To solve the trigonometric equation 2 sin(x/2 - pi/6) = -1, we first need to isolate the sin function:

sin(x/2 - pi/6) = -1/2

Next, we need to find the angle x/2 - pi/6 that corresponds to a sin value of -1/2. Since sin(-30 degrees) = -1/2, we can write:

x/2 - pi/6 = -pi/6

Now, we solve for x:

x/2 = 0

x = 0

Therefore, the solution to the equation 2 sin(x/2 - pi/6) = -1 is x = 0.