To solve the equation \( \frac{1}{3} (9 + 6x) = 2x + 3 \), we need to simplify and solve for \( x \).
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Start by distributing \( \frac{1}{3} \): \[ \frac{1}{3} \cdot 9 + \frac{1}{3} \cdot 6x = 3 + 2x \] So we have: \[ 3 + 2x = 2x + 3 \]
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Now, we can see that both sides of the equation are the same: \[ 3 + 2x = 2x + 3 \]
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This equation holds true for all values of \( x \). Hence, there are infinitely many solutions.
Therefore, the answer is infinitely many solutions.
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