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 \( 23 \): \[ 23(6m) + 23(9) - 6 = 4m \] This becomes: \[ 138m + 207 - 6 = 4m \]
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Combine the constant terms: \[ 138m + 201 = 4m \]
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Now, isolate the \( m \) terms on one side: \[ 138m - 4m + 201 = 0 \] This simplifies to: \[ 134m + 201 = 0 \]
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Solving for \( m \): \[ 134m = -201 \] \[ m = -\frac{201}{134} \]
Since we found one specific value for \( m \), there is one solution to the equation.
Thus, the correct response is: one solution.
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