To determine how many solutions the equation \( 23(6m+9)−6=4m \) has, let's simplify and solve it step by step.
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Start with the equation: \[ 23(6m + 9) - 6 = 4m \]
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Distribute \( 23 \) on the left side: \[ 138m + 207 - 6 = 4m \] Simplifying this gives: \[ 138m + 201 = 4m \]
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Next, isolate \( m \) by subtracting \( 4m \) from both sides: \[ 138m - 4m + 201 = 0 \] Which simplifies to: \[ 134m + 201 = 0 \]
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Now, isolate \( m \): \[ 134m = -201 \] \[ m = -\frac{201}{134} \]
Since we arrived at a single value of \( m \), this means there is exactly one solution to the equation.
Thus, the answer is:
one solution