To solve the equation 2x - |x| = -1, we will consider the two cases when x is positive and when x is negative.

Case 1: x ≥ 0
When x is positive or zero, the absolute value function is simply the value of x. So the equation becomes:
2x - x = -1
x = -1

But since x is assumed to be greater than or equal to 0 in this case, x = -1 is not a valid solution.

Case 2: x < 0
When x is negative, the absolute value of x is -x. So the equation becomes:
2x - (-x) = -1
2x + x = -1
3x = -1
x = -1/3

Therefore, the solution to the equation 2x - |x| = -1 is x = -1/3.