Simplify $-2xy + 3x - 2xy + 3x$
A) $-4xy + 6x$
B) $4xy + 6x$
C) $4xy - 6x$
D) $2xy
Answer (2)
Identify like terms: The expression contains terms with 'xy' and terms with 'x'.
Combine 'xy' terms: − 2 x y − 2 x y = − 4 x y .
Combine 'x' terms: 3 x + 3 x = 6 x .
Write the simplified expression: − 4 x y + 6 x
Explanation
Understanding the Problem We are asked to simplify the expression − 2 x y + 3 x − 2 x y + 3 x and choose the correct answer from the given options.
Identifying Like Terms First, let's identify the like terms in the expression. We have two types of terms: terms containing x y and terms containing x .
Combining 'xy' Terms Now, let's combine the like terms. The terms with x y are − 2 x y and − 2 x y . Combining them, we get: − 2 x y − 2 x y = − 4 x y
Combining 'x' Terms Next, let's combine the terms with x . We have 3 x and 3 x . Combining them, we get: 3 x + 3 x = 6 x
Writing the Simplified Expression Now, we can write the simplified expression by combining the results from the previous steps: − 4 x y + 6 x
Selecting the Correct Option Finally, let's compare our simplified expression − 4 x y + 6 x with the given options: A) − 4 x y + 6 x B) 4 x y + 6 x C) 4 x y − 6 x D) 2 x y Our simplified expression matches option A.
Final Answer Therefore, the simplified expression is − 4 x y + 6 x .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics. It's used in various real-life situations, such as calculating the total cost of items with discounts or calculating the total distance traveled when you have multiple segments with the same speed. For example, if you buy two items that cost 'x' dollars each and have a discount of 2 dollars on each item, the total cost can be expressed as 2(x - 2) = 2x - 4. Simplifying expressions helps in making quick and accurate calculations in everyday scenarios.
To simplify the expression − 2 x y + 3 x − 2 x y + 3 x , we combined the like terms to get − 4 x y + 6 x . The correct answer is option A) − 4 x y + 6 x .
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