Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x

Question

?

Answer 1

To simplify the expression \( 23 - 9(2x + 5) + 11x \) using the Distributive Property of Multiplication Over Addition, we need to distribute \(-9\) to both terms inside the parentheses \( (2x + 5) \).

Let's apply the Distributive Property:

1. Distribute \(-9\) to \(2x\): \[ -9 \times 2x = -18x \]

2. Distribute \(-9\) to \(5\): \[ -9 \times 5 = -45 \]

Now combine these results into the original expression:

\[ 23 - 9(2x + 5) + 11x = 23 - 18x - 45 + 11x \]

Next, simplify by combining like terms. First, let's combine the constant terms \(23\) and \(-45\): \[ 23 - 45 = -22 \]

Now combine the \(x\) terms \(-18x\) and \(11x\): \[ -18x + 11x = -7x \]

Putting it all together, we have: \[ -22 - 7x \]

Thus, the simplified expression is: \[ -7x - 22 \]

So, the correct application of the Distributive Property and simplification yields \(-7x - 22\).

Answer 2

wrong

Answer 3

Let's carefully go through the steps of simplifying the expression \(23 - 9(2x + 5) + 11x\) using the Distributive Property of Multiplication Over Addition.

Step 1: Apply the Distributive Property

Start with the original expression: \[ 23 - 9(2x + 5) + 11x \]

Distributing \(-9\) across the terms in the parentheses: \[ -9 \cdot 2x = -18x \] \[ -9 \cdot 5 = -45 \]

Now, substitute these back into the expression: \[ 23 - 18x - 45 + 11x \]

Step 2: Combine Like Terms

Now, we'll combine the constant terms and the \(x\) terms separately:

First, combine the constants \(23\) and \(-45\): \[ 23 - 45 = -22 \]

Now, combine the \(x\) terms \(-18x\) and \(11x\): \[ -18x + 11x = -7x \]

Final Expression

Putting it all together, we have: \[ -22 - 7x \]

Or if you want to write it in standard format, it can be: \[ -7x - 22 \]

If this is incorrect, please clarify what you would like to see or if there's a specific mistake you want me to address!

Answer 4

the answer is wrong

Answer 5

I apologize for any confusion earlier. Let's go through the simplification step-by-step once more to ensure everything is correct.

We start with the expression:

\[ 23 - 9(2x + 5) + 11x \]

Step 1: Apply the Distributive Property

Using the Distributive Property, we distribute \(-9\) over the terms inside the parentheses \((2x + 5)\):

\[ -9 \cdot 2x = -18x \] \[ -9 \cdot 5 = -45 \]

So, substituting these into the expression gives us:

\[ 23 - 18x - 45 + 11x \]

Step 2: Combine Like Terms

Next, we combine the constant terms and the \(x\) terms:

Combine Constants: \[ 23 - 45 = -22 \]

Combine \(x\) Terms: \[ -18x + 11x = -7x \]

Final Result

Combining everything together yields:

\[ -22 - 7x \]

Rearranging it gives:

\[ -7x - 22 \]

After reviewing all steps, I stand by the simplified answer being \(-7x - 22\). If there is a specific aspect you’d like me to correct or address, please let me know! Your clarification would help greatly.