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

Question

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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.