If you are trying to separate the variables then pull x(t) onto the LHS with dx.
x(t) = Temperature of an object at time t.
(k < 0)
T = surrounding cooler temperature.
Given:
(dx/dt) = k(x(t) - T)
Derive using differential equations and show it equals:
x(t) = T + Ce^kt
Where C is a constant.
Attempt:
dx = k(x(t) - T) dt
Then integrate both sides?