To solve the equation tan(x - π/4) = -1, we can use the inverse tangent function to find the value of x.

Taking the inverse tangent of both sides, we have:

x - π/4 = arctan(-1)

The inverse tangent of -1 is -π/4, so we have:

x - π/4 = -π/4

Adding π/4 to both sides, we get:

x = 0

Therefore, the solution to the equation tan(x - π/4) = -1 is x = 0.