Simplify: $8-4 x+10-6 x$
A. $7 x$
B. $5 x-4$
C. $18-19 x$
D. $18-10 x$
Answer (2)
Combine the constant terms: 8 + 10 = 18 .
Combine the x terms: − 4 x − 6 x = − 10 x .
Write the simplified expression by combining the results: 18 − 10 x .
The simplified expression is 18 − 10 x .
Explanation
Understanding the Expression We are asked to simplify the expression 8 − 4 x + 10 − 6 x . This involves combining the constant terms and the terms with the variable x .
Grouping Like Terms First, let's identify and group the like terms. We have two constant terms, 8 and 10 , and two terms with x , which are − 4 x and − 6 x .
Combining Constants Now, let's combine the constant terms: 8 + 10 = 18 .
Combining x Terms Next, let's combine the terms with x : − 4 x − 6 x = − 10 x .
Simplified Expression Finally, we write the simplified expression by combining the results from the previous steps: 18 − 10 x . Therefore, the simplified expression is 18 − 10 x .
Examples
Simplifying expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are buying items at a store, you might use this skill to calculate the total cost. Suppose you buy 8 apples and then later buy 10 more apples. If each apple costs $x, then the total cost can be represented as 8 x + 10 x , which simplifies to 18 x . This skill is also useful in more complex scenarios, such as calculating the total cost of materials for a construction project or determining the total amount of ingredients needed for a recipe.
To simplify the expression 8 − 4 x + 10 − 6 x , we combine the constants 8 and 10 to get 18 , and combine the x terms − 4 x and − 6 x to get − 10 x . The final result is 18 − 10 x . Therefore, the answer is option D: 18 − 10 x .
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