To determine which linear equation has the same solution set as the equation \(9d^4 + 3 - 2d = -2(3 + d)\), we need to simplify that initial equation first.
Starting with the original equation:
\[ 9d^4 + 3 - 2d = -2(3 + d) \]
We can simplify the right side:
\[ 9d^4 + 3 - 2d = -6 - 2d \]
Next, we can add \(2d\) to both sides to eliminate \(-2d\):
\[ 9d^4 + 3 = -6 \]
Now, we want to bring everything to one side:
\[ 9d^4 + 3 + 6 = 0 \] \[ 9d^4 + 9 = 0 \]
This implies:
\[ 9(d^4 + 1) = 0 \]
This means \(d^4 + 1 = 0\), which does not have a real solution.
Next, let's check the equations provided in the responses to see which one has the same solution set:
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\(14 = \frac{7}{4}x - \frac{19}{4} + 2x\)
We can re-write this equation, but it involves \(x\) which is different from our original variable \(d\). It's not equivalent.
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\(4w - 2(7 - 3w) = \frac{w}{3} - 6\)
Similar case as the first one, it involves a different variable \(w\).
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\(\frac{3x}{5} - 10 = -7\)
Again, involves \(x\) and is not equivalent to our \(d\) equation.
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\(35 - 15b = 95\)
Involves \(b\) and is not in accordance with \(d\).
None of the provided options directly applies to the original equation we simplified since they include different variables. However, we can analyze its fundamental nature: since the left side is a polynomial that cannot equal zero in real numbers, any linear equation that does not yield real solutions would share the same solution set (which is empty).
None of the listed equations seem to have no real solutions either. However, if we subtract all variable terms from each linear equation, the essence of the equation and its solution set can be analyzed.
Ultimately, based on the way the equations are presented and without the capacity to solve all of them specifically for their values, if we want to find a match based solely on the nature of solutions and formulation, none of the given options represent a linear equation that achieves the same output as our derived equation showing no attainable real result:
Thus, the best choice among the options, considering all above and lack of any being a direct counterpart, would be to conclude:
None of the responses have the same solution set as \(9d^4 + 3 - 2d = -2(3 + d)\).