Question

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

Answer 1

wrong

Answer 2

the answer is wrong

Answer 3

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 4

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 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.