Dual problemn -> what to do with summand in objective function not connected to variable

Question

say I have the simple primal problem $$ \text{max } Z = 3x_1 + 2x_2 -7 $$ s.t. \begin{align*} 3x_1 + 5x_2 &\ge 6 \\ 7x_1 + 55 x_2 &\ge 44 \\ x_1,x_2 &\ge 0 \end{align*} Now would I be able to use the summand $-7$ is the dual problem? Where does it belong there and why?

Thank you in advance and have a wonderful day. :)

Answer 1

Since $-7$ is not linked to any variable, it will always be added to the objective function.

So you can simply add $-7$ to the dual objective function.