To determine how many solutions the equation \(\frac{2}{3}(6m + 9) - 6 = 4m\) has, we'll first simplify and solve for \(m\).
- Start by distributing \(\frac{2}{3}\) on the left side:
\[ \frac{2}{3}(6m + 9) = \frac{2}{3} \cdot 6m + \frac{2}{3} \cdot 9 = 4m + 6 \]
- Substitute this back into the equation:
\[ 4m + 6 - 6 = 4m \]
- The \(6\) and \(-6\) cancel out, simplifying to:
\[ 4m = 4m \]
This equation is true for all values of \(m\).
Since it holds true for any value of \(m\), we conclude that there are infinite solutions.
Thus, the answer is:
infinite/many solutions.
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