d. \( m x+(m+2)(3 x-1)=3(2 x+1) \)

To solve the equation \( m x+(m+2)(3 x-1)=3(2 x+1) \), let's first expand both sides: On the left side: \[ m x + (m+2)(3 x-1) = m x + (m+2)(3 x) - (m+2)(1) = m x + (3mx + 6x) - (m+2) \] \[ = (m + 3m + 6)x - (m + 2) = (4m + 6)x - (m + 2) \] On the right side: \[ 3(2x + 1) = 6x + 3 \] Now the equation becomes: \[ (4m + 6)x - (m + 2) = 6x + 3 \] Setting coefficients equal gives us two equations: 1. \( 4m + 6 = 6 \) 2. \( -(m + 2) = 3 \) Let's solve these. For the first equation: \[ 4m + 6 = 6 \Rightarrow 4m = 0 \Rightarrow m = 0 \] For the second equation: \[ -m - 2 = 3 \Rightarrow -m = 5 \Rightarrow m = -5 \] So, we have two possible values for \( m \): \( m = 0 \) and \( m = -5 \).