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7(2m - 1) - 3 = 12m + 6

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To solve the equation \( 7(2m - 1) - 3 = 12m + 6 \), we will first simplify the left side of the equation.

  1. Distribute \( 7 \) into \( (2m - 1) \): \[ 7(2m) - 7(1) = 14m - 7 \] Now, substitute back into the equation: \[ 14m - 7 - 3 = 12m + 6 \]

  2. Combine like terms on the left side: \[ 14m - 10 = 12m + 6 \]

  3. Now, let's isolate \( m \). First, subtract \( 12m \) from both sides: \[ 14m - 12m - 10 = 6 \] which simplifies to: \[ 2m - 10 = 6 \]

  4. Next, add \( 10 \) to both sides: \[ 2m = 16 \]

  5. Finally, divide by \( 2 \): \[ m = 8 \]

So the solution is: \[ \boxed{8} \]