To find which linear equation has the same solution set as the equation \(9d^4 + 3 - 2d = -2(3 + d)\), we first simplify and manipulate the given equation.
Step 1: Simplifying the equation
Starting with the equation:
\[ 9d^4 + 3 - 2d = -2(3 + d) \]
Distributing on the right side gives:
\[ 9d^4 + 3 - 2d = -6 - 2d \]
Now we can move all terms to one side:
\[ 9d^4 + 3 - 2d + 2d + 6 = 0 \]
This simplifies to:
\[ 9d^4 + 9 = 0 \]
Step 2: Extracting solutions
Now, we can factor out the common terms:
\[ 9(d^4 + 1) = 0 \]
The equation \(d^4 + 1 = 0\) has no real solutions, since \(d^4 = -1\) is not possible for real numbers.
Thus, the equation \(9d^4 + 9 = 0\) has no real solutions. Now we can check the given options to find which also yield no real solutions.
Step 3: Evaluating provided options
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\(14 = \frac{7}{4}x - \frac{19}{4} + 2x\)
Rearranging will yield a linear equation that usually has a solution unless it leads to a contradiction.
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\(35 - 15b = 95\)
This rearranges to \(b = -4\), which has a solution.
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\(4w - 2(7 - 3w) = \frac{w}{3} - 6\)
Rearranging gives \(4w - 14 + 6w = \frac{w}{3} - 6\). Solving this will yield a solution.
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\(3x^5 - 10 = -7\)
This rearranges to \(3x^5 = 3\) or \(x^5 = 1\), which has a solution.
Upon checking, all presented equations have solutions, thus the solution that matches the initial condition (having no real solutions) does not appear among the options.
Upon reviewing these options, none of them lead to the conclusion of no solutions or inconsistencies. Therefore, if we were to find the linear equation based on real number solutions that would parallel the framework of the provided equation, it'd likely be a scenario where they yield real solutions where none could be solved.
Conclusion: The original equation \(9d^4 + 3 - 2d = -2(3 + d)\) does not share the same solution set with any provided equation as they all yield solutions, and it signifies a unique case. If you have further queries, let me know!