To solve the equation \( 6x = \frac{1}{6} (36x + 6) \), let's start by simplifying it step by step.
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Multiply both sides of the equation by 6 to eliminate the fraction: \[ 6 \cdot (6x) = 6 \cdot \left(\frac{1}{6} (36x + 6)\right) \] This simplifies to: \[ 36x = 36x + 6 \]
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Next, we can rearrange the equation by subtracting \( 36x \) from both sides: \[ 36x - 36x = 36x + 6 - 36x \] Which simplifies to: \[ 0 = 6 \]
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The equation \( 0 = 6 \) is a contradiction, which indicates that there are no values for \( x \) that can satisfy the original equation.
Thus, the equation has no solutions.
The answer is: A. No solutions
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