Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x?
well, 9(2x+5) = 9(2x)+9(5) = 18x+45
23−9(2x+5)+11x
= 23 - 18x - 45 + 11x
= -7x - 22 <------ expect to see this
Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x?
To apply the Distributive Property of Multiplication Over Addition correctly in the expression 23−9(2x+5)+11x, we need to multiply the -9 term by both the terms inside the parentheses: 2x and 5.
Let's break it down step by step:
First, distribute -9 to 2x and 5:
-9 * 2x = -18x
-9 * 5 = -45
Next, we rewrite the expression with the distributed terms:
23 - 18x - 45 + 11x
Finally, we can simplify the expression by combining like terms:
Combine the x terms: -18x + 11x = -7x
Combine the constants: 23 - 45 = -22
Therefore, the correct simplification of 23−9(2x+5)+11x is:
-7x - 22
Remember, the Distributive Property of Multiplication Over Addition states that a(b + c) = ab + ac.