b) \( \frac{2(x+1)}{\text { b }}-\frac{3(x-1)}{10}=\frac{7 x+1}{10} \)

Let’s solve the equation step by step! First, we can eliminate the fractions by multiplying through by 10b: \[ 10b \left( \frac{2(x+1)}{b} \right) - 10b \left( \frac{3(x-1)}{10} \right) = 10b \left( \frac{7x+1}{10} \right) \] This simplifies to: \[ 20(x+1) - 3b(x-1) = 7bx + b \] Now, distribute: \[ 20x + 20 - 3bx + 3b = 7bx + b \] Combine like terms: \[ 20x - 3bx - 7bx = b - 20 + 3b \] That gives us: \[ 20x - 10bx = 4b - 20 \] Now factor out \(x\): \[ x(20 - 10b) = 4b - 20 \] Finally, solve for \(x\): \[ x = \frac{4b - 20}{20 - 10b} \] And there you have the solution for \(x\)!