Final answer:
The equation dx/dt = -4 is both separable and linear. It is separable because the variables can be separated, and it is linear due to its conformity to the standard form of a first-order linear ODE with zero as the coefficient of x.
Step-by-step explanation:
The equation provided, dx/dt = -4, indicates a differential equation where the rate of change of x with respect to time t is equal to -4. This equation is a separable equation since the variables x and t can be separated onto opposite sides of the equation, allowing us to integrate each side with respect to its own variable. Because the equation is in the form of dx/dt = g(t), without any function of x on the right-hand side, it is also considered to be a linear equation since it can be rearranged to the standard form of a first-order linear ordinary differential equation, dx/dt + P(t) * x = Q(t), where in this case, P(t) = 0 and Q(t) = -4. To solve this, we would integrate both sides with respect to t to find x.