Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x
?(1 point)
Responses
14(2x+5+11x)
14 left parenthesis 2 x plus 5 plus 11 x right parenthesis
23−18x−45+11x
23 minus 18 x minus 45 plus 11 x
14(2x+5)+11x
14 left parenthesis 2 x plus 5 right parenthesis plus 11 x
23−7x−4+11x
?(1 point)
Responses
14(2x+5+11x)
14 left parenthesis 2 x plus 5 plus 11 x right parenthesis
23−18x−45+11x
23 minus 18 x minus 45 plus 11 x
14(2x+5)+11x
14 left parenthesis 2 x plus 5 right parenthesis plus 11 x
23−7x−4+11x
Answers
Answered by
7 of 107 of 10 Items Question Which of the fo
just choose the closes one
Answered by
GPT-4o mini
To apply the Distributive Property of Multiplication Over Addition correctly, we need to simplify the expression \( 23 - 9(2x + 5) + 11x \).
Using the Distributive Property, we distribute \(-9\) across the terms inside the parentheses:
\[
-9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45
\]
Now we can substitute this back into the equation:
\[
23 - 18x - 45 + 11x
\]
Next, we combine like terms. First, simplify the constant terms:
\[
23 - 45 = -22
\]
Now, combine the \(x\) terms:
\[
-18x + 11x = -7x
\]
Putting it all together, we have:
\[
-22 - 7x
\]
Now let's compare this to the given choices.
1. \(14(2x + 5 + 11x)\) - Incorrect as it does not apply the distributive property but factors instead.
2. \(23 - 18x - 45 + 11x\) - Correct at an intermediate step but doesn't represent a final simplified form.
3. \(14(2x + 5) + 11x\) - Incorrect as it doesn't represent the initial form at any point.
4. \(23 - 7x - 4 + 11x\) - Incorrect because the \( -4 \) does not resemble part of the original expression.
Considering these points, the best partial answer before completing the simplification is:
**23 − 18x − 45 + 11x** (though ideally you want the final simplified form, which is \( -22 - 7x \) which isn't listed among the choices). However, it's the most correct option regarding recognizing the distribution application.
Using the Distributive Property, we distribute \(-9\) across the terms inside the parentheses:
\[
-9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45
\]
Now we can substitute this back into the equation:
\[
23 - 18x - 45 + 11x
\]
Next, we combine like terms. First, simplify the constant terms:
\[
23 - 45 = -22
\]
Now, combine the \(x\) terms:
\[
-18x + 11x = -7x
\]
Putting it all together, we have:
\[
-22 - 7x
\]
Now let's compare this to the given choices.
1. \(14(2x + 5 + 11x)\) - Incorrect as it does not apply the distributive property but factors instead.
2. \(23 - 18x - 45 + 11x\) - Correct at an intermediate step but doesn't represent a final simplified form.
3. \(14(2x + 5) + 11x\) - Incorrect as it doesn't represent the initial form at any point.
4. \(23 - 7x - 4 + 11x\) - Incorrect because the \( -4 \) does not resemble part of the original expression.
Considering these points, the best partial answer before completing the simplification is:
**23 − 18x − 45 + 11x** (though ideally you want the final simplified form, which is \( -22 - 7x \) which isn't listed among the choices). However, it's the most correct option regarding recognizing the distribution application.
Answered by
GPT-4o mini
The closest option to the correct application of the Distributive Property of Multiplication Over Addition for simplifying \(23 - 9(2x + 5) + 11x\) is:
**23 − 18x − 45 + 11x**
This option represents the correct intermediate step after applying the Distributive Property.
**23 − 18x − 45 + 11x**
This option represents the correct intermediate step after applying the Distributive Property.
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