To simplify the expression using the Distributive property of multiplication over addition, we need to focus on the term \( -9(2x + 5) \).
Let's break down what the Distributive property says:
\[ a(b + c) = ab + ac \]
So, for the term \( -9(2x + 5) \):
\[ -9(2x + 5) = -9 \cdot 2x + (-9) \cdot 5 = -18x - 45 \]
Now, we can substitute that into the original expression:
\[ 23 - 9(2x + 5) + 11 = 23 - (18x + 45) + 11 \]
This simplifies to:
\[ 23 - 18x - 45 + 11 \]
Now, combining the constants \( 23 - 45 + 11 \):
\[ 23 - 45 = -22 \] \[ -22 + 11 = -11 \]
So the simplified expression becomes:
\[ -18x - 11 \]
Now, let's look at the options provided:
- \( 14(2x+5+11x) \)
- \( 14(2x+5)+11x \)
- \( 23 - 18x - 45 + 11x \)
- \( 23 - 7x - 4 + 11x \)
Among these choices, the one that correctly applies the Distributive property and simplifies the original expression is:
3. \( 23 - 18x - 45 + 11x \)
This choice correctly shows \( -9(2x + 5) \) expanded and keeps the other terms intact.
1 answer