Solve for \( b \). Give an exact answer. \( 0.75(8 b+4)-1=4 b+14 \)

First, let's simplify the equation step by step. Start by distributing \(0.75\) in the equation: \[ 0.75(8b + 4) - 1 = 4b + 14 \] This simplifies to: \[ 6b + 3 - 1 = 4b + 14 \] Now, combine like terms on the left side: \[ 6b + 2 = 4b + 14 \] Next, isolate \(b\) by subtracting \(4b\) from both sides: \[ 6b - 4b + 2 = 14 \] This simplifies to: \[ 2b + 2 = 14 \] Now, subtract \(2\) from both sides to eliminate the constant: \[ 2b = 12 \] Finally, divide by \(2\): \[ b = 6 \] So, the exact answer for \(b\) is \(6\).