Solve $$u_t + u_x +7u = 0$$
After using an integrating factor to reduce the ODE to a transport equation PDE I got $$\left(e^{7x}\right)u_t + \left(e^{7x}\right)u_x + 7\left(e^{7x}\right)u = 0$$
The solution then says to compress the equation to $$\left(ue^{7x}\right)_t + \left(ue^{7x}\right)_x = 0$$ which is in a transport equation with $v = u\left(e^{7x}\right)$.
Can you explain how they compressed the equation and what that means?