To determine how many solutions the equation \( 23(6m + 9) - 6 = 4m \) has, let's first simplify the equation step by step.
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Distribute the 23 on the left side: \[ 23 \cdot 6m + 23 \cdot 9 - 6 = 4m \] This simplifies to: \[ 138m + 207 - 6 = 4m \]
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Combine like terms: \[ 138m + 201 = 4m \]
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Move \(4m\) to the left side: \[ 138m - 4m + 201 = 0 \] This simplifies to: \[ 134m + 201 = 0 \]
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Solve for \(m\): \[ 134m = -201 \] \[ m = -\frac{201}{134} \]
Since this results in a single specific value for \(m\), the equation has exactly one solution.
Thus, the answer is: one solution.
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