answer choice is B. $2x - 3$.
Q: What are the steps to simplify the expression $5(x-2)-3x+7$?
A: The steps to simplify the expression $5(x-2)-3x+7$ are:
- Expand the expression $5(x-2)$ using the distributive property.
- Rewrite the original expression using the expanded expression.
- Combine like terms by adding the coefficients of the like terms.
- Simplify the expression by combining the constant terms.
Common Mistakes
Mistake 1: Not applying the distributive property
One common mistake when simplifying expressions is not applying the distributive property. This can lead to incorrect simplifications.
Mistake 2: Not combining like terms
Another common mistake is not combining like terms. This can also lead to incorrect simplifications.
Mistake 3: Not simplifying the expression
Finally, a common mistake is not simplifying the expression after combining like terms. This can lead to incorrect final answers.
Conclusion
In conclusion, simplifying algebraic expressions requires a clear understanding of the rules of arithmetic operations. By applying the distributive property, combining like terms, and simplifying the expression, we can arrive at the correct final answer. The correct answer to the problem is $2x - 3$.
Final Answer
The final answer is $2x - 3$.