Which of the following expressions is equivalent to 5x-4-8x+10? This question often arises in algebraic simplification exercises, as it tests one’s ability to combine like terms and understand the distributive property. By exploring this question, we can delve into the fundamental principles of algebra and enhance our understanding of how to manipulate algebraic expressions effectively.
In this article, we will analyze the given expression, 5x-4-8x+10, and compare it with various expressions to determine their equivalence. By doing so, we will gain insight into the process of simplifying algebraic expressions and the importance of maintaining the balance between like terms and the distributive property.
First, let’s simplify the given expression by combining like terms. The expression 5x-4-8x+10 contains two like terms, 5x and -8x, as well as two constant terms, -4 and 10. Combining the like terms, we get:
5x – 8x = -3x
-4 + 10 = 6
Therefore, the simplified expression is -3x + 6.
Now, let’s examine the provided options and determine which one is equivalent to the simplified expression -3x + 6. We will compare each option by simplifying them and checking if they yield the same result as the simplified expression.
Option A: 3x + 6
Simplifying this expression, we get:
3x + 6 = 3x + 6
Option B: -3x – 6
Simplifying this expression, we get:
-3x – 6 = -3x – 6
Option C: 3x – 6
Simplifying this expression, we get:
3x – 6 = 3x – 6
Option D: -3x + 10
Simplifying this expression, we get:
-3x + 10 = -3x + 10
Upon comparing the simplified expressions, we find that Option A, 3x + 6, is equivalent to the simplified expression -3x + 6. This demonstrates that when combining like terms and applying the distributive property, the expression 5x-4-8x+10 can be simplified to 3x + 6.
In conclusion, the expression which is equivalent to 5x-4-8x+10 is 3x + 6. This example highlights the importance of understanding the principles of algebraic simplification, such as combining like terms and applying the distributive property. By mastering these concepts, we can effectively manipulate algebraic expressions and solve a wide range of mathematical problems.
