To solve the equation \(2(n-1) + 4n = 2(3n-1)\), we will first simplify both sides. 1. Distribute on both sides: \[ 2(n-1) + 4n = 2n - 2 + 4n = 6n - 2 \] \[ 2(3n-1) = 6n - 2 \] So our equation now looks like: \[ 6n - 2 = 6n - 2 \] 2. Subtract \(6n\) from both sides: \[ -2 = -2 \] This statement is true and indicates that the original equation is an identity. This means that the equation is true for all values of \(n\). Thus, the solution to the equation is that \(n\) can be any real number.