which of the following answers applies the destructive property of multiplication over addition correctly for simplifying
23-9(2x+5) +11x
23-7x-4+11x
14(2x+5+11x)
23-18x-45+11x
14(2x+5)+11x
What is the correct answer?
To simplify the expression using the destructive property of multiplication over addition, we need to distribute the number outside the parentheses to everything inside.
Given the expression: 23 - 9(2x + 5) + 11x
Distributing -9 to (2x + 5) gives: -18x - 45
Now, we can simplify the expression as follows:
23 - 18x - 45 + 11x
Combining like terms:
-7x - 22
Therefore, the correct answer is: 23 - 18x - 45 + 11x = -7x - 22
In order to apply the distributive property of multiplication over addition, you need to multiply each term inside the parentheses by the number outside of it.
Let's go through each option and simplify the expression:
Option 1: 23 - 7x - 4 + 11x
Option 2: 14(2x + 5 + 11x)
Option 3: 23 - 18x - 45 + 11x
Option 4: 14(2x + 5) + 11x
By comparing these options to the original expression, we can see that Option 4, which is 14(2x + 5) + 11x, correctly applies the distributive property.
Therefore, the correct answer is 14(2x + 5) + 11x.