To determine how many solutions the equation \( 23(6m + 9) - 6 = 4m \) has, we can simplify and solve the equation step by step.
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Distribute the \(23\) on the left side: \[ 23(6m) + 23(9) - 6 = 4m \] \[ 138m + 207 - 6 = 4m \] Combine constants: \[ 138m + 201 = 4m \]
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Move all terms involving \(m\) to one side and constants to the other: \[ 138m - 4m = -201 \] \[ 134m = -201 \]
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Divide both sides by \(134\): \[ m = -\frac{201}{134} \]
Since we have derived a unique value for \(m\), the equation has one solution.
Therefore, the answer is: one solution.