Question
Which linear equation has the same solution set as 9d4+3−2d=−2(3+d)
(1 point)
Responses
4w−2(7−3w)=w3−6
4 w minus 2 times open paren 7 minus 3 w close paren is equal to w over 3 minus 6
3x5−10=−7
3 x over 5 minus 10 is equal to negative 7
35−15b=95
(1 point)
Responses
4w−2(7−3w)=w3−6
4 w minus 2 times open paren 7 minus 3 w close paren is equal to w over 3 minus 6
3x5−10=−7
3 x over 5 minus 10 is equal to negative 7
35−15b=95
Answers
GPT-4o mini
To find which linear equation has the same solution set as the equation \( 9d^4 + 3 - 2d = -2(3 + d) \), we first need to solve that equation.
1. Start by expanding the right side:
\[
-2(3 + d) = -6 - 2d
\]
So, the original equation becomes:
\[
9d^4 + 3 - 2d = -6 - 2d
\]
2. Next, simplify by adding \( 2d \) to both sides:
\[
9d^4 + 3 = -6
\]
3. Now, add \( 6 \) to both sides to isolate the polynomial:
\[
9d^4 + 9 = 0
\]
4. This can be simplified to:
\[
9d^4 = -9
\]
5. Dividing both sides by \( 9 \):
\[
d^4 = -1
\]
This indicates that there are no real solutions for \( d \) because \( d^4 \) cannot be negative.
Now, let's analyze the provided equations to find one that has the same solution set (in this case, no real solution).
- **1. \( 4w - 2(7 - 3w) = \frac{w}{3} - 6 \)**
- **2. \( 3x - 10 = -7 \)**. Solving this, we get:
\[
3x = 3 \implies x = 1
\]
This has a real solution.
- **3. \( 35 - 15b = 95 \)**. Solving this, we get:
\[
-15b = 60 \implies b = -4
\]
This also has a real solution.
None of the provided equations result in an empty solution set like \( d^4 = -1 \). However, since the task is to find a linear equation equivalent to a linear form leading to no real solution, we note that none of the choices actually yield that. Therefore, based on the analysis of the original equation, no provided equation has the same solution set.
If you meant a modified form (e.g., leading to a false statement), none of the options seem to provide one.
Conclusively, there is no available answer that matches the criteria for having no real solution as \( 9d^4 + 9 = 0 \) represents. If guided to check for false equivalences, we need further details or options.
1. Start by expanding the right side:
\[
-2(3 + d) = -6 - 2d
\]
So, the original equation becomes:
\[
9d^4 + 3 - 2d = -6 - 2d
\]
2. Next, simplify by adding \( 2d \) to both sides:
\[
9d^4 + 3 = -6
\]
3. Now, add \( 6 \) to both sides to isolate the polynomial:
\[
9d^4 + 9 = 0
\]
4. This can be simplified to:
\[
9d^4 = -9
\]
5. Dividing both sides by \( 9 \):
\[
d^4 = -1
\]
This indicates that there are no real solutions for \( d \) because \( d^4 \) cannot be negative.
Now, let's analyze the provided equations to find one that has the same solution set (in this case, no real solution).
- **1. \( 4w - 2(7 - 3w) = \frac{w}{3} - 6 \)**
- **2. \( 3x - 10 = -7 \)**. Solving this, we get:
\[
3x = 3 \implies x = 1
\]
This has a real solution.
- **3. \( 35 - 15b = 95 \)**. Solving this, we get:
\[
-15b = 60 \implies b = -4
\]
This also has a real solution.
None of the provided equations result in an empty solution set like \( d^4 = -1 \). However, since the task is to find a linear equation equivalent to a linear form leading to no real solution, we note that none of the choices actually yield that. Therefore, based on the analysis of the original equation, no provided equation has the same solution set.
If you meant a modified form (e.g., leading to a false statement), none of the options seem to provide one.
Conclusively, there is no available answer that matches the criteria for having no real solution as \( 9d^4 + 9 = 0 \) represents. If guided to check for false equivalences, we need further details or options.